Leakage Management and Pipe System Efficiency. Its Influence in the Improvement of the Efficiency Indexes
Abstract
:1. Introduction
2. Leakages Evaluation and KPIs
2.1. Torricelli Teorem
2.2. Minimum Night Flow (MNF) Analysis
2.3. FAVAD Concept
2.4. FAVAD and the N1 Power Law
2.5. Background Leakage and Emitter Coefficient (BABE)
2.6. Summary of Leak Calculation Methodologies
2.7. Leakages Modelling and Calibration
2.8. Leakages Key Performance Indicators (LKPIs)
 (1)
 Volumetric efficiency (${\eta}_{v}$); One of the most important ratios among the system’s efficiency indicators is volumetric performance. It is defined as the relationship between the registered volume ${V}_{Reg}$ and the total volume ${V}_{Tot}$ contributed in the same reference period [102]:$${\eta}_{v}=\frac{{V}_{Reg}}{{V}_{Tot}}$$
 (2)
 Performance Indicators for Water Supply Services; International water association (IWA) provides performance indicators of water supply systems to compare the management of water losses, these are (i) Water losses and real losses as a % of system input volume; (ii) Water losses per house connection and km of mains per day $(\mathrm{density}\mathrm{of}\mathrm{connections}20\mathrm{per}\mathrm{km}\mathrm{of}\mathrm{mains})$, and (iii) Infrastructure Leakage Index (ILI) [103].
 (3)
 Infrastructure Leakage Index (ILI); The ILI is a measure of how well a distribution network is managed (maintained, repaired, rehabilitated, etc.) for the control of real losses, at the current operating pressure. It is the ratio of the Current Annual volume of Real Losses (CARL) to Unavoidable Annual Real Losses (UARL) [104].$$ILI=\frac{CARL}{UARL}$$
 (4)
 Unavoidable Annual Real Losses (UARL); UARL is a useful concept as it can be used to predict the lowest technically annual real losses for any combination of mains length $\left(18\mathrm{L}/\mathrm{km}\mathrm{mains}/\mathrm{day}/\mathrm{meter}\mathrm{of}\mathrm{pressure}\right)$, number of connections $\left(0.8\mathrm{L}/\mathrm{service}\mathrm{connection}/\mathrm{day}/\mathrm{meter}\mathrm{of}\mathrm{pressure}\right)$, customer meter location and average operating pressure $\left(25\mathrm{L}/\mathrm{km}/\mathrm{day}/\mathrm{m}\mathrm{of}\mathrm{pressure}\right)$ assuming that the system is in good condition with high standards for the management of real losses [105].
 (5)
 Absolute annual consumed energy (IAAE); this index is sum of the total active consumed energy in the network subtracted by the sum of the total energy recovered in the network, the units are $\mathrm{kWh}/\mathrm{year}$ [106].
 (6)
 Absolute consumed energy per unit volume (IAEFW); Ratio between IAAE and the total volume of water introduced in the network, the units are $\mathrm{kWh}/{\mathrm{m}}^{3}$ [107].
3. Results
3.1. Case Studies
3.2. Influence of the Leakages in the KPI of the Water Systems
3.3. Pump Working as Turbine Using Leakages Models
3.4. Energy Index Calculation Case Study
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Material  α  β 

Cement  ${10}^{7}\le \alpha \le {10}^{5}$  $0.75\le \beta \le 1.10$ 
Steel  ${10}^{6}\le \alpha \le {10}^{4}$  $1\le \beta \le 1.3$ 
PVC  ${10}^{5}\le \alpha \le {10}^{4}$  $1.1\le \beta \le 1.5$ 
Reference  ID  Emitter Exponent  Material 

[29,43,44,45,46,47,48]  7, 9, 12, 13, 27, 33  0.5  PVC, HDPE, steel, asbestos cement and cast iron 
[49]    0.61  PVC, asbestos cement, galvanized steel 
[50]  8  0.5–1  PVC, Polyethylene (PE), iron, steel. 
[51]  1  0.91–1.13–1.41  PVC, metal, ambient. 
[52,53]  2, 10  1.1  PVC, iron. 
[54]  5  0.5–1.18   
[55]  3  1.1–1.18  Ductile iron, Steel, HighDensity Polyethylene (HDPE) 
[56,57,58]  11, 14, 15, 18  1.18  PVC, asbestos cement, galvanized steel 
[37,41,59,60,61]    0.5–2.5  PVC, iron, galvanised iron, asbestos cement. 
[16,31]  16  0.5–2.79  PVC, asbestos cement. 
[59,62]    0.5–2.95   
Failure Type  uPVC  Asbestos Cement  Mild Steel 

