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Article

The Impact Assessment of Water Supply DMA Formation on the Monitoring System Sensitivity

Department of Water Supply and Wastewater Disposal, Faculty of Environmental Engineering, Lublin University of Technology, Nadbystrzycka 40 B, 20-618 Lublin, Poland
*
Author to whom correspondence should be addressed.
Appl. Sci. 2023, 13(3), 1554; https://doi.org/10.3390/app13031554
Submission received: 30 December 2022 / Revised: 18 January 2023 / Accepted: 23 January 2023 / Published: 25 January 2023
(This article belongs to the Section Environmental Sciences)

Abstract

:
One of the main tasks that water companies face is limiting water losses through the distribution network. This issue is becoming more and more relevant because of progressive climate changes and rising water resource deficiencies. The first step to reducing water losses is the proper detection of leakages, including their location and size. A common approach, called active leakage control, is to divide the water network into District Metered Areas (DMAs) to detect unreported leaks in the water distribution system (WDS). The operating flow meter device at the border of the DMA allows the determination of the number of water losses by balancing water inflows into the zone and billed water consumption. However, to precisely locate a water leak it is necessary to equip the DMA with an adequate number of pressure sensors. The aim of this paper is to evaluate the impact of water supply DMA formation on the sensitivity of the monitoring system in accordance with the number and location of the pressure sensors and the geometric structure of the water pipes in the DMA in order to successfully detect water leakage. The research was conducted on a model grid network with a constant node number but a differential pipe structure. Subsequently, results were verified in the conditions of a real water supply network. The obtained tests showed no clear relationship between the effectiveness of leak detection and the network complexity but confirmed a significant improvement in leak detection after equipping the monitoring system with an additional pressure gauge.

1. Introduction

Limiting water leakages from water supply pipelines is one of the main tasks water companies face during their operation. The size of these leakages determines, among other things, the economic efficiency of the water supply companies [1,2]. The role of leakages is growing along with increases in energy prices and the operating costs of enterprises. However, actions aimed at reducing the size of water leakages have an economic barrier, i.e., their cost should not be higher than the cost of lost water [3]. This is one of the reasons for limiting the number and quality of network monitoring sensors. Recently, the problem of limiting leakages has also begun to be considered in a different context—the availability of water. The deepening water stress caused by climate change does not concern only areas with a traditional shortage of water [4,5] but also countries located in the temperate climate zone. Sometimes even a small reduction in water losses is necessary for meeting the entire water demand of the residents or maintaining the required environmental conditions in the river that is its source [6]. In such cases, the economic issues of limiting water losses recede into the background. This is reflected in the new European Union Water Directive [7] which recommends limiting water losses in operating water supply systems. The detection and limiting of leakages are also the basis for the implementation of so-called smart cities [8].
There are numerous methods of water loss reduction. Their foundation, however, is the quick detection and localisation of a leak [9,10]. A number of methods can be distinguished here, such as the use of hardware, biological and software-based systems [11,12]. In all cases, the key role in the detection process is played by the proper arrangement of the measuring sensors used and the accuracy of their indications [13,14]. A number of methods are used to locate these sensors [15,16,17,18] which can be divided into heuristics and explicit and implicit methods [19]. One of the methods facilitating both the location of measuring sensors as well as the implementation of IT systems supporting the leak detection process is the division of water distribution systems into District Metered Area (DMA) zones [20,21]. Many methods are used to locate these zones [22,23,24], including commercial software [25]. When determining DMA zones, parameters such as the number of water intake nodes, the number of connection nodes, the possibility of separating the zone from a larger distribution system with a minimum number of water supply sources for the zone, and the hydraulic conditions for the zone's operation under various water consumption scenarios are most often taken into account. For the assessment and location of leaks in these zones, water flow rate sensors are primarily used, including water meters for water consumers and manometers [26,27,28].
However, research carried out in real water supply networks shows that, despite the use of these sensors, there is a problem with the lack of leak detection [29,30,31,32]. A frequent solution to this problem is to increase the number of sensors, as well as the additional use of acoustic or vibration sensors [33,34,35]. However, while limiting ourselves to pressure and flow sensors, it is worth asking whether the lack of leak detection is dependent on the degree of complexity of the geometric structures of water supply networks and whether it results from the measurement uncertainty of these sensors.
According to the literature review, there is a research gap in analyses of the impact of the geometric structure complexity on the accuracy of leak detection combined with analyses of the measurement uncertainties of the devices used. In the present article, the authors attempt to find answers to the above issues. For this purpose, simulation studies were carried out for a model water supply network with a fixed and variable number of nodes and the structure of connections between them. In a further section of the article, the results of an experiment carried out in an actually existing water supply network are presented, aimed at demonstrating the effectiveness of the leakage monitoring system functioning there.

