Development of pressure management analytical equations in water distribution networks

Extended abstract

Abstract
Pressure management is an effective method for water demand management. For evaluation of the effects of pressure changes on leakage level of water networks, the FAVAD equation is usually used. However, in this equation, exponent of pressure parameter (N) needs to be determined. For estimation of N, either some information about the leak opening is necessary or network’s leakage level needs to be known which is very difficult to measure. On the other hand, available studies about the effects of pressure changes on water consumptions and leakage don’t seem to be enough. In the present study, a new analytical method is proposed for calculation of N, in which direct measurement of leakage level, does not need. In order to test ability of the proposed method as well as the pressure effects on leakage and water consumption, an isolated water network in Tehran city has been selected.
Different pressure patterns were implemented on outlet of a pressure reducing valve and variation of the minimum night flows, customers’ water consumption and inlet flow discharge were then measured in the pilot network. In this study, implementation of the pressure management could reduce the minimum night flow, water inflow and customers' consumption up to 50, 21 and 30 percent, respectively. Furthermore, using the obtained data, different equations for estimation of pressure effects on reducing of night flow, total inflow and water consumption are presented.

Introduction
Considering water scarcity, population growth, increase of water consumption per capita and high cost of drinking water production, optimum usage of existing water resources is a vital issue. Pressure management is one of the most effective solutions among the water demand management methods to help solving these problems.
Although pressure management is one of the best methods for water demand management, some operation managers ignore using this method in their water distribution networks and would prefer to use other methods such as water rationing when they face water scarcity. It may be because of lack of experience on pressure management. The main objective of this paper is to show the good results and practicability of pressure management especially for old and existing water distribution networks.
N parameter in the FAVAD’s pressure-leakage formula, represents the power-law relationship between leakage rate and pressure. The value of the exponent N may vary from 0.5 for “Fixed Area” leaks to 1.5 or more for “Variable Area” leaks where leak area varies with pressure. In this paper a new modified method of calculation the N exponent is shown.

Materials & Methods
An isolated water distribution network in Tehran city was chosen for this study (Figure 1). Region is supplied with only one reservoir. After isolation of the region, a modulated PRV in the entrance of the isolated region was assembled, moreover, a pressure regulator were installed to induce different pressure patterns. Also an ultrasonic flowmeter was used in downstream of the reservoir to measure input flow to the isolated region.
Since at the begging of study the optimum pressure pattern was not exactly known, therefore after preparation of isolated region and setting up the equipment, different pressure patterns were applied to the modulated PRV as try and error process to find the best pattern. These patterns are shown in Figure 2. This process continued by applying more pressure reduction to the PRV until the first complaint was received from the customers. On the other hand, by having different pressure patterns and measurement of night flow for each one, it could be possible to follow changing of night flow with water pressure variation.
For each patterns inflow was recorded in 10 minute intervals and the measurements were continued for a week. Output pressure of PRV before installation of modulated PRV was 50 meters. It should be noticed that output pressure patterns of PRV were adjusted such that the costumers didn’t face any pressure shortage and no complaint was reported during the study.
Different conditions and information of measurements are shown in Table 1. For better comparison of mentioned patterns (Figure 2), average amount of applied pressure patterns during 24 hours is also mentioned in table.
Results & Discussion
After completion of measurements, the data was analysed and following results are obtained:
Results show that with no complaints of consumers, total inlet flow reduced about 21 percent in final week. Inlet flow is composed of network leakage and consumer’s consumption, reduction of inlet flow means lower consumers’ consumption and/or lower network leakage.
To study the effects of pressure management on the consumers’ consumption, 64 consumers were selected as sample of total consumers and their domestic water consumptions measured by reading their flow meters in different weeks during the study period. Results for domestic water consumptions are shown in Table 2.
Results show more than 30 percent water saving for the consumers’ consumption in final week. Minimum night flow is composed of network leakage and consumer’s night consumption. Since amount of consumer’s night consumption is almost constant, the minimum night flow could be a convenient indicator for estimation of network’s leakage. Minimum night flow occurs at midnight hours and especially between 12 to 4 AM.
The trend of results shows a reduction of minimum night flow with reduction of pressure and a potential for reduction of night flow more than 30 percent. It should be also mentioned that no complaint was received from consumers when final pattern was applied to the modulated PRV. Table 3 shows the measurement results of minimum night flow in the different weeks (weeks).
In this study, using data obtained from the pilot, a novel analytical method for estimation of the pressure exponent (N) has been presented. Using this method N=1.15 was estimated for the network under study.

Conclusions
In present study, results of pressure management on distribution network show that with no complaints of consumers, some benefits such as leakage reduction and consumer’s consumption are practically achievable.
A novel analytical method for estimation of the pressure exponent (N) in the FAVAD equation as well as analytical equations for evaluation of pressure management’s effects on leakage and water consumption have been recommended.
Considering complexity of water networks in term of flow hydraulic, geometrical and material of pipes, more research are still needed to study the relation between pressure, leakage and consumers’ water consumption.
Keywords: Water distribution networks, Pressure management, Leakage, Leakage-pressure relationship, N exponent.