Round hole  0.52    0.52 
Longitudinal crack  1.38–1.85  0.79–1.04   
Circumferential crack  0.41–0.53     
Corrosion cluster      0.67–2.30 
Technique  Reference  Equation  Calib.  Advantages  Disadvantages 

Torricelli  [16,69,70,71,72,73]  ${Q}_{leak}={C}_{d}A\sqrt{2gh}$ 

 
MNF  [28,29,35,44,47,70,74,75,76]  ${L}_{DMA}={Q}_{MNF}{Q}_{LNC}$$Q=Q\left({t}_{MNF}\right)\xb7{\left[\frac{{P}_{AZP\left(t\right)}}{{P}_{AZP}\left({t}_{MNF}\right)}\right]}^{\alpha}$ 

 
FAVAD (Fixed and Variable Area Discharges)  [6,16,29,30,31,34,36,37,42,45,49,50,53,55,59,62,64,65,69,71,73,77,78,79,80,81,82,83,84]  The equation can be written in different ways: ${Q}_{i,l}\left(t\right)={K}_{i}{\left[{P}_{i}\left(t\right)\right]}^{\alpha}$ $L=c{P}^{\gamma}$ $q{l}_{i}={c}_{i}\xb7{P}_{i}^{\beta}$ ${Q}_{leak}=\beta {P}^{\alpha}$  ${K}_{i},C,\beta $ [59,66,78] 


The N1 Power Law  [29,31,34,37,43,63,65,66,67,76,84]  $Q={C}_{d}{h}_{AZP}^{{N}_{1}}$  ${N}_{1}$ [59,66] 


Background leakages model  [5,16,37,43,60,68,76,83,84,85,86,87,88,89,90,91]  $Q={\beta}_{k}{l}_{k}{({P}_{k})}^{{\alpha}_{k}}+{C}_{k}{({P}_{k})}^{0.5}$  β and α [4], β [85,89] 


Reference  Algorithm  Parameters  Objective Function  Error 

[4,39,52,54,61,62,81,83,89,92,96,97,98]  Genetic algorithm.  Operation conditions, flows, demands, pressures, total leakage.  Minimize network pressure and producing a new generation of solutions α and β.  0.5 to 23%, with an average value of 11%. 
[6,29,91]  Algorithm for detecting and estimating background leakage.  Operation conditions flow, pressure and fluid temperature.  Detect critical causes and their location for possible pressure control.   
[88]  Pseudogenetic algorithm.  Basic network  Operational costs, capital costs (pipe and pump replacement, tank expansion, and PRVs), and constraints.   
[76]  Global Gradient Algorithm.  Flow, pressure.  Reduce excess pressure.   
[1]  Neural networks.  Flow, pressure.  Detection of water leaks.  
[99]  Differential evolution with temporal analysis.  Water distribution network.  Estimation and location to leakage.  Root mean squared error: 0.05 
[85]  Differential evolution.  Flow, pressure, network data.  Estimation of leakage.   
[100]  Algorithm with convergence analysis.  Operation conditions, flows, demands, pressures.  Estimation to leakage   
[54]  Sequential Quadratic programming.  Water distribution network.  Leakage minimization   
ID  Case Study  Year  Ref  ID  Case Study  Year  Ref 