2. Materials and Methods

The research presented in this article was carried out in two stages. In the first stage, a model network was used. The simulation calculations performed on its basis were intended to answer the question of whether the degree of complexity of the geometric structure of the network affects the effectiveness of large leak detection. The second stage, aimed at testing the existing leak detection system, presents the results of an experiment carried out in a real water supply network.

2.1. Model Network

The model grid network selected for study consisted of 25 nodes with the same elevations, located symmetrically in five columns and five rows. The distances between the rows and columns were 100 m each. A water demand of 4 dm3/s was provided for each node which corresponds to the simultaneous withdrawal of water from the tap above the tub (0.2 dm3/s) by 20 customers. The total water consumption in the entire network was 100 dm3/s. A total of 12 variants (A–L, Figure 1) of connections between nodes with different geometric structures were used in the research. The total length of the pipes ranged from 2400 to 4000 m. In all variants, the same method of supplying the network through a water source located 40 m above the level of nodes was adopted. The internal diameters of the pipes varied, depending on the variant, from 80 (assumed minimum diameter) to 300 mm. Diameters were selected to maintain a water flow velocity as close as possible to 1.0 m/s. The roughness of the pipes was assumed as 0.01 mm.
Steady state simulations of the hydraulic conditions of the model grid networks were carried out using the Bentley WaterGEMS software. A reservoir, the water source for the model network, was located 40 m higher than the network nodes. Initially, simulations of operation in normal hydraulic conditions for each of the network variants were carried out. The obtained results of the flow rate in the mains and the pressure in the nodes constituted the comparative material for further analyses.
A significant water leak, corresponding to the opening of a fire hydrant (10 dm3/s, 36 m3/h), was assumed in simulation studies as an additional water demand in selected nodes. Each time, only one fire hydrant was considered opened at the time. In all variants, the same locations of the opening hydrants H1, H2, and H3 were assumed (Figure 2).
In the first phase of the research, it was assumed that the pressure gauges used are characterised by an uncertainty of readings of ±2.0%. Assuming the maximum pressure in the analysed network (40 m H2O), this uncertainty can be defined as ±0.8 m H2O. The problem of uncertainty of the flowmeter sensors was omitted due to the fact that the simulated leakage increases the flow by 10%, which is much higher than the accuracy of most devices for measuring flow rate. At this stage, the number of nodes was sought where the difference in the pressure head in normal conditions and after opening the hydrant was equal to or greater than this uncertainty. At this stage of the research, the problem of the number and location of measuring sensors was not considered, assuming that all nodes are subject to the assessment of pressure differences. The calculated number of nodes was compared with the total length of all pipes and the number of loops in all considered network variants. Due to the fact that in several variants the length of the network pipelines and the number of loops were repeated, the calculated number of nodes was also compared with the parameter describing the degree of complexity ("density") of the geometric structure of the considered network variants. The fractal dimension (Equation (1)) was selected for this purpose, calculated by the box-counting method [36], often used in image analysis. The calculations of the fractal dimension were carried out with the Fractalyse 3.0 software [37].
D = lim δ 0 l o g N δ ( F ) l o g δ
where D—fractal dimension, F—analysed fractal set, δ—image resolution, and Nδ(F)—minimum number of sets of maximum δ diameter which can cover the F set.
In the second phase of the research, the problem of the uncertainty of pressure sensor indications was omitted. In the simulation studies, a network monitoring system was used, including the measurement of the pressure in four, identical in all variants, water demand nodes (p0, p1, p2, and p3), and the flow rate of water supplying the first node (q0). The location of the measurement points is shown in Figure 2. Simulation studies of the effectiveness of leak detection by the system of sensors designed in this way were carried out in three phases. In the first phase, during the simulation tests, each of the selected hydrants was assumed to open again and an attempt was made to find its location using the p0 and q0 sensors. Then, the monitoring system was gradually expanded to include the p1 sensor, then the p2 and p3. In total, 144 simulations were carried out at this stage. In order to locate the leakage, the Darwin Calibrator module of the Bentley WaterGEMS software was used. The Darwin Calibrator uses a genetic algorithm (GA). The general idea of the Darwin Calibrator is to compare the measured and calculated values of the same parameter and search for the most appropriate solution based on the principles of natural evolution and genetic reproduction [38]. The leakage is figuratively presented as an emitter coefficient, which is most often used for fire flows in hydrants [39]. The emitter flow varies as a function of the pressure available at the associated node, in accordance with the formula (Equation (2)) [40,41].
q = Cpn,
where q—flow rate (dm3/s), C—emitter coefficient (dm3/(s mn)), p—pressure head (m H2O), and n—pressure exponent (0.5).
Evaluation of the effectiveness of leak detection was considered as the distance between the most probable location indicated by the Darwin Calibrator module and the actual open fire hydrant location. The distance, referred to in the article as the "length of the error", was measured along the route of the water supply pipes, i.e., the shortest path connecting the open hydrant with the location defined as the leakage node. The obtained results were compared with the total length of the pipes, the number of loops, and the fractal dimension in each network variant. The results of the tests carried out in the first and second stages provided an answer to the question of whether the commonly used leak detection system based only on network sensors and a flow meter at the point of supplying the zone with water can be effective.

