A double free boundary problem on microbially induced corrosion in wastewater concrete

Microbially influenced corrosion (MIC) refers to any corrosion process caused or fostered by microbial activity, and represents a global concern, impacting infrastructure, economies, and the environment worldwide. MIC affects a wide range of materials and is particularly common in wastewater concrete pipes, where it is associated with the proliferation of biofilm colonies of sulfur-oxidizing bacteria (SOBs). SOBs oxidize hydrogen sulfide produced within wastewater effluents and generate corrosive sulfuric acid that triggers the degradation of concrete. We propose here a one-dimensional, two-layer diffusion model with double free boundaries to investigate the proliferation of SOB biofilms and the related corrosion process in wastewater concrete pipes. The domain is composed of two free boundary regions: a monospecies SOB biofilm in contact with the sewer atmosphere, which grows towards the interior cavity of the pipe, sitting on a gypsum layer formed from corrosion, that penetrates the concrete pipe. Diffusion-reaction equations govern the transport and metabolic production or consumption of hydrogen sulfide, oxygen, and sulfuric acid within the biofilm layer. The biofilm free boundary tracks the growth of the microbial community, regulated by metabolic activity of SOBs and detachment phenomena. The corrosion process is incorporated in the model through a Stefan-type condition, which drives the advancement of the gypsum free boundary into the concrete pipe, governed by microbial production of sulfuric acid. Numerical simulations are carried out to investigate the model behavior, encompassing the development and progression of the biofilm as well as the corrosion advancement, with the aim of elucidating the influence of key factors such as hydrogen sulfide level in the sewer, calcium carbonate concentration in concrete, detachment phenomena, and acid diffusivity in the gypsum layer. Interestingly, the model suggests that, under specific conditions, biofilms may impose limitations on sulfuric acid diffusion and act as a partial protective barrier for the underlying concrete.