Convergence Analysis of Mixed Numerical Schemes for Reactive Flow in a Porous Medium

Kumar, Kundan; Pop, Sorin; Radu, Florin A.

doi:10.1137/120880938

Cited by 26 publications

(38 citation statements)

References 34 publications

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“…As proved in (Kumar et al 2013), in the limit as δ approaches zero, one ends up with the original (3). Thus, by f δ (T f , u , y), we mean the reaction rate f where w (dist(x, B ), T f , u ) is replaced with w δ (dist( y, B )).…”

Section: The Level Set Equationmentioning

confidence: 87%

Upscaling of Non-isothermal Reactive Porous Media Flow with Changing Porosity

et al. 2015

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Upscaling of non-isothermal reactive porous media flow with changing porosityBringedal, C.; Berre, I.; Pop, I.S.; Radu, A.F. Published in: Transport in Porous Media DOI:10.1007/s11242-015-0530-9Published: 01/09/2016 Document VersionAccepted manuscript including changes made at the peer-review stage Please check the document version of this publication:• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Link to publication• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Abstract Motivated by rock-fluid interactions occurring in a geothermal reservoir, we present a two-dimensional pore scale model of a periodic porous medium consisting of void space and grains, with fluid flow through the void space. The ions in the fluid are allowed to precipitate onto the grains, while minerals in the grains are allowed to dissolve into the fluid, and we take into account the possible change in pore geometry that these two processes cause, resulting in a problem with a free boundary at the pore scale. We include temperature dependence and possible effects of the temperature both in fluid properties and in the mineral precipitation and dissolution reactions. For the pore scale model equations, we perform a formal homogenization procedure to obtain upscaled equations. A pore scale model consisting of circular grains is presented as a special case of the porous medium.

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Section: The Level Set Equationmentioning

confidence: 87%

Upscaling of Non-isothermal Reactive Porous Media Flow with Changing Porosity

et al. 2015

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“…For the core scale model, the convergence of the semi-discrete and of the fully discrete (conformal and mixed finite element) numerical schemes have been analyzed [33,34]. The rigorous derivation of the macro scale model from the pore scale model in the classical homogenization context is carried out in [30].…”

Section: Known Resultsmentioning

confidence: 99%

Rigorous upscaling of rough boundaries for reactive flows

Kumar

Helvoort²,

Pop

2014

Z Angew Math Mech

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We consider a mathematical model for reactive flow in a channel having a rough (periodically oscillating) boundary with both period and amplitude ε. The ions are being transported by the convection and diffusion processes. These ions can react at the rough boundaries and get attached to form the crystal (precipitation) and become immobile. The reverse process of dissolution is also possible. The model involves non‐linear and multi‐valued rates and is posed in a fixed geometry with rough boundaries. We provide a rigorous justification for the upscaling process in which we define an upscaled problem defined in a simpler domain with flat boundaries. To this aim, we use periodic unfolding techniques combined with translation estimates. Numerical experiments confirm the theoretical predictions and illustrate a practical application of this upscaling process.

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“…Of course, also other, mass conserving, methods could have been applied like the mixed finite element method (MFEM) or the finite volume (FV) method; see, for example, Kumar et al (2013), Kumar et al (2014), and , in which the convergence is studied as well. In Radu et al (2013), the mixed finite element method is applied on a concrete carbonation model with a variable porosity.…”

Section: Methodsmentioning

confidence: 99%

Simulation of Front Instabilities in Density-Driven Flow, Using a Reactive Transport Model for Biogrout Combined with a Randomly Distributed Permeability Field

et al. 2016

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Biogrout is a method to strengthen granular soil, which is based on microbialinduced carbonate precipitation. To model the Biogrout process, a reactive transport model is used. Since high flow rates are undesirable for the Biogrout process, the model equations can be solved with a standard Galerkin finite element method. The Biogrout process involves the injection of dense fluids in the subsurface. In this paper, we present our reactive transport model for Biogrout and use it to simulate an experiment in which a pulse of a dense fluid is injected in a porous medium filled with water. In this experiment, front instabilities were observed in the form of fingers. The numerical simulations showed that the fingering phenomenon was less pronounced than in the experiment. By reducing the dispersion length and implementing a randomly distributed permeability field, the fingering phenomenon could be induced. Furthermore, the results of a case study to a Biogrout application are reported.

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Convergence Analysis of Mixed Numerical Schemes for Reactive Flow in a Porous Medium

Cited by 26 publications

References 34 publications

Upscaling of Non-isothermal Reactive Porous Media Flow with Changing Porosity

Upscaling of Non-isothermal Reactive Porous Media Flow with Changing Porosity

Rigorous upscaling of rough boundaries for reactive flows

Simulation of Front Instabilities in Density-Driven Flow, Using a Reactive Transport Model for Biogrout Combined with a Randomly Distributed Permeability Field

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