Modification of Shannon Entropy to Quantify Mixing in UV Reactors

Abstract

Mixing or mixedness in ultraviolet (UV) wastewater reactors has been identified by many as a key factor in reactor performance. However, the current methods for determining mixing are either qualitative, and cannot be correlated directly with reactor performance, or use ideal mixing states that are not practical. In this paper, a modified Shannon entropy mixedness metric was used to quantify mixing in UV reactors. Contrary to the current literature which has shown that the mixedness only decreases when the number of regions into which the system is divided is increased, it is shown here numerically that mixedness can increase or decrease when the number of regions are increased. As well, it was proven numerically and theoretically that the mixedness will converge to a finite value with a sufficiently high number of regions. Furthermore, a highly simulated system that achieved perfect mixing under the modified mixedness equation produced a reduction equivalent dose (RED) almost 50% higher than the perfect mixing state under the original mixedness. The modification made to the mixedness equation suits the need of a UV reactor, but can also be applied to other process flow systems where mixing and reactor performance are linked. Finally, a very strong correlation between mixedness and UV reactor performance was found for two idealized single-lamp UV reactors. This means that the mixedness calculated here can be used as a proxy for reactor performance, allowing modelers to significantly reduce the computational cost required when comparing the performance of different reactors.