Leakage Calibration in Water Distribution Networks with Pressure-Driven Analysis: A Real Case Study ^†

Abstract

Leakage in water distribution networks (WDN) is still a major concern for water companies. In recent years, the scientific community has dedicated some effort to the leakage calibration issue to obtain accurate models. But leakage modelling implies the use of a pressure-driven approach as well as specific data to define the pressure/leakage relationship. This paper presents the calibration process of a real case study WDN model. The process started with pressure step tests, the model was built in WaterNetGen and the leakage calibration process was performed by a simulated annealing algorithm. As illustrated, after calibration the model was able to produce accurate results.

1. Introduction

Water loss in water distribution networks (WDN) is still a major concern for water companies. They are known to be the cause of many negative impacts, like economic losses, technical and social problems, environmental damages and difficulties in guaranteeing the water quality safety. Water losses include both apparent and real losses. While apparent losses are related to customer meter inaccuracies and unauthorized consumption, real losses correspond to the water lost due to leakage and overflows at storage tanks and leakage on transmission and distribution mains and in service connections up to the point of customer metering [1]. Unreported leaks (in mains and service connections) are a major cause of real losses because, even if the flow is relatively small, as they can last for a long time the total volume lost can be huge. Unreported leaks are difficult to locate, particularly in plastic pipes, large diameters and low-pressure conditions. In recent years, the scientific community has dedicated some effort to the leakage calibration issue in order to obtain accurate models for WDN, supported by flow and pressure measurements, and using modelling and optimization tools, considering both demand-driven analysis (DDA) [2,3] or pressure-driven analysis (PDA) [4,5]. However, the theoretically correct leakage modelling implies the use of PDA, which is far more complex than the more traditional DDA and needs specific data to define the pressure/leakage relationship.

This paper presents the calibration process of a real case study WDN model. Section 2 is dedicated to the theoretical background and presentation of the calibration methodology, Section 3 presents the case study and the results and finally Section 4 is dedicated to the conclusions.

2. Materials and Methods

2.1. Leakage Modelling

Leakage is assumed to be a function of the pressure and can be modelled with two components, bursts and background leakage [6]:

$$q_k^{leak}\left(P_k\right)=\{\begin{array}{cc}{\beta }_k·L_k·{\left(P_k\right)}^{{\alpha }_k}+C_k·{\left(P_k\right)}^{{\delta }_k}& P_k>0\\ 0& P_k\le 0\end{array}$$

(1)

where q_k^leak is the total leakage along pipe k; L_k is the length of pipe k; α_k and β_k are parameters of the background leakage model; C_k and δ_k are parameters of the bursts leakage model; and P_k is the average pressure in pipe k computed as the mean of the pressure values of its end nodes.

The exponent α_k depends on the network characteristics (pipe material and failure mode) and can take values between 0.5 and 2.5. The parameter β_k must be set by calibration (initial values can be set around 10^-7) [7].

2.2. Calibration Methodology

The first goal of this work is to calibrate leakage in WDN models, that is to estimate the pipe background leakage parameters (α_k and β_k) from Equation (1). The α_k parameter is network specific and can be obtained by performing pressure step tests in the network being studied. The β_k parameter is pipe specific and here is estimated by solving an optimization problem in which the objective function is the difference between measured and observed flows and pressures and the decision variables are the β_k values for each pipe in the WDN model. This optimization problem is solved by a simulated annealing algorithm [8], with the help of a pressure-driven hydraulic simulation model, implemented in WaterNetGen [9,10]—an EPANET [11] extension, to assess the hydraulic constraints and estimate the pipe leakage.

