Pipe Wall Reactions
While flowing through pipes, dissolved substances can be transported to the pipe wall and react with material such as corrosion products or biofilm that are on or close to the wall. The amount of wall area available for reaction and the rate of mass transfer between the bulk fluid and the wall will also influence the overall rate of this reaction. The surface area per unit volume, which for a pipe equals 2 divided by the radius, determines the former factor. The latter factor can be represented by a mass transfer coefficient whose value depends on the molecular diffusivity of the reactive species and on the Reynolds number of the flow (Rossman et. al, 1994).
For first-order kinetics, the rate of a pipe wall reaction can be expressed as:
For zero-order kinetics, the reaction rate cannot be any higher than the rate of mass transfer, so:
Mass transfer coefficients are usually expressed in terms of a dimensionless Sherwood number (Sh):
In fully developed laminar flow, the average Sherwood number along the length of a pipe can be expressed as:
For turbulent flow, the empirical correlation of Notter and Sleicher (1971) can be used: