Substantial advances have been made in the last decade in the development of practical methods for understanding and predicting how leakage rates and burst frequencies in distribution systems are influenced by pressure (Greyvenstein and Zyl, 2005). Lambert (2001a) further wrote that members of the Pressure Management Team of the Water Losses Task Force of the IWA continue to try to improve the practical methods available for analysis and prediction by studying for relationships among the leakage parameters. Even Thornton and Lambert (2005) indicated that with the prediction methods, it is now possible to make overview predictions of pressure management opportunities, and the likely effect on leak flow rates, new burst frequencies and residential consumption. Fantozzi and Fantozzi (2008) pointed out that using the inlet pressure or the pressure at the critical point for such calculations may produce unreliable results and conclusions, as the ratio of new pressure/old pressure is unlikely to be the same as the ratio at the AZP point.
With this type of low cost (or no-cost) analysis, it is hoped that many utilities will be motivated to get started (step 4 of water loss reduction strategy), and take action to manage their real losses more efficiently (Fantozzi et al., 2006). Practical predictions can usually be made rapidly without the need for network analysis models and this could be a useful tool in leakage management since any gains from any pressure reductions arising from pressure management could be easily determined and utilities could be encouraged to apply it knowing the savings to be realised (Thornton and Lambert, 2005).
2.9.1 Calculation of average pressure in water distribution systems
As pressure is a key parameter in modelling and understanding leakage, it is worthwhile to adopt a systematic approach to its calculation (Fantozzi and Fantozzi, 2008). They indicated that there are six methods of calculating average zone point (AZP) such as:
Using network analysis model node points
Calculated average value from pressure measurements taken in the zone
Count number of service connections between contours
Count number of hydrants between contours
Count number of properties between contours
Use mains length between contours
The procedure followed for each individual zone or DMA is that the weighted average ground level is calculated (Fantozzi and Fantozzi, 2008). They explained that the identified AZP is a convenient pressure measurement point which has the same weighted average ground level, and that pressure for all calculations is then measured at the AZP as the surrogate average pressure for the zone. Night pressures at the AZP point are known as average zone night pressures, AZNPs (McKenzie et al., 2004a).
For relatively small sectors with well-sized mains in good condition, with reliable information on average zone inlet pressure at a single inlet point, preliminary estimates of average zone pressure can be made (McKenzie et al., 2002a; Tooms and Morrison, 2005). They said that the procedure followed assumes that there is no or minimal frictional losses between inlet point and AZP, and as such AZNP could be estimated from the measured average pressure at the inlet point taking into account the difference in datum levels.
2.9.2 Relationship of pressure and minimum night flow
McKenzie, et al. (2002b) indicated that prior to 1994, a single relationship between minimum night flow and pressure was normally assumed in the UK, based on the leakage index curve.
They however said that in 1994, it was recognised that there was not a single relationship, but did not offer an alternative method. On the other hand, Marunga et al. (2006) in studies that were undertaken in Zimbabwe found that a pressure reduction from 80m to 50m resulted in a 40% reduction in MNF, and that further reductions of pressure resulted in further reduction in MNF. From the finding, it shows that there is a relationship between MNF and pressure, but need to be defined properly.
2.9.3 Relationship of pressure and leakage
An understanding of pressure – leakage relationship is fundamental in leakage control since leakage is influenced by pressure (Tooms and Morrison, 2005). They indicated that practical guidance could be offered on appropriate equations for data analysis, and predictions in individual situations if such relationship is understood properly. Lambert (2001a) and Greyvenstein and Zyl (2005) indicated that the principle of conservation of energy dictates that the flow rate (Q m/sec) of a jet of water passing through an orifice varies with the square root of the pressure (P metres) and as such:
2 N1
dA gP cP
C
Q= = ………..…..…(2.9)
Where Q is the leakage flow rate, Cd the discharge coefficient, A the orifice area, g acceleration due to gravity, P the pressure head, c is the leakage coefficient and N1 the leakage exponent (coefficient relating leakage and pressure). A number of field studies have shown
that the value of N1 can be considerably larger than 0.5 and typically varies between 0.5 and 2.79 with a median of 1.15 (Farley and Trow, 2003). Due to the position of N1 in the equation (as exponent), its value is the overriding factor in determining the flow rate from a particular leak opening. Lambert (2001a) and Fantozzi et al. (2006) indicated that FAVAD concepts can be used to rationally interpret a wide range of experimental test data on pressure – leakage relationships from pipe samples and sectors of distribution systems, and also to categorise relationships between pressure and components of consumption by customers.
