Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Analysis and numerical computation of geochemical systems with kinetic precipitation and dissolution reactions involving several minerals

Bastien Hamlat 1, 2 Jocelyne Erhel 1 Anthony Michel 2 Thibault Faney 2
1 FLUMINANCE - Fluid Flow Analysis, Description and Control from Image Sequences
IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique , INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Abstract : In this paper, we study underground media where chemical interactions involve aqueous and mineral species. In most kinetic models, a mineral species is involved in a single precipitation or dissolution reaction. In this work, we consider more general precipitation and dissolution kinetic reactions, which can include several minerals, which can each participate in several reactions. We propose a differential inclusion model, with reaction rates defined by set-valued functions, in order to ensure positive quantities of species. We also develop a regularized model, with reaction rates defined by regularized Heaviside functions and blendings if several minerals dissolve in the same reaction. We prove that the unique solution of this system of ODEs converges towards a solution of the differential inclusion model. We run numerical experiments by using a classical ODEs solver for computing the regularized solution. We get good numerical approximations of the quantities of species and the discontinuous reaction rates.
Complete list of metadata

https://hal.inria.fr/hal-03157970
Contributor : Jocelyne Erhel <>
Submitted on : Wednesday, March 3, 2021 - 3:35:23 PM
Last modification on : Friday, March 5, 2021 - 3:10:35 AM

File

kineticmineral.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-03157970, version 1

Citation

Bastien Hamlat, Jocelyne Erhel, Anthony Michel, Thibault Faney. Analysis and numerical computation of geochemical systems with kinetic precipitation and dissolution reactions involving several minerals. 2021. ⟨hal-03157970⟩

Share

Metrics

Record views

98

Files downloads

115