A Dimensionless Two-Dimensional Model of Chlorine Transport and Pathogen Inactivation in Baffled Contact Tanks: Analysis, a Stable Dufort–Frankel Scheme and Numerical Experiments

Chlorine contact tanks are usually modelled in one dimension, which cannot represent baffles or short-circuiting. We extend a one-dimensional modified convection–diffusion model of chlorine transport to a depth-averaged planar advection–dispersion–decay model, derived from the three-dimensional transport law and written in dimensionless form with a Péclet number and a Damköhler number . With a Danckwerts inlet condition the model has a unique weak solution that satisfies 0 ≤ c ≤ 1.. We solve it with an explicit two-dimensional Dufort–Frankel scheme, which is consistent only when tends to zero and is stable if and only if Cx2 + Cy2 ≤ 1/2 in the absence of decay, for every diffusion number; the bound is proved in closed form. The scheme is second-order accurate on an exact solution. A new contribution is a one-way coupled Chick–Watson pathogen equation, from which we define an efficiency index relative to plug flow and a conservatism ratio for the residual-times- rule. In experiments on three baffle layouts with ideal (potential) flow, adding four baffles to an open basin raised the baffling factor from 0.28 to 0.75 at Pe = 1 and from 0.70 to 0.88 at . The efficiency index rose from 0.41 to 0.86 at and from 0.85 to 0.97 at , and the rule gave only about half of the computed log inactivation. We also correct an error in the algorithm of the earlier one-dimensional study. The results are verified numerically but not yet calibrated against tracer data. Chlorine contact tanks are usually modelled in one dimension, which cannot represent baffles or short-circuiting. We extend a one-dimensional modified convection–diffusion model of chlorine transport to a depth-averaged planar advection–dispersion–decay model, derived from the three-dimensional transport law and written in dimensionless form with a Péclet number and a Damköhler number . With a Danckwerts inlet condition the model has a unique weak solution that satisfies . We solve it with an explicit two-dimensional Dufort–Frankel scheme, which is consistent only when tends to zero and is stable if and only if in the absence of decay, for every diffusion number; the bound is proved in closed form. The scheme is second-order accurate on an exact solution. A new contribution is a one-way coupled Chick–Watson pathogen equation, from which we define an efficiency index relative to plug flow and a conservatism ratio for the residual-times-t10 rule. In experiments on three baffle layouts with ideal (potential) flow, adding four baffles to an open basin raised the baffling factor from 0.28 to 0.75 at and from 0.70 to 0.88 at Pe = 50. The efficiency index rose from 0.41 to 0.86 at Pe = 1 and from 0.85 to 0.97 at Pe = 50, and the t10 rule gave only about half of the computed log inactivation. We also correct an error in the algorithm of the earlier one-dimensional study. The results are verified numerically but not yet calibrated against tracer data.