2.2. Case Study Network

In the second stage of the research, a selected zone of the real water supply network was used. The analysed water distribution system (WDS) has a very complex geometric structure and consists of 24 pressure zones, with several pumping stations and tanks (Figure 3). The WDS delivers water to approx. 30,000 inhabitants. Among the typical household customers in the analysed WDS, there are several industrial customers, demanding water in significant amounts at random times of the day. The prevalent pipe material is PVC and PE, but the oldest parts of the network consist of asbestos cement, ductile iron, and steel pipes, mainly in the old-town district. The total pipe length equals approx. 260 km and the total daily water demand is approx. 3850 m3/day (128.3 dm3/(d∙person)). However, the demand for water can periodically increase to 7120 m3/day (237.3 dm3/(d∙person)). The analysed WDS is characterised by great water losses, varying from 7% up to 43% of the total input volume between zones. In the majority of the 24 pressure zones, the population density can be described as low or medium, which usually results in a long leakage detection time—the water outflow to the surface is noticed in a couple to several days.
The research studies were conducted for the zone marked in blue in Figure 3. In this area, three DMA zones were separated (Figure 4). The DMA zones were equipped with flow meters (one at the entrance to each zone) and additional network manometers. The sensor readings were transferred to the existing GIS database through the online SCADA system. A calibrated numerical model of the network, developed in the Bentley WaterGEMS software, was integrated with the GIS database, equipped with the Darwin Calibrator module that enables searching for water leak locations.
The DMA 02 zone, which covers approx. 6500 m of water pipes and 443 junctions, was selected for experimental research. There are two monitoring points in this zone: KP1 (flow rate and pressure measurement) and KP2 (pressure measurement). The location of the measurement points is shown in Figure 5. The considered zone is characterised by a significant capacity reserve, resulting in a stable spatial distribution of the pressure head. The difference between its minimum and maximum values during normal operation ranges from 7.49 to 7.87 m H2O.
In the first phase of the case study, the size of the pressure head drop in the network, caused by the successive opening of the five fire hydrants indicated in Figure 5, was checked using a calibrated numerical model, analogically to Section 2.1. The hydrants were opened at the hour of maximum water demand in the analysed DMA 02 zone. The abnormal situation alarm threshold was assumed to be a pressure drop of 5.0 m H2O. This value resulted from both the measurement uncertainty of the installed manometers (±2.0%) and the existence of continuous, up to 4 m H2O, pressure fluctuations in the analysed zone. The observed amount of pressure head drop due to the opening of the hydrant is presented in the form of a contour plot graph.
The subsequent phase of the experiment consisted of the physical opening of the fire hydrants indicated in Figure 5. Then, the pressure drops recorded by the SCADA system at the measurement points existing in the zone were used as input data to the numerical model of the network. As in the case of model grid networks, these data were the basis for carrying out simulation calculations aimed at searching for the location of water leakage. The calculations were carried out in a manner analogous to that presented in Section 2.1. The most probable places of leakage were compared with the location of the open hydrants. This comparison was the basis for evaluating the effectiveness of the existing monitoring system for leak detection.
The further phase of the experiment was carried out in a manner analogous to the first one, but after installing additional five portable hydrant manometers in the analysed DMA zone. In the third stage, the measuring system was equipped with two portable flowmeters. The location of additional pressure gauges and flow meters is shown in Figure 6.

