Effective reaction at a fluid–solid interface: Applications to biotransformation in porous media

Wood, Brian D.; Radakovich, Karen; Golfier, Fabrice

doi:10.1016/j.advwatres.2006.05.032

Cited by 63 publications

(54 citation statements)

References 56 publications

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“…Indeed, from a correlation length analysis [55] it was found that the medium characteristic length is about 0.12L, which can be used as a rough estimate for the minimum REV length. This figure is not dramatically changed by the introduction of the biofilm structure, given its generation characteristics.…”

Section: Effective Coefficients Given By the Closure Problems Detailementioning

confidence: 99%

A dual-porosity theory for solute transport in biofilm-coated porous media

Orgogozo

Golfier

Buès

et al. 2013

Advances in Water Resources

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Section: Effective Coefficients Given By the Closure Problems Detailementioning

confidence: 99%

A dual-porosity theory for solute transport in biofilm-coated porous media

Orgogozo

Golfier

Buès

et al. 2013

Advances in Water Resources

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“…In the fixed geometry case the Taylor dispersion mechanism is investigated in [2,4,29]. In the same context, reactive flow under dominating convective transport or reaction is studied in [1,5,9,15,17,28,34], presenting either a formal derivation of dispersion models, or rigorous convergence proofs for the upscaling procedure. In a similar context, in [16] an upscaled model of hyperbolic type is derived, sustained by rigorous mathematical arguments.…”

Section: Introductionmentioning

confidence: 99%

Effective Dispersion Equations for Reactive Flows Involving Free Boundaries at the Microscale

Kumar¹,

Noorden²,

Pop³

2011

Multiscale Model. Simul.

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We consider a pore-scale model for reactive flow in a thin 2-D strip, where the convective transport dominates the diffusion. Reactions take place at the lateral boundaries of the strip (the walls), where the reaction product can deposit in a layer with a non-negligible thickness compared to the width of the strip. This leads to a free boundary problem, in which the moving interface between the fluid and the deposited (solid) layer is explicitly taken into account. Using asymptotic expansion methods, we derive an upscaled, one-dimensional model by averaging in the transversal direction. The result is consistent with (Taylor dispersion) models obtained previously for a constant geometry. Finally, numerical computations are presented to compare the outcome of the effective (upscaled) model with the transversally averaged, two dimensional solution.

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“…If the interface velocity w is small enough and the second term in the parenthesis on the r.h.s is negligible in comparison with ε b (Hesse et al 2009;Wood et al 2007), we obtain:…”

Section: Appendix 1 Derivation Of Average-scale Equations Of Solute Tmentioning

confidence: 82%

“…It is found that ξ * increases dramatically under severe mass-transfer limitations, such as at large Damköhler numbers and small diffusivity ratios. Over the past few years, several researchers (Golfier et al 2009;Hesse et al 2009;Orgogozo et al 2010;Wood et al 2007) have attempted to solve a closure problem of pore-scale concentration fluctuation filed, in order to obtain the effective reaction rate, dispersion tensor, etc. But, each closure problem needs to be numerically solved for pre-specified pore structure and flow condition.…”

Section: Mass Exchange Coefficient For the Case Of Circular Cross Secmentioning

confidence: 99%

Solute Mass Exchange Between Water Phase and Biofilm for a Single Pore

Qin

Hassanizadeh

2015

Transp Porous Med

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Currently, there are no tractable approaches available for modeling nonequilibrium mass exchange of a solute between water phase and biofilm in porous media. The present work contributes to a quantitative description of the mass exchange of a solute over a single pore domain under a wide range of prevailing conditions. First, we developed a semiempirical model for the rate of solute mass exchange between water phase and biofilm. Then, extensive microscale simulations in a single pore were conducted. Results were averaged over a single pore domain, in order to determine a tube-scale kinetic rate coefficient as a function of various transport and biofilm properties. We illustrated the dependencies of the coefficient on a number of variables like Péclet number, Damköhler number, and biofilm volume fraction. Based on those results, we developed empirical formulae for the tube-scale mass exchange coefficient as a function of Damköhler number and biofilm volume fraction. Finally, we verified the proposed mass exchange rate against microscale simulations of solute transport in a long capillary tube. Good match was obtained over a wide range of conditions. Keywords Porous media with biofilm · Non-equilibrium condition · Pore-scale modeling · Mass exchange coefficient · Solute transport List of symbols Latin symbols

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Effective reaction at a fluid–solid interface: Applications to biotransformation in porous media

Cited by 63 publications

References 56 publications

A dual-porosity theory for solute transport in biofilm-coated porous media

A dual-porosity theory for solute transport in biofilm-coated porous media

Effective Dispersion Equations for Reactive Flows Involving Free Boundaries at the Microscale

Solute Mass Exchange Between Water Phase and Biofilm for a Single Pore

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