1  Skiathos, Greece  2020  [51]  24  Zarqa, Jordan  2020  [70] 
2  Leicester, UK  2012  [52]  25  Zarqa, Sana’a, Yemen  2020  [70] 
3  Benevento, Italy  2017  [55]  26  Mwanza, Tanzania  2020  [70] 
4  Pretoria, South Africa  2017  [29]  27  Mutarea, Zimbabwe  2006  [47] 
5  Polokwane, South Africa  2019  [54]  28  Skopje, Macedonia  2011  [108] 
6  Villarreal, Spain  2014  [109]  29  Pittsburgh, Pensilvania  2005  [110] 
7  Guayaquil, Ecuador  2015  [46]  30  Azogues, Ecuador  2019  [13] 
8  Antalya, Turkey  2017  [50]  31  Mankessim, Ghana  2014  [74] 
9  Konyaalti, Turkey  2012  [44]  32  Rzesów, Poland  2019  [1] 
10  Valencia, Spain  2015  [53]  33  Gorino Ferrarese, Italy  2021  [48] 
11  Palermo, Italy  1999  [56]  34  Salzburg, Austria  2011  [111] 
12  Nagpur, India  2016  [45]  35  Belgium  2014  [112] 
13  Nagpur, India  2016  [45]  36  Dryanovo, Bulgaria  2014  [112] 
14  London, UK  1989  [57]  37  Pula, Croatia  2014  [112] 
15  London, UK  1989  [57]  38  Lemesos, Cyprus  2013  [112] 
16  Nourhan Samir, Egypt  2017  [16]  39  Odense, Denmark  2013  [112] 
17  CTown  2015  [113]  40  England  2013  [112] 
18  Verona, Italy  2019  [58]  41  Bordeaux, France  2012  [112] 
19  Udine, Italy  2014  [114]  42  Munich, Germany  2014  [112] 
20  Patras, Greece  2016  [115]  43  Italy  2010  [112] 
21  Case I—San Gregorio, México  2014  [70]  44  Lisbon, Portugal  2014  [112] 
22  Case II—San Gregorio, México  2014  [70]  45  Scottish, UK  2014  [112] 
23  Drama, Greece  2016  [70] 
ID Case  Leakage (%)  Average Pressure (m)  Annual Volume Consumed (m^{3})  Energy Consumed per m^{3} Injected (kWh/m^{3})  Annual Consumption (kWh)  Annual Energy Lost by Leaks (kWh) 

1  57.56  54  33,016  0.15  115,093  66,252 
2  51.00  93  629,552  0.25  325,600  166,056 
3  12.03  50  807,216  0.14  1,250,363  150,387 
4  25.00  63  12,772,080  0.17  2,923,529  730,882 
5  27.16  70  27,899,748  0.19  7,306,457  1,984,580 
6  3.05  60  2,332,019  0.16  393,260  11,975 
7  23.00  55  320,397  0.15  62,363  14,343 
8  34.94  45  1,436,640  0.12  268,653  93,873 
9  34.38  47  513,336  0.13  101,834  35,010 
10  31.37  40  1,277,500  0.11  202,904  63,656 
11  45.60  41  3,190,939  0.11  659,074  300,538 
12  15.00  40  5,361,120  0.11  687,485  103,123 
13  15.00  40  7,505,568  0.11  962,479  144,372 
14  14.90  59  11,003,226  0.16  2,068,799  308,251 
15  17.20  34  4,047,330  0.09  452,881  77,895 
16  54.00  30  169,243  0.08  30,077  16,242 
17  26.05  40  5,370,085  0.11  791,534  206,194 
18  23.92  65  1,577,530  0.18  367,280  87,860 
19  28.31  31  8,842,478  0.09  1,052,511  297,966 
20  55.00  30  9,855,000  0.08  1,790,325  984,679 
21  28.45  40  251,605  0.11  38,328  10,903 
22  34.41  40  308,260  0.11  51,230  17,630 
23  19.80  30  9,358,600  0.08  953,945  188,879 
24  63.27  50  24,588,597  0.14  9,122,084  5,771,888 
25  38.24  50  13,766,774  0.14  3,037,055  1,161,332 
26  46.06  50  16,231,357  0.14  4,100,160  1,888,637 
27  57.00  77  18,049,250  0.21  8,750,213  4,987,622 
28  52.50  40  426,919  0.11  97,967  51,432 
29  40.00  114  862,194  0.31  446,401  178,560 
30  46.86  75  157,946  0.20  60,746  28,465 
31  12.00  56  430,151  0.15  74,592  8951 
32  30.00  40  2,571,680  0.11  400,623  120,187 
33  13.33  30  81,994  0.08  7734  1031 
34  5.57  46  12,210,000  0.13  1,620,776  90,252 
35  20.70  38  130,180,000  0.10  16,998,768  3,518,629 
36  74.96  42  1,780,000  0.11  813,740  610,019 
37  22.55  40  6,630,000  0.11  933,040  210,370 
38  23.22  40  10,120,000  0.11  1,436,620  333,540 
39  47.00  30  530,009  0.08  81,751  38,423 
40  17.54  44  330,660,000  0.12  48,079,900  8,433,766 
41  15.87  37  40,010,000  0.10  4,795,237  76,1229 
42  13.33  60  91,000,000  0.16  17,167,500  2,289,000 
43  24.71  44  33,830,000  0.12  5,387,107  1,330,890 
44  12.99  51  26,524,047  0.14  4,236,514  550,334 
45  58.69  45  147,752,776  0.12  43,854,719  25,736,535 
Method  Zarqa, Jordan  Sana’a, Yemen  Mwanza, Tanzania  Gavankola, Iran 