3. Results and Discussion

3.1. Model Network

3.1.1. First Phase Analysis

Figure 7 shows an exemplary contour plot of networks with the smallest (A) and the highest (L) degree of complexity and the size of the pressure head changes caused by the opening of the hydrant. The range of correct pressure readings by the installed manometers was assumed as 0.8 m H2O. The open hydrant was marked by a red dot in Figure 7. In the case of the A network, the assumed range of reduced pressure covers two nodes, and in the case of the L network, three nodes.
Table 1 summarises the number of nodes located in the area of the pressure head lowered by at least 0.8 m H2O after opening the H1, H2, and H3 hydrants. Figure 8 presents graphs showing the average number of these nodes depending on the total length of the pipes, the number of loops, and the fractal dimension of the analysed network.
In analysing the data presented in Table 1 and Figure 8, it should be stated that the range of reduced pressure area caused by a large leak (opening of a fire hydrant) is relatively small, limited to a few nodes. There is no clear dependence of the number of these nodes on the complexity of the network. In 11 cases (opening of the H3 hydrant), this number is 0, which suggests that in the conditions of using pressure gauges with a measurement error of ±2%, an indication of a location of a leak, even as large as in the paper, will be subject to high uncertainty or even impossible. The solution to this problem may be a significant increase in the accuracy and number of pressure gauges, and the parallel use of other types of sensors, e.g., measuring the water flow rate or acoustic sensors.

3.1.2. Second Phase Analysis

In the second stage, it was assumed that there were no measurement uncertainties in the sensors used. The simulation tests carried out showed that in each case the tested monitoring system detected a leak. However, it did not always correctly indicate the leak location. Only in 70 out of 144 cases did the location of the leak coincide with the location of the open hydrant. In other cases, the so-called length of the error (the distance between the indication of the leakage location and the open hydrant, calculated along the network pipelines) ranged from 100 to 1100 m. Figure 9 shows the exemplary results of indicating the leakage location represented by opening the H1 hydrant in network A, in the case of using only the sensors: (a) p0 and q0; (b) p0, p1, and q0; (c) p0, p1, p2, and q0; and (d) p0, p1, p2, p3, and q0. The location of the open hydrant is marked with a red dot in Figure 9. The estimation of the leak location is marked with a purple circle. The so-called length of the error is marked with a blue line. In the case of (d), the location of the leak coincided with the location of the open hydrant. Table 2 lists all the error lengths calculated during the simulations in networks AL.
Figure 10 shows the average error length for each of the analysed network variants, depending on the number of monitoring sensors used. There is a clear tendency to decrease the average error length with the increase in the number of network sensors used. Interestingly, adding the p3 sensor to the system consisting of q0, p0, p1, and p2 sensors did not cause a significant change in the calculated average error length. The calculated average error length was compared with the total length of the pipes (Figure 11), the number of loops (Figure 12), and the fractal dimension (Figure 13) of the analysed networks. In all cases presented in Figure 11, Figure 12 and Figure 13, there seems to be no clear relationship between the calculated average error length and the total length of the pipes, the number of loops, or the fractal dimension, which may suggest the lack of such relationships. However, it is worth noticing that there is a significant reduction in the average error length after adding the p1 sensor to the analysed networks, supplementing the measurement of the network entrance. Adding more pressure sensors did not cause significant changes in the size of this error, regardless of the complexity of the network.

