Macroscopic corrosion front computations of sulfate attack in sewer pipes based on a micro-macro reaction-diffusion model

TL;DR

This paper develops a two-scale reaction-diffusion model to simulate sulfate-induced corrosion in sewer pipes, enabling computation of key corrosion indicators like pH drop and gypsum profiles through numerical methods.

Contribution

It introduces a coupled micro-macro reaction-diffusion system with transmission conditions to accurately model concrete corrosion at different scales.

Findings

Numerical computation of pH drop and gypsum profiles.

Identification of a persistent kink in gypsum concentration.

Numerical illustration of the corrosion front position.

Abstract

We consider a two-scale reaction diffusion system able to capture the corrosion of concrete with sulfates. Our aim here is to define and compute two macroscopic corrosion indicators: typical pH drop and gypsum profiles. Mathematically, the system is coupled, endowed with micro-macro transmission conditions, and posed on two different spatially-separated scales: one microscopic (pore scale) and one macroscopic (sewer pipe scale). We use a logarithmic expression to compute values of pH from the volume averaged concentration of sulfuric acid which is obtained by resolving numerically the two-scale system (microscopic equations with direct feedback with the macroscopic diffusion of one of the reactants). Furthermore, we also evaluate the content of the main sulfatation reaction (corrosion) product---the gypsum---and point out numerically a persistent kink in gypsum's concentration profile. Finally, we illustrate numerically the position of the free boundary separating corroded from not-yet-corroded regions.