In this paper we deal with the numerical analysis of an upscaled model of a reactive flow in a porous medium, which describes the transport of solutes undergoing precipitation and dissolution, leading to the formation/degradation of crystals inside the porous matrix. The model is defined at the Darcy scale, and it is coupled to a Darcy flow characterized by a permeability field that changes in space and time according to the precipitated crystal concentration. The model involves a non-linear multi-valued reaction term, which is treated exactly by solving an inclusion problem for the solutes and the crystals dynamics. We consider a weak formulation for the coupled system of equations expressed in a dual mixed form for the Darcy field and in a primal form for the solutes and the precipitate, and show its well posedness without resorting to regularization of the reaction term. Convergence to the weak solution is proved for its finite element approximation. We perform numerical experiments to study the behavior of the system and to assess the effectiveness of the proposed discretization strategy. In particular we show that a method that captures the discontinuity yields sharper dissolution fronts with respect to methods that regularize the discontinuous term.

Analysis of a model for precipitation and dissolution coupled with a Darcy flux

AGOSTI, ABRAMO;FORMAGGIA, LUCA;SCOTTI, ANNA
2015-01-01

Abstract

In this paper we deal with the numerical analysis of an upscaled model of a reactive flow in a porous medium, which describes the transport of solutes undergoing precipitation and dissolution, leading to the formation/degradation of crystals inside the porous matrix. The model is defined at the Darcy scale, and it is coupled to a Darcy flow characterized by a permeability field that changes in space and time according to the precipitated crystal concentration. The model involves a non-linear multi-valued reaction term, which is treated exactly by solving an inclusion problem for the solutes and the crystals dynamics. We consider a weak formulation for the coupled system of equations expressed in a dual mixed form for the Darcy field and in a primal form for the solutes and the precipitate, and show its well posedness without resorting to regularization of the reaction term. Convergence to the weak solution is proved for its finite element approximation. We perform numerical experiments to study the behavior of the system and to assess the effectiveness of the proposed discretization strategy. In particular we show that a method that captures the discontinuity yields sharper dissolution fronts with respect to methods that regularize the discontinuous term.
2015
Dissolution phenomena, Porous media flow, Multivalued right hand side
File in questo prodotto:
File Dimensione Formato  
abramo.pdf

Accesso riservato

: Publisher’s version
Dimensione 1.88 MB
Formato Adobe PDF
1.88 MB Adobe PDF   Visualizza/Apri
Analysis of a model for precipitation and dissolution coupled with a Darcy flux_11311-960989_Formaggia.pdf

accesso aperto

: Post-Print (DRAFT o Author’s Accepted Manuscript-AAM)
Dimensione 1.71 MB
Formato Adobe PDF
1.71 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/960989
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 22
  • ???jsp.display-item.citation.isi??? 21
social impact