3.2. Case Study

The research began with the preparation of a contour map that shows the areas of pressure drop in the analysed DMA zone after each of the selected hydrants has been opened (Figure 14). The marked isolines are described by the values of the pressure drop in m H2O. Only the opening of hydrants 69669 (located mostly to the west) and 69984 (centre) caused the pressure to drop above the assumed alarm threshold of 5.0 m H2O. As at the first stage of the research on model networks, this means that it is necessary to use more pressure gauges to correctly locate leaks in the entire zone.
As indicated in the description of the case study network (Section 2.2), the analysed DMA zone covers a relatively large area and serves a large number of customers. Due to the significant reserve of water transmission capacity that characterises this zone, the increase in water demand, corresponding to the opening of the fire hydrant, did not result in a significant increase in the flow velocity in the network pipelines. This was the reason for the slight differences in the pressure head in the network caused by these openings. The detailed measurement indications of the monitoring system in the analysed DMA zone are presented in Table 3. The monitoring system indications are divided into three groups: (1) existing monitoring points (KP1 and KP2), (2) additional portable hydrant loggers J1-J5, and (3) additional portable flowmeters (Q1 and Q2). The existing monitoring system triggered an alarm only in the case of the opening of the H01 (ID: 69669) and H03 (ID: 69984) hydrants due to the recorded pressure drop above 5 m H2O in the KP2 monitoring point (marked grey in Table 3). The KP1 pressure monitoring sensor, located and the entrance of the analysed DMA zone, proved not to be sensitive to opening fire hydrants in the zone. Therefore, the alarm at the KP1 monitoring station was triggered only by the increase in the metered flow (marked yellow in Table 3). Adding additional pressure loggers in five different locations in the DMA zone proved to be of little improvement in terms of triggering alarms; in only 3 out of 25 cases, the pressure drop recorded by the portable loggers was above 5 m H2O. On the contrary, the additional flowmeters turned out to be very effective in terms of triggering alarms in the analysed DMA zone. In 8 out of 10 cases, the increase in flow caused by the hydrant opening was noticed (an increase above 10% of flow compared to normal conditions) in portable flowmeters (marked green in Table 3).
In the second phase of the case study experiment, the Darwin Calibrator leak detection module was applied, using the indications of the pressure and flow sensors installed in the analysed zone. The obtained location indications turned out to be unsatisfactory. The so-called length of the error ranged from 178 to almost 1300 m. Increasing the number of pressure gauges by five additional portable loggers resulted in a decrease in this length in three cases and an increase in two (hydrants 69984 and 351864). However, the average value of error length decreased by almost 60%. Interestingly, adding two additional flowmeters to the monitoring system in the third stage of the experiment did not improve and even slightly worsened the effectiveness of leak location indications. The full list of calculated error lengths is presented in Table 4.
As the referenced example, the case of the open hydrant H05 (ID: 69717) with three groups of monitoring points is presented in Figure 15a–c. At first, while using only the existing KP1 and KP2 monitoring points, the length of error equalled 762 m. Adding five additional pressure loggers enabled the Darwin Calibrator module to limit this distance (error length) to 234 m. Data from two additional flowmeters resulted in very precise leakage detection: the length of the error was 13 m. Similarly, in cases H01 and H02 the additional pressure loggers resulted in reducing the length of the error. Paradoxically, in cases H03 and H05 additional monitoring sensors resulted in increasing the length of the error.
Interestingly, although the increase in the number of network manometers improved the effectiveness of leak detection, the subsequent introduction of additional network flow meters did not translate into a further improvement in the effectiveness of the diagnostic system. The solution to this problem may be the division of the analysed zone into smaller subzones in terms of territory and number of recipients, as recommended by Morrison et al. [20]. It is also worth considering the possibility of equipping such subzones with additional acoustic sensors, which is recommended by Wong and McCann [32].