Greyvenstein and Zyl (2005) discussed the effect of pressure on leakage and proposed a number of possible mechanisms that are responsible for the observed range of leakage exponents that included leak hydraulics, pipe material behaviour, soil hydraulics and water demand. It is believed that pipe material behaviour is the main cause of observed leakage exponents, which are above theoretical orifice value of 0.5 (Lambert, 2001a; Farley and Trow, 2003). Greyvenstein and Zyl (2005) investigations found that leakage type is a better indicator of leakage exponent than pipe material. They pointed out that for round holes in otherwise good quality pipes, the leakage exponents are close to the theoretical orifice exponent of 0.5, and are similar for uPVC and steel pipes. They further found the highest exponents in corrosion clusters in steel pipes, which were explained as probably due to corrosion that reduces the support material around the hole. This is contrary to the perception of Farley and Trow (2003) who indicated that plastic pipes will have higher leakage exponents due to their lower modulus of elasticity.
Walski et al. (2006) conducted several other tests to confirm effects of soil hydraulics on the observed range of leakage exponents. The studies were aimed at determining the effects of head loss that occur between the leak and the soil surface as the water moves through the soil.
A dimensionless number was introduced, which is the ratio of the orifice head loss and soil head loss and was called OS for “orifice/soil number.” Walski et al. (2006) defined the OS number by the following equation:
s
d h
h A
C gL
OS KAQ 0
2
0
1
2 ⎟⎟ =
⎠
⎜⎜ ⎞
⎝
= ⎛ ………(2.10)
Where ho and hs are head losses in orifice flow and in soil. They said that when the OS number has magnitude of 1, both the soil loss and orifice loss are equally important, and when the OS number is small (<0.1), the soil losses are dominant. When it is large (>10), the orifice losses are dominant. Walski et al. (2006) conducted experiments at different OS numbers and found that for a large OS number (OS>1), the power exponent (N1) was equal to 0.5, indicating that the leakage is controlled by the orifice conditions and further indicated that in these cases, the head loss from the soil matrix is negligible. The results also demonstrated that for small OS numbers, the power exponent (N1) is near 1, which indicates that the leakage is controlled by the head losses in the soil matrix. The transition range was found to be relatively small, implying that in most cases either the orifice or the soil matrix controls the leakage. It should however be mentioned that in real world cases, the OS number for bursts is large, and as such the value of N1 would be equivalent to 0.5 (Walski et al., 2006). For background losses, the OS number is small and this explains the reason for values of 1.5 (McKenzie et al., 2002b;
Thornton and Lambert, 2005).
Consequently, whilst the N1 exponent may be anywhere between 0.5 and 2.5 for individual small zones, the average pressure leakage rate relationship for large systems with mixed pipe materials is usually close to linear, N1 = 1.0 (Thornton, 2003). In the absence of knowledge of pipe materials and leakage level, Lambert (2001a) recommended that a linear relationship (N1
= 1.0) should be assumed. The ‘N1’ approach can also be used to analyse and predict relationships between pressure and individual components of customer use (Lambert, 2001a).
McKenzie et al. (2002b) pointed out that estimation of N1 values could be done by simply selecting between 2 and 4 pairs of pressures and flows and inserting them into the appropriate cells in the hour day factor (HDF) model. Sample of HDF model is shown in Fig. 2.5.
