Modelling Discolouration in WDS Caused by Hydraulic Transient Events

The occurrence of hydraulic transients in water transmission and distribution systems and their impact on the deterioration of water quality is a topic which is beginning to attract a significant interest among scientists and system operators. Hydraulic transients are traditionally associated with large scale system failures. However, experimental studies carried out by the authors of this paper demonstrate that the hydraulic conditions are rarely steady-state and various fast and gradual transient events are frequently occurring due to the operation of pumps, control valves and stochastic demand. Furthermore, an analysis of the shape of acquired turbidity traces and field based experience have illustrated that it is the rate of flow change, represented by the unsteady-state shear stress, rather than the change in the magnitude of the flow (represented by the steady-state shear) that is responsible for particle mobilisation from the material layer in the pipe and the resulting discolouration events. Despite their importance, transient flow and the resulting unsteady-state forces are neglected by existing discolouration models, frequently resulting in incorrect turbidity predictions. This paper describes the development of a 1-D transient simulation model to describe discolouration caused by hydraulic transient events, by which the turbidity of the water is modelled with a transport equation which is coupled to a comprehensive hydraulic transient model. The hydraulic model estimates the unsteady shear stress generated during the transient using the Vardy Brown equation. A previously proposed approach (Boxall et al. 2001) is used to model the release of the discolouration material from the pipe wall into the flow, due to the excess shear stress applied at the wall. The presented transient discoloration model was assessed using hydraulic and discolouration data provided in the literature. Simulation results of the hydraulic transient model demonstrate that the magnitude of the unsteady shear could be as much as two times the magnitude of the steady shear during the initial change in the flow velocity. Two variants of the transient discolouration model are compared; one in which the unsteady shear stress is considered in the estimation of the shear stress applied at the wall, which is responsible for the material mobilisation and is included in Boxall's mobilization model, and another where it is not. The results show that the consideration of unsteady shear stress does not influence the turbidity behaviour obtained by the discolouration model based on the Boxall's particle mobilisation approach. This illustrates its limitations to describe the release of material from the wall caused by hydraulic transient events and emphasizes the need to investigate further the physics underlying this process.