Water Balance  40  7.1  12.2   
MNF  16.2    12.2  34.9 
BABE  4.2  0.4  5.8  39.4 
Reference  ID  Flow (L/s)  H (m)  Annual Energy Recovered by Installing PATs (kWh/year)  Annual Volume Recovered by Use of PATs (m^{3})  Leakage Reduction by Use of PATs (%)  ${\mathit{\eta}}_{\mathit{v}}$ before Installing PATs  ${\mathit{\eta}}_{\mathit{v}}$ after Installing PATs 

21  
[102]  46  29  59  43,800    20     
[102]  47  74  54  87,600    32     
[102]  48  19  67  39,420    18     
[102]  49  33  55  43,800    21     
[102]  50  19  63  35,040    29     
[102]  51  14  71  26,280    65     
[102]  52  31  65  52,560    21     
[128]  53  29  21  28,470  22,813  63  0.73  0.90 
[128]  54  183  33  169,360  1,634,590  52  0.73  0.87 
[128]  55  72  36  130,305  98,185  63  0.73  0.90 
[27]  56  302  61  55,626  2,475,059  26  0.73  0.80 
[27]  57  212  39  71,876  667,554  10  0.73  0.76 
[27]  58  314  50  66,485  1,829,359  19  0.73  0.78 
[120]  59  187  70  54,985         
[122]  60  110  45  125,213  339,085  10  0.73  0.76 
[125]  61  110  45  113,880  328,865  9  0.73  0.75 
[126]  62  350  45  714,670  248,504  3  0.73  0.74 
Reference  ID  IAAE (kWh/Year)  IER (kWh/Year)  ERP (%)  IEFW (kWh/m^{3})  IRLGP (m^{3}/kW) 

[128]  53  52,335  28,470  54  0.06  8 
[128]  54  518,965  169,360  3  0.09   
[128]  55  222,745  130,305  58  0.10  4 
[27]  56  1,583,106  55,626  4  0.17  2 
[27]  57  710,516  71,876  10  0.11  16 
[27]  58  1,349,189  66,485  5  0.14  13 
[120]  59  1,124,897  54,985  5  0.19   
[122]  60  141,794  125,213  29  0.12  5 
[125]  61  141,794  113,880  27  0.12  5 
[126]  62  751,937  714,670  53  0.12  4 
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Ávila, C.A.M.; SánchezRomero, F.J.; LópezJiménez, P.A.; PérezSánchez, M. Leakage Management and Pipe System Efficiency. Its Influence in the Improvement of the Efficiency Indexes. Water 2021, 13, 1909. https://doi.org/10.3390/w13141909
Ávila CAM, SánchezRomero FJ, LópezJiménez PA, PérezSánchez M. Leakage Management and Pipe System Efficiency. Its Influence in the Improvement of the Efficiency Indexes. Water. 2021; 13(14):1909. https://doi.org/10.3390/w13141909
Chicago/Turabian StyleÁvila, Carlos Andrés Macías, FranciscoJavier SánchezRomero, P. Amparo LópezJiménez, and Modesto PérezSánchez. 2021. "Leakage Management and Pipe System Efficiency. Its Influence in the Improvement of the Efficiency Indexes" Water 13, no. 14: 1909. https://doi.org/10.3390/w13141909