Population : 6525 number Normal Night Use : 1.96 m3/hr
% active during MNF : 3.0 % Exceptional Users : 0.00 m3/hr
Cistern Capacity : 10.0 litres Expected Night Use : 1.96 m3/hr Measured
Night Pressures Calculated Values of N1
Stage Start Time (h:m) End
Time
(h:m) Inlet Point (m)
AZP (m)
Zone Inflow (m3/hr)
Night Use (m3/hr)
Distribution Losses
(m3/hr) Stage 1
Stage 2
Stage 3
Average
Start 54.0 43.4 1.96 41.44
Stage 1 58.0 46.5 1.96 44.54 1.0 1.0
Stage 2 61.5 49.8 1.96 47.84 1.1 1.2 1.2
Stage 3 66.0 53.5 1.96 51.54 1.1 1.1 1.1 1.1
Calculated N1 Value 1.1
Fig. 2.5 Sample calculation of N1 from HDF model (Adopted from McKenzie et al., 2002b) 2.9.4 Relationship of pressure and burst frequency
Maggs (2005) stated that it had been shown that there is a strong relationship between burst rates and pressure levels. However, Maggs indicated that further work is required but it is currently thought burst frequency may be proportional to pressure cubed. McKenzie et al.
(2002b) also pointed out that through considerable research it has been shown that burst frequency is very sensitive to maximum system pressure. Marunga et al. (2005) in a study conducted in Zimbabwe also found that with the increase in pressure, there was also an increase in number of bursts. Furthermore, data on changes in break frequency following pressure management for a relatively low-pressure and high break frequency pumped system in the Bahamas showed that there is a relationship between pressure and burst frequency at low pressures (Fanner and Thornton, 2005). Conversely, UKWIR (2005) indicated that there is no evidence of a relationship between pressure and burst frequency. Similarly, Lambert (2001a) on investigating data from UK concluded that there is no unique relationship between maximum pressure and new leak frequency, but evidence shows that excess pressures in systems subject to continuous supply result in higher frequencies, and higher repair costs, than are necessary. From the discussion, it shows that there is a relationship between pressure and burst frequency but it may be a complicated relationship.
Thornton and Lambert (2005) indicated that this topic was not well studied and indicated that the IWA Pressure Management Team would seek good quality data of recorded burst frequencies ‘before’ and ‘after’ pressure management in order to improve the current practical methods of analysing and predicting the effect of pressure management on frequency of new bursts, using the provisional relationship that: ‘burst frequency (or repairs cost) varies with pressure to the power N2’, where N2 is coefficient relating pressure and burst frequency.
Investigations on data from UK, Japan, and Australia indicated that N2 values normally ranges from 0.5 to 6.5 as reported by Thornton and Lambert (2005). However, Thornton and Lambert (2007) showed that the N2 approach is inappropriate and recommended:
that the N2 approach to analysis should be abandoned as inappropriate
that additional ‘before’ and ‘after’ break data should be collected and published
that an alternative conceptual approach, based on failures being due to a combination of factors, needed to be developed.
Thornton and Lambert (2007) suggested reasons for the inappropriateness that as years pass adverse factors based on age (including corrosion) gradually reduce the pressure at which the pipes will fail. They pointed out that depending upon local factors such as traffic loading, ground movement and low temperatures (which will vary from country to country, and from system to system), at some point in time the maximum operating pressure in the pipes will interact with the adverse factors, and break frequencies will start to increase. This effect can be expected to occur earlier in systems with pressure transients or re-pumping, than in systems supplied by gravity (Thornton, 2003; Thornton and Lambert, 2007). Warren (2005) affirms this in that he indicated that the link between burst frequency and pressure is related more to pressure variation, which may also influence the burst shape factor. From the discussion, it can be seen that the reason as to why mains and/or service connections in some systems show large % reductions in new break frequency with pressure management, but in others the % reduction is only small, can be proposed using this concept.