The rate of water quality reactions occurring at or near the pipe wall can be considered to be dependent on the concentration in the bulk flow, by using an expression of the form:
where Kw = the wall reaction rate coefficient, and (A/V) = the surface area per unit volume within a pipe (equal to 4 divided by the pipe diameter). The latter term converts the mass reacting per unit of wall area to a per unit volume basis. EPANet limits the choice of wall reaction order to either 0 or 1, so that the units of Kw are either mass/area/time or length/time, respectively. As with Kb the value for Kw must be supplied to the program by the modeller. First-order Kw values can range anywhere from 0, to as much as 1,7 m (5 ft/day).
Kw should be adjusted to account for any mass transfer limitations, in moving reactants and products between the bulk flow and the wall. EPANet does this automatically, basing the adjustment on the molecular diffusivity of the substance being modelled, and on the flow's Reynolds number. See Appendix D for details. (Setting the molecular diffusivity to zero will cause mass transfer effects to be ignored).
The wall reaction coefficient can depend on temperature, and can also be correlated to pipe age and material. It is well known that as metal pipes age, their roughness tends to increase due to encrustation and tuburculation of corrosion products on the pipe walls. This increase in roughness produces a lower Hazen-Williams C-factor, or a higher Darcy-Weisbach roughness coefficient, resulting in greater frictional head loss in flow through the pipe.
There is some evidence to suggest that the same processes that increase a pipe's roughness with age, also tend to increase the reactivity of its wall with some chemical species, particularly chlorine and other disinfectants. EPANet can make each pipe's Kw be a function of the coefficient used to describe its roughness. A different function applies, depending on the formula used to compute head loss through the pipe:
Head loss Formula Wall Reaction Formula
Hazen-Williams Kw = F / C
Darcy-Weisbach Kw = -F / log(e/d)
Chezy-Manning Kw = F n
where C = Hazen-Williams C-factor, e = Darcy-Weisbach roughness, d = pipe diameter, n = Manning roughness coefficient, and F = wall reaction - pipe roughness coefficient. The coefficient F must be developed from site-specific field measurements, and will have a different meaning depending on which head loss equation is used. The advantage of using this approach is that it requires only a single parameter, F, to allow wall reaction coefficients to vary throughout the network in a physically meaningful way.