Un Mod\`ele simple d'injection diphasique avec phase condensable

TL;DR

This paper introduces a simple mathematical model to explain the experimental observation of water vapor penetration and condensation on concrete walls, providing bounds for the penetration front's position over time.

Contribution

A homogenized mathematical model for vapor injection in porous media is proposed, offering insights into the penetration front's asymptotic behavior.

Findings

Model matches experimental penetration patterns

Provides bounds for the front's position over time

Simplifies understanding of vapor condensation in concrete

Abstract

L'objectif de cette note est de proposer un mod\`ele math\'ematique simple permettant de comprendre l'arr\^et de la p\'en\'etration d'un flux de vapeur d'eau condensable sur un mur de b\'eton, observ\'e exp\'erimentalement (voir par exemple les diff\'erentes exp\'eriences d'injection de vapeur dans du b\'eton pr\'esent\'ees dans [11], et [7]). Un mod\`ele homog\'en\'eis\'e simple d'injection dans un milieu poreux est propos\'e, donnant une borne pour la position asymptotique en temps du front de p\'en\'etration. The aim of this paper is to propose a simple mathematical model to understand the decision of the penetration of a stream of water vapor condensing on a concrete wall, observed experimentally (see for example the situations described in [11], and [7]). A simple homogenized model for the injection in a porous medium is proposed, giving a bound for the asymptotic-time position at the front of penetration.