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Dissolution of carbonate stones caused by CO2 pollutant: an erosion model

Elishan Christian Braun, Gabriella Bretti, Samuele Ferri, Maria Laura Santarelli, Matteo Semplice

Abstract

In this paper we introduce a new mathematical model describing the erosion process caused in carbonate stones by the dissolution of the porous matrix due to the penetration of carbonic acid present in the environment. Such model is formulated as nonlinear reaction-transport system in porous media governed by Darcy flow. We propose a numerical algorithm based on finite difference approximation that relies on level-set method at the boundaries and we show numerical tests that are in accordance with the literature in terms of the advancement of the erosion front.

Dissolution of carbonate stones caused by CO2 pollutant: an erosion model

Abstract

In this paper we introduce a new mathematical model describing the erosion process caused in carbonate stones by the dissolution of the porous matrix due to the penetration of carbonic acid present in the environment. Such model is formulated as nonlinear reaction-transport system in porous media governed by Darcy flow. We propose a numerical algorithm based on finite difference approximation that relies on level-set method at the boundaries and we show numerical tests that are in accordance with the literature in terms of the advancement of the erosion front.

Paper Structure

This paper contains 11 sections, 30 equations, 7 figures, 6 tables.

Table of Contents

  1. Introduction
  2. The mathematical model describing the effects of carbonic acid in carbonate stones
  3. Definition of function $B$
  4. The symmetric absorption function $B'$ Clarelli2010
  5. The asymmetric absorption function $B_{kP}'$ bretti-belfiore
  6. Numerical approximation of the model
  7. Numerical tests
  8. Order of the scheme
  9. Catastrophic condition.
  10. Discussion on numerical tests
  11. Conclusions

Figures (7)

  • Figure 1: Marble altar from the Archaeological Park of Ostia Antica.
  • Figure 2: Plot of the profile of the absorption function $B'$ and $B'_{kP}$.
  • Figure 3: Plots of the humidity of 1D simulation at two different timestamps. Left panel: output of symmetric and non-symmetric models after 1 week. Right panel: output of symmetric and non-symmetric models after 1 year.
  • Figure 4: Plots of the variables of 1D simulation at three different timestamps: one week, 180 days and one year. The simulation is performed with the asymmetric $B'_{kP}(s)$. From top left: humidity, $CO_2$, carbonic acid and porosity.
  • Figure 5: Plots of the moving boundaries. Left panel: left side of the specimen. Right panel: right side of the specimen.
  • ...and 2 more figures

Theorems & Definitions (1)

  • Remark 1