Theoretical and Conceptual Framework - Pattern Recognition for Reliability Assessment of Water Distribution Networks - page 23

Step 4 : After the modification of the network, the model simulation runs again. If one or more
virtual reservoirs have received more water than the original demand of the corresponding
node, those virtual reservoirs are removed from the network and the original nodal demands
are restored. For example, the demand of virtual reservoir 7 (86.09 l/s) has exceed the
original demand of node 2 (20.10 l/s) and this reservoir can be removed from the network in
the next iteration. The reservoir in node 4 receives 34.23 l/s, which is less than the original
demand of 40.20 l/s. For that reason, this reservoir stays attached to node 4 in the next
iteration, as is the case with those in nodes 3, 5 and 6.

Step 5 : With the original demand of node 2 restored, the simulation is run again. In nodes
where the reservoirs receive less water than the original nodal demand, their supply shows
the degree of the demand reduction. The iterative process continues until there is no change
in the setup of the virtual reservoirs and ordinary nodes in two consecutive iterations. In this
example, the total available demand stabilises at 93.38 l/s. The overall available demand
fraction resulting from the burst of pipe 6 (ADF 6 ) is therefore 61.94% (93.38/150.75). The
original demand of nodes 2, 3, and 4 is fully satisfied, whilst the demand of node 5 will be
partially satisfied (ADF 5 = 9.72 %). Node 6 will receive no water as a result of the pipe burst
(ADF 6 = 0 %).

Step 6 : In the final step, the actual nodal pressures are calculated based on the true demand.

The above procedure is rather complex if it is to be applied for extended period simulations
and any larger network, where each pipe is to be failed in the availability/ reliability analysis.
Using the programme for ADF calculation, developed by Yoo et al. (2005), the results of the
test network calculated for the applied demand pattern are shown in Figure 2.6, with the
average availability factor of 0.8789, higher than the average reliability factor of 0.7742. This
is normal knowing that the availability assumes possibility of repair of the failed system
component. Also logical is that the higher demand in the system inflicts the lower values of
the availability and reliability factors, during particular hours of the day.

Applying the same procedure for any other demand scenario, makes possible to compile the
reliability and availability curves for 24-hour period, as is shown in Figure 2.6.

1.00

Availability - A(t)

0.90

0.80

0.70

Reliability - R(t)

0.60

0.50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time - t (hours)

Figure 2.6 Hydraulic reliability and availability for network from Figure 2.5 (Yoo et al., 2005)