The objective function (OF) can be written as:

$$\mathrm{Min}.\mathrm{OF}={\mathrm{W}}_{\mathrm{P}}·{\displaystyle \sum }_{\mathrm{Nodes}}\left|{\mathrm{P}}_{\mathrm{m}}-{\mathrm{P}}_{\mathrm{e}}\right|+{\mathrm{W}}_{\mathrm{F}}·{\displaystyle \sum }_{\mathrm{Pipes}}\left|{\mathrm{F}}_{\mathrm{m}}-{\mathrm{F}}_{\mathrm{e}}\right|$$

(2)

where W_P is the weight for the pressure errors, Nodes is the set of nodes with pressure measurements, P_m and P_e are the pressures measured and estimated, respectively, W_F is the weight for the flow errors, Pipes is the set of pipes with flow measurements, F_m and F_e are the flows measured and estimated, respectively.

The constraints that define the hydraulic behavior of the WDN, as well as the leakage estimates, are assessed by WaterNetGen.

The simulated annealing algorithm was implemented as described in

Table 1. Simulated annealing algorithm implementation.

Part of the Algorithm	Implementation
Initial solution	Assign a βk value to each pipe (Xo)
Initial temperature	$T_i=-0.1\frac{OF\left(X_0\right)}{Log\left(0.5\right)}$
Control parameters	If Pa > 70% Ti+1 = 0.5 Ti and IAi+1 = 10 If Pa > 50% Ti+1 = 0.6 Ti and IAi+1 = 20 If Pa > 35% Ti+1 = 0.7 Ti and IAi+1 = 30 If Pa > 20% Ti+1 = 0.8 Ti and IAi+1 = 40 If Pa ≤ 20% Ti+1 = 0.9 Ti and IAi+1 = 50
Number of evaluations (Li) at each temperature (Ti)	IAi × Number of pipes in the network
Stopping criteria	Pa < 5% and 2 temperatures without improvement

. The procedure starts by assigning an initial value to the β_k parameter for each pipe in the WDN model (in this case it was assigned β_k = 0). A starting temperature is calculated and a certain number of candidate solutions are evaluated. Each candidate solution is obtained from the current solution by randomly choosing a pipe and changing its β_k value (up or down) and its objective function is calculated with the results from the PDA simulation performed by WaterNetGen. The number of candidate solutions (L_i) generated at each temperature (T_i) varies according to the percentage of solutions accepted at the last temperature (Pa_i−1). Each new solution is accepted or not, according to the Metropolis criterion. If it is accepted, this solution becomes the current solution and will be used to produce the next candidate solution. If not, the original current solution will be used. The algorithm ends if the stopping criteria are reached, that is, for two successive temperatures the number of solutions accepted remains lower than 5% and there is no improvement.

All this procedure was embedded in WaterNetGen and the user just has to build the WDN model (topology, tank properties, junction properties, pipe properties, base demand, demand patter, and other operational parameters or rules) and ask the software to solve the optimization problem (perform the calibration procedure).

3. Results and Discussion

The proposed methodology was applied to a real case study WDN model, namely the Loureira District Metered Area (DMA), Figure 1, which is a part of the Fatima WDN, managed by the water company Be Water—Águas de Ourém. This DMA is supplied by a pressure reduction valve (PRV) to manage the pressure, which was introduced in the model as a reservoir with a head pattern obtained from the pressure measurements obtained downstream the PRV. The pipes from this network are all made of PVC, with diameters between 63 and 315 mm, in a total of about 13 km. The WDN model was built from Geographical Information System (GIS) files containing information about the topology of the network and the characteristics of the network components.

The leakage calibration process started by performing pressure step tests to obtain the data for the pressure/leakage relationship (pressures were gradually reduced at the PRV while monitoring the effect on the minimum night flows). The data obtained (Figure 2) lead to a α_k parameter equal to 1.8, which was introduced in the WDN model.

The flow measurements at the DMA Loureira entrance were used to estimate the leakage flow, by analyzing the minimum night flow. The difference between the flow measurements and the water demand is the water losses that should be assigned to the pipes to obtain a calibrated model, here estimated as about 5 m³/h (1.4 L/s). At the roundabout located in southeastern part of the network there is a garden irrigating during the night, with a flow of about 5 m³/h (1.4 L/s). As this consumption is known (value and location) it was decided to exclude it from the water demand and consider it as a leak to be located and, to a certain extent, to confirm the accuracy of the results.

