Emitter Based Algorithm for Pressure-Driven Demand Calculations of Water Distribution Networks - Pattern Recognition for Reliability Assessment of Water Distribution Networks - page 40

A layout of this version of EPANET programme, called EPANET-EMITTER is shown in
Figure 3.5. In the iteration process, for:
1. p i /ρg > ECUP , Q i,PDD = Q i,DD ,
2. 0 < p i /ρg < ECUP , Q i,PDD = k i (p i /ρg) α
3. p i /ρg < 0, Q i,PDD = 0
Before the iteration process starts, the values for emitter coefficients in each node will be
estimated based on Equation 3.8.

Q

i , DD

k = 3.8

i

α

ECUP

3.3 EMITTER PERFORMANCE UNDER EXTREME TOPOGRAPHIC

CONDITIONS

As shown above, in cases the nodal pressure tends to become negative in the PDD mode of
calculation, the nodal demand should be set to zero, which is the situation that can occur in
cases of extreme topography i.e. where negative pressures are mostly inflicted by high
elevations. Setting the demand to zero only in the nodes with negative pressures assumes that
the effect of high elevation is restricted only to that particular node, whilst based on the
situation in the network, this effect can propagate i.e. affect the demand in surrounding nodes,
too. On the other hand, without additional intervention on the nodal demand, emitters in the
nodes with negative pressure will cause a negative demand i.e. a dummy supply, as shown in
Figure 3.6.

Figure 3.6 Negative demand resulting from negative pressures in PDD models using emitters

Piller and Van Zyl (2009) summarise the deficiencies of emitters used for PDD algorithm,
reported by other researchers, namely Todini (2003, 2006), Cheung et al. (2005) and Wu et
al. (2006). They point three inconveniences of the emitter use: the negative demands, the
reduced convergence of the solving method, and the upper bound of consumption that in
reality is not only dependant on the available head but also on physical characteristics such as
the number of connected premises. They further propose the algorithm for solving a problem
of network section connected to a source via a high-altitude node, causing negative pressure.
These situations in reality inflict reduction of pipe conveying capacity because of the air
entrainment through air valves and taps. The algorithm based on the energy minimisation
concept that avoids definition of PDD relationship, based on their work published in 2007, is
however tested on rather small case network restricted to a single node/route connection.