Page 124 - Water Loss Control

106 Cha pte r Ni ne

background leakage, that is, leakage below the level of detection, plus the leakage from
reported leaks plus the leakage from unreported leaks during the period they run
between detection and repair, resulting from any given leakage control policy. This is
sometimes referred to as the policy minimum level of leakage.
There has been much debate about the shape of the curve between these asymp-
totes. In the most simplistic model of regular sounding, the curve will be hyperbolic.
This is based on the fact that the curve will be defined by the leakage during the period
which unreported leaks run until they are detected. This will be directly related to the
length of time they run before being detected and hence the intervention interval. As
the intervention interval will be inversely related to the resources (doubling the
resources will half the intervention interval) then leakage will be inversely proportional
(i.e., a hyperbole) to the level of resources and hence the ALC cost. If the area is sector-
ized, or if other forms of flow measurement are used to direct resources more efficiently
compared to simple regular sounding, the curve will be flatter than a pure hyperbole.
If the cost of the water lost at different levels of leakage is plotted on the same graph
this would be represented by the line C-C. The cost will be the simple difference in cost in
producing one more or less unit of water in terms of power, chemicals, and possibly
labour. The slope of this line is referred to as the marginal cost of water. If the marginal
cost of water is constant, line C-C will be a straight line. If the marginal cost of water pro-
duction is not constant, then line C-C will be made up of a number of straight lines; usu-
ally increasing in slope with higher leakage as more expensive water is used. Curve D-D
is the total cost of operation, that is, cost of leakage control plus cost of water production.
As can be seen, the curve will be high initially due to the high cost of leakage detection
required to achieve very low levels of leakage. The total cost then reduces before increas-
ing again as the cost of water production increases with increasing levels of leakage. The
point at which the total cost is lowest will be the short-run economic level of leakage. At
this point, the marginal cost of leakage detection activity will be equal to the marginal cost
of water. This point will also define the economic level of resources to be deployed on
leakage detection and the economic period between interventions.
It can be shown that the minimum total cost of lost water and intervention costs
occur when the accumulated value of lost water since the last intervention equals the
cost of intervention. This simple relationship has been used by a number of people to
develop methodologies to calculate the economic intervention period for a system.
The solution to the calculation of the economic intervention period in the case of
regular sounding, that is, where all parts of the system are swept with the same fre-
3
4
quency, is reasonably straightforward and this has been developed into methodolo-
gies that can be readily applied to distribution systems.
Where the system has been sectorized and information therefore exists for the rate
at which leakage accumulates on different parts of the network then a more specific
5,6
approach can be taken. In this approach, the actual volume of leakage is accumulated
using night-line information since the last intervention and proactive detection is initi-
ated when the value of this is equal to the cost of intervention on that sector. The advan-
tage of this approach is that it can take into account sector-specific cost of water (say
due to local boosting of water) and also sector-specific survey costs (say due to urbani-
sation or pipe materials).
An alternative approach has been to try and define the ALC curve itself. This can be
carried out in a number of ways, which can be classified as either empirical or theoretical.
The former relies on the establishment of a number of points along the curve by
analysing the results from actual ALC operations. When a number of points have been