On a moving-boundary system modeling corrosion in sewer pipes

Transport of sewage in sewer pipes leads to the release of hydrogen sulfide (H2S) which reacts to form a corrosive compound (H2SO4) in sewers. Biological generation of SO42- from H2S and transport of H2S and SO42- from the interior of the pipe to the corrosion front, which separates the corroded and the uncorroded parts of the pipe walls, is modeled by a system of three weakly coupled diffusion-reaction equations. This system takes the porous structure of the corroded part into account and addresses the generation of SO42- in that part of the pores of the corroded material which is water filled. The system is complemented by boundary and initial conditions and by an equation relating the corrosion speed with the concentration of SO42- at the corrosion interface. Mathematically, the problem is a one-dimensional one-phase moving boundary problem. Numerical algorithms and calculations are presented. They indicate that the corrosion speed behaves like t(s) with s close to 1/2 as t increases. This is reminiscent of the Stefan problem, although the boundary conditions are different. Comparison with available data shows that the model predicts the actual corrosion rate within a reasonable range. (C) 1998 Elsevier Science Inc. All rights reserved.