4. Conclusions

The problem of detecting and locating leaks in water supply networks is a very complex and still valid research task. In order to solve it, it is necessary to combine monitoring sensors and specialised software into one integrated diagnostic system. The model tests carried out as part of the paper, using such a system based on the indications of a pressure gauge and a flow meter located at the entrance to the analysed network structures and commercial software for searching for leak locations, showed no clear relationship between the effectiveness of leak detection and the network complexity. This result contributes to the existing research gap in the field of monitoring systems sensitivity and its dependence on the network complexity and accuracy of measurement devices. As in the case of other researchers, these studies allowed us to find a significant improvement in the correctness of indications for this location if the monitoring system was supplemented with an additional network pressure gauge. The further addition of successive network manometers did not result in the expected significant improvement of location indications.
A major difficulty in the process of locating leaks is the uncertainty of the manometers used. This problem is exacerbated by the constant oscillations of pressure present during normal operation of the real water supply network. The model tests presented in the article showed that, when taking it into account, the detection area of the pressure drop caused by the opening of a hydrant may be very small, which suggests the need to use a large number of pressure sensors or acoustic or vibration sensors to locate leaks. The experiment carried out in real network conditions confirmed the existence of the still unsatisfactory level of leak detection using a flow meter and pressure sensor at the supplying border of the zone. In addition, the increase in the number of these sensors in our study improved the quality of leak location indications. Interestingly, the application of two additional network flowmeters did not improve this quality.
A promising direction to increase the accuracy of leak indications is to limit the size of the DMAs and the number of supplied consumers in the implemented DMA zones. Another direction is the integration of various types of sensors, including manometers, flow meters, and acoustic and vibration sensors into an integrated leak detection and search system.

