Employing Tank Constraints to Present Total Cost and Water Age Trade-Offs in Optimal Operation of Water Distribution Systems
Abstract
1. Introduction
2. Methodology
2.1. Water Distribution System Optimal Operation Problem Formulation
2.2. Modification of Tank Operation Constraint
2.3. Conceptual Definition of Water Age
3. Results
3.1. Case Study 1
3.2. Case Study 2
3.3. Case Study 3
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Component | Attribute | Value |
---|---|---|
Source | Elevation [m] | 0 |
Pipes | Diameter [mm] | 600 |
Length [km] | 3 | |
Roughness [-] | 110 | |
Nodes | Base demand [CMH] | 475 |
Elevation [m] | 0 | |
Service pressure [m] | 30 | |
Pump | Efficiency [%] | 85 |
Curve coefficients | [1 × 10−5, 200] | |
Rotation speed range [rpm] | [0, 50] | |
Tank | Pipe length [km] | 0.5 |
Elevation [m] | 35 | |
Cross-section area [m2] | 1000 | |
Level range [m] | [0, 7] | |
Initial level [m] | 7 |
Component | Attribute | Value |
---|---|---|
Source | Elevation [m] | 0 |
Pipes | Diameter [mm] | 600 |
Roughness [-] | 120 | |
Pipes 3, 4, 5, 6, 7, 9 | Length [km] | 2 |
Pipe 8 | 4 | |
Nodes | Elevation [m] | 0 |
Service pressure [m] | 30 | |
Nodes 4, 5 | Base demand [CMH] | 150 |
Node 6 | 300 | |
Node 7 | 400 | |
Pumps | Efficiency [%] | 85 |
Curve coefficients | [1 × 10−5, 200] | |
Rotation speed range [rpm] | [0, 50] | |
Tanks | Pipe length [km] | 0.4 |
Pipe diameter [mm] | 750 | |
Elevation [m] | 30 | |
Cross-section area [m2] | 490.87 | |
