A Mathematical Model for the Sulphur Dioxide Aggression to Calcium Carbonate Stones: Numerical Approximation and Asymptotic Analysis

Abstract

We introduce a degenerate nonlinear parabolic system that describes the chemical aggression of calcium carbonate stones under the attack of sulphur dioxide. For this system, we present some finite element and finite difference schemes to approximate its solutions. Numerical stability is given under suitable CFL conditions. Finally, by means of a formal scaling, the qualitative behavior of the solutions for large times is investigated, and a numerical verification of this asymptotics is given. Our results are in qualitative agreement with the experimental behavior observed in the chemical literature.

A mathematical model of sulphite chemical aggression of limestones with high permeability. Part I. Modeling and qualitative analysis

“…In Section 2, we introduce in some detail a basic model starting from the main ideas of macroscopic modelling of filtration in porous media (Barenblatt et al 1990, Nield andBejan 1992). Next, we shall present a qualitative discussion of the asymptotic behavior of the solutions, for unbounded domain x > 0, by using scaling arguments similar to the ones used in Hilhorst et al (1996), Aregba-Driollet et al (2004), and Guarguaglini and Natalini (2005b). In the present case we find that, for large values of the reaction rate, and small values of the external concentration of SO 2 , the solutions still present formation of sharp fronts, as in the case of system (2).…”

“…Notice that a similar model has been recently considered in Stakgold (2000) for general gas-solid reactions, but assuming constant diffusivity. The numerical approximation and a qualitative analysis of system (2) is contained in Aregba-Driollet et al (2004). Global existence of smooth solutions for the Cauchy problem in one space dimension has been established (Guarguaglini and Natalini 2005a), while the time asymptotic behavior for large times has been rigorously investigated in Guarguaglini and Natalini (2005b).…”

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

“…2.3. Another macroscopic approach for a closely related sulfatation problem has been reported in [12]. In this paper, we keep a reduced size of the micro-model.…”

Chemomechanical Equilibrium of Bars

“…For example, in the degradation of historical monuments, in particular those made of marble, a well-known phenomenon is the chemical aggression on CaCO 3 (Calcium Carbonate) due to the presence of SO 2 (Sulphur Dioxide) in the surrounding polluted atmosphere. This attack, traditionally described through empirical laws, has been mathematically modelled recently [2] by describing the kinetics of reaction through a degenerate nonlinear parabolic system of partial differential equations. This model accounts for the competition between the filtration of the aggressive substance inside the material, described through Darcy's law, and the variation in the material porosity due to the chemical reaction.…”

“…Thus, some understanding is provided for the kinetics of the formation of a gypsum crust in monuments, which inevitably is associated with a drastic change in volume (200%-300%). However, in [2] the deformation of the associated material is not taken into account. If the surrounding material prevented swelling of the contaminated portions, an internal state of stress of the same order of magnitude as the material elastic moduli may be generated, inevitably leading to failure.…”