Diffusion, convection, adsorption, and reaction of chemicals in porous media

Hornung, Ulrich; Jäger, Willi

doi:10.1016/0022-0396(91)90047-d

Cited by 124 publications

(104 citation statements)

References 4 publications

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“…Notice that the quantity ε is called the homogenization parameter or the scale factor. The perforated domain Ω ε ⊂ R d herein approximates a porous medium and its precise description can be found in [5,7]. As an example, we depict in Figure 2.1 an admissible geometry of our medium and the corresponding microstructure.…”

Section: Problem Settingsmentioning

confidence: 99%

A high-order corrector estimate for a semi-linear elliptic system in perforated domains

Khoa¹

2017

Comptes Rendus. Mécanique

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We derive in this note a high-order corrector estimate for the homogenization of a microscopic semi-linear elliptic system posed in perforated domains. The major challenges are the presence of nonlinear volume and surface reaction rates. This type of correctors justifies mathematically the convergence rate of formal asymptotic expansions for the two-scale homogenization settings. As main tool, we follow the standard approach by the energy-like method to investigate the error estimate between the micro and macro concentrations and micro and macro concentration gradients. This work aims at generalizing the results reported in [2,7].

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Section: Problem Settingsmentioning

confidence: 99%

A high-order corrector estimate for a semi-linear elliptic system in perforated domains

Khoa¹

2017

Comptes Rendus. Mécanique

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“…We refer the reader to [13] for a discussion on uniform descriptions of heterogeneous media, while the working technique is detailed for instance in [14, pp. 11-22] [18][19][20] contain more theoretical approaches able to justify the asymptotics at least for simpler PDE models.…”

Section: A Few Comments On Related Literaturementioning

confidence: 99%

“…2 (left) and to [21] for connections between locally periodic perforated domains and quasi-periodic functions. See [19] for a notation strategy for the periodic case.…”

Section: Locally Periodic Array Of Perforationsmentioning

confidence: 99%

Homogenization of a reaction–diffusion system modeling sulfate corrosion of concrete in locally periodic perforated domains

Fatima¹,

Arab²,

Zemskov

et al. 2010

J Eng Math

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A reaction-diffusion system modeling concrete corrosion in sewer pipes is discussed. The system is coupled, semi-linear, and partially dissipative. It is defined on a locally periodic perforated domain with nonlinear Robin-type boundary conditions at water-air and solid-water interfaces. Asymptotic homogenization techniques are applied to obtain upscaled reaction-diffusion models together with explicit formulae for the effective transport and reaction coefficients. It is shown that the averaged system contains additional terms appearing due to the deviation of the assumed geometry from a purely periodic distribution of perforations for two relevant parameter regimes: (a) all diffusion coefficients are of order of O(1) and (b) all diffusion coefficients are of order of O(ε 2 ) except the one for H 2 S(g) which is of order of O(1). In case (a) a set of macroscopic equations is obtained, while in case (b) a two-scale reaction-diffusion system is derived that captures the interplay between microstructural reaction effects and the macroscopic transport.

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“…As in Remark 2.10, if the medium is -periodic, the constant C in Lemma 2.11 does not depend on . To see this we recall (1.7), and Lemma 3 of [9], saying that there exists a constant C > 0, independent of ε, such that…”

Section: A Priori Estimatesmentioning

confidence: 99%

“…The particularity of the model is in the description of the precipitation processes taking place on the surface of the grains Γ G , involving a multi valued function. Models of similar type are analyzed in a homogenization context in [9,10,17].…”

Section: Introductionmentioning

confidence: 99%

A Numerical Scheme for the Pore-Scale Simulation of Crystal Dissolution and Precipitation in Porous Media

Devigne¹,

Pop²,

Duijn³

et al. 2008

SIAM J. Numer. Anal.

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Abstract.In this paper we analyze a numerical scheme for a dissolution and precipitation in porous media. We focus here on the chemistry, which is modeled by a parabolic problem that is coupled through the boundary conditions to an ordinary differential inclusion defined on the boundary. We use a regularization approach for constructing a semi-implicit scheme that is stable and convergent. For dealing with the emerging time discrete nonlinear problems, we propose a simple fixed point iterative procedure. The paper is concluded by numerical results.

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Diffusion, convection, adsorption, and reaction of chemicals in porous media

Cited by 124 publications

References 4 publications

A high-order corrector estimate for a semi-linear elliptic system in perforated domains

A high-order corrector estimate for a semi-linear elliptic system in perforated domains

Homogenization of a reaction–diffusion system modeling sulfate corrosion of concrete in locally periodic perforated domains

A Numerical Scheme for the Pore-Scale Simulation of Crystal Dissolution and Precipitation in Porous Media

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