Author Contributions

Conceptualisation, D.K. and P.S.; methodology, D.K.; software, P.S.; validation, D.K. and P.S.; formal analysis, D.K.; investigation, P.S.; resources, P.S.; data curation, P.S.; writing—original draft preparation, D.K.; writing—review and editing, D.K. and P.S.; visualisation, D.K. and P.S. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Geometric structures of the model grid network (AL). Total pipe lengths (m): (A): 2400; (B): 2400; (C): 2400; (D): 2600; (E): 2600; (F): 2600; (G): 2700; (H): 2800; (I): 2900; (J): 3200; (K): 3200; and (L): 4000 m.
Figure 1. Geometric structures of the model grid network (AL). Total pipe lengths (m): (A): 2400; (B): 2400; (C): 2400; (D): 2600; (E): 2600; (F): 2600; (G): 2700; (H): 2800; (I): 2900; (J): 3200; (K): 3200; and (L): 4000 m.
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Figure 2. Location of open fire hydrants (H1, H2, and H3) and monitoring points: q0; p0; p1; p2; and p3.
Figure 2. Location of open fire hydrants (H1, H2, and H3) and monitoring points: q0; p0; p1; p2; and p3.
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Figure 3. Geometric structure of the water supply network along with the location of the water intake, pumping station, and water tanks. The blue line designates the analysed zone.
Figure 3. Geometric structure of the water supply network along with the location of the water intake, pumping station, and water tanks. The blue line designates the analysed zone.
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Figure 4. The division of the selected zone of the network into DMAs.
Figure 4. The division of the selected zone of the network into DMAs.
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Figure 5. Location of monitoring points and open fire hydrants in the analysed DMA 02 zone.
Figure 5. Location of monitoring points and open fire hydrants in the analysed DMA 02 zone.
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Figure 6. Location of the additional pressure manometers and flow meters.
Figure 6. Location of the additional pressure manometers and flow meters.
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Figure 7. Contour plot of the pressure head drop caused by the opening of the H1 hydrant (red dot) in A model grid network (left) and L network (right). The area of the reduced pressure head (0.8 m H2O) is marked in grey.
Figure 7. Contour plot of the pressure head drop caused by the opening of the H1 hydrant (red dot) in A model grid network (left) and L network (right). The area of the reduced pressure head (0.8 m H2O) is marked in grey.
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Figure 8. The average number of nodes detecting a pressure drop equal to or above 0.8 m H2O depending on total pipe length, number of loops, and fractal dimension of the analysed networks.
Figure 8. The average number of nodes detecting a pressure drop equal to or above 0.8 m H2O depending on total pipe length, number of loops, and fractal dimension of the analysed networks.
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Figure 9. Leakage locations (purple circles) in network A in reference to the open fire hydrant H1 (red dots) taking into account different quantities of monitoring points: (a) monitoring flow meter q0 and pressure sensor p0 at the border of the network; (b) including one additional network pressure logger (p1); (c) including two network pressure loggers (p1 and p2); and (d): including three network pressure loggers (p1, p2, and p3).
Figure 9. Leakage locations (purple circles) in network A in reference to the open fire hydrant H1 (red dots) taking into account different quantities of monitoring points: (a) monitoring flow meter q0 and pressure sensor p0 at the border of the network; (b) including one additional network pressure logger (p1); (c) including two network pressure loggers (p1 and p2); and (d): including three network pressure loggers (p1, p2, and p3).
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Figure 10. Length of the error depending on the network variant and the number of monitoring sensors applied.
Figure 10. Length of the error depending on the network variant and the number of monitoring sensors applied.
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Figure 11. The average length of the error in relation to the total pipe length and the number of monitoring sensors applied.
Figure 11. The average length of the error in relation to the total pipe length and the number of monitoring sensors applied.
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Figure 12. The average length of the error relative to the number of loops and the number of monitoring sensors applied.
Figure 12. The average length of the error relative to the number of loops and the number of monitoring sensors applied.