The flow measurements, after excluding the water losses and the garden irrigation, resulted in the demand pattern used in the model (Figure 3).

The leakage calibration process was supported by the flow measurements obtained at the DMA Loureira entry point and the pressure measurements obtained in three points of the network (P3, P4 and P5), Figure 4.

All these data, together with the GIS files data, were used to build the WDN model (Figure 5) in WaterNetGen, an EPANET extension including a PDA engine.

The topology of this WDN, with a radial shape, does not ease the leakage calibration process since there are no long pipes with significant head losses making them quite sensitive to flow changes. On the other hand, this WDN has another particular characteristic that can make things even more difficult for the calibration. This network is in the vicinity of the Fatima sanctuary, a world-famous religious destination. In a few days of the year (particularly in the 13th of May) this place becomes full of pilgrims and the water demand increases a lot. Consequently, this WDN is designed to face those huge water demands but in most of the year it is oversized, presenting low sensitivity to pressure; even so, it is worth a try.

The leakage calibration process (assignment of the leakage parameters, β_k, to the pipes) was performed by the simulated annealing algorithm used to solve the optimization problem aimed at minimizing the differences between the field measurements and the PDA simulation results. The process took about one hour to produce the results and the calibration reports (for flow and pressure) presented in Figure 6 seem to confirm the accuracy of the proposed methodology, showing a very good fitting between the observed (measurements) and the computed (results of the PDA simulation) values.

Although the calibration results seem to be quite accurate, many different combinations of flows in the model can fit the measurements and be quite different from the flow distribution occurring in the real network. The only way to check the accuracy of the calibration is to confirm the existence of leaks in the pipes pointed out by the methodology in the WDN model.

The leakage calibration process identified a few potential leaky pipes in the surroundings of the roundabout (probably related to the garden irrigation used as a known leak) and a concentration of potential leaky pipes at the western zone of the network (1.2 L/s), Figure 7. Before the closure of the paper submission period, it was still possible to execute a step-test (closing isolation valves during the night) and this confirmed the existence of a considerable night flow at the western zone of the network, probably due to the existence of leaks. Further work will include an acoustic survey in that part of the network to confirm/locate those leaks. There were also other pipes in the WDN that were pointed out as probable leaky pipes but without any considerable significance.

The first goal of this work was to estimate the pipe background leakage parameters (β_k) in order to obtain a calibrated WDN model. The results obtained apparently lead to the conclusion that the goal was accomplished because the calibration reports show that the simulation results fit well with the field measurements. However, the final conclusion can only be drawn after carrying out field acoustic inspection works to check if there are really leaks in the pipes identified as probable leaky pipes.

4. Conclusions

This paper presents the calibration process of a real case study WDN model. The process started by performing pressure step tests to obtain the exponents of the pressure/leakage relationship (pressures were gradually reduced while monitoring the effect on the minimum night flows). The WDN model was built in WaterNetGen, an EPANET extension including a PDA engine, which is used to assess the hydraulic constraints and estimate the pipe leakage. The leakage calibration process (assignment of the pipe background leakage parameters, β_k) was performed by a simulated annealing algorithm used to solve an optimization problem aimed at minimizing the differences between field measurements (flows and pressures) and simulation results. The calibration reports show a good fit between the simulation results and the field measurements, leading to the conclusion that the proposed leakage calibration methodology is accurate. However, the final conclusion can only be drawn after carrying out field acoustic inspection works to check if there are really leaks in the pipes identified as probable leaky pipes. By identifying the most probable leaky pipes, the results from this leakage calibration methodology will certainly be of great help in the context of active leakage control, optimizing the resources allocated to the leak location process.