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Figure 13. The average length of the error in relation to the fractal dimension and the number of monitoring sensors applied.
Figure 13. The average length of the error in relation to the fractal dimension and the number of monitoring sensors applied.
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Figure 14. Contour map of pressure drop areas caused by open hydrants in the DMA 02 zone.
Figure 14. Contour map of pressure drop areas caused by open hydrants in the DMA 02 zone.
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Figure 15. Length of the error for open hydrant H05: (a) length of the error equal to 762 m, (b): 234 m, and (c): 13 m.
Figure 15. Length of the error for open hydrant H05: (a) length of the error equal to 762 m, (b): 234 m, and (c): 13 m.
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Table 1. Model grid network characteristics (total length, number of loops, and fractal dimension) and numbers of nodes detecting a pressure drop equal to or above 0.8 m H2O.
Table 1. Model grid network characteristics (total length, number of loops, and fractal dimension) and numbers of nodes detecting a pressure drop equal to or above 0.8 m H2O.
NetworkABCDEFGHIJKL
Total length (m)240024002400260026002600270028002900320032004000
Number of loops (-)0001114448816
Fractal dimension (-)1.0101.0131.0391.0551.0561.0441.0701.0751.0691.0921.0921.109
Open hydrantThe number of nodes detecting a pressure drop equal to or above 0.8 m H2O
H1
H2
H3
2
4
0
1
5
0
8
7
0
10
10
6
6
3
0
7
7
0
7
7
0
3
4
0
10
10
0
3
3
0
6
7
0
3
3
0
Average (nodes number)225935527242
Table 2. Calculated length of the error (m) and total pipe length, number of loops, and fractal dimensions for all AL networks.
Table 2. Calculated length of the error (m) and total pipe length, number of loops, and fractal dimensions for all AL networks.
NetworkABCDEFGHIJKL
Open hydrantq0, p0
H1
H2
H3
900
900
900
1100
100
900
900
300
500
500
300
500
100
300
800
200
400
200
200
200
400
600
400
400
0
0
800
300
500
300
200
400
500
500
500
300
average900700567433400267267467267367367433
Open hydrantq0, p0, p1
H1
H2
H3
600
0
0
100
100
100
500
0
100
0
0
100
0
0
300
200
100
200
0
0
400
0
0
300
0
0
300
0
0
300
0
0
100
0
0
300
average2001002003310016713310010010033100
Open hydrantq0, p0, p1, p2
H1
H2
H3
100
200
0
100
0
100
0
0
0
0
0
0
100
300
0
0
200
100
0
200
0
0
0
0
0
0
100
0
0
0
0
0
100
0
0
300
average100670013310067033033100
Open hydrantq0, p0, p1, p1, p3
H1
H2
H3
0
0
0
200
100
100
0
100
0
0
0
0
0
200
0
0
200
100
0
200
0
0
0
0
0
0
100
0
0
0
0
0
100
0
0
300
average01333306710067033033100
Total length (m)240024002400260026002600270028002900320032004000
Loops number (-)0001114448816
Fractal dimension1.0101.0131.0391.0551.0561.0441.071.0751.0691.0921.0921.109
Table 3. Measurement indications of the monitoring system (existing and additional) in the analysed DMA zone.
Table 3. Measurement indications of the monitoring system (existing and additional) in the analysed DMA zone.
Open Hydrant
Hydrant ID:
H01
69669
H02
69714
H03
69984
H04
351864
H05
69717
Normal Conditions
Monitoring PointsUnitMeasurement Indication
KP1
KP1
KP2
(m3/h)
(m H2O)
(m H2O)
58,45
40,28
58,45
58,45
40,28
46,70
58,45
40,28
42,58
58,45
40,28
48,03
58,45
40,28
48,03
22,45
41,69
50,40
J1
J2
J3
J4
J5
(m H2O)
(m H2O)
(m H2O)
(m H2O)
(m H2O)
11,11
43,79
43,82
43,92
40,68
43,77
43,36
43,71
44,17
40,68
39,65
44,18
43,92
43,41
40,68
45,10
44,74
44,09
44,24
33,83
44,47
44,03
43,68
44,19
40,68
47,47
47,11
46,45
46,61
43,05
Q1
Q2
(m3/h)
(m3/h)
10,90
33,60
4,03
40,47
17,49
25,99
1,29
7,21
2,88
41,62
1,29
7,20
Table 4. Calculated length of the error of leakage indications in the analysed DMA zone.
Table 4. Calculated length of the error of leakage indications in the analysed DMA zone.
Open Hydrant
Hydrant ID:
H01
69669
H02
69714
H03
69984
H04
351864
H05
69717
Average
Monitoring PointsLength Error (m)
KP1, KP21781299381155762555
KP1, KP2
J1–J5
321635192234219
KP1, KP2
J1–J5
Q1, Q2
3230163520713238
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Kowalski, D.; Suchorab, P. The Impact Assessment of Water Supply DMA Formation on the Monitoring System Sensitivity. Appl. Sci. 2023, 13, 1554. https://doi.org/10.3390/app13031554

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Kowalski D, Suchorab P. The Impact Assessment of Water Supply DMA Formation on the Monitoring System Sensitivity. Applied Sciences. 2023; 13(3):1554. https://doi.org/10.3390/app13031554

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Kowalski, Dariusz, and Paweł Suchorab. 2023. "The Impact Assessment of Water Supply DMA Formation on the Monitoring System Sensitivity" Applied Sciences 13, no. 3: 1554. https://doi.org/10.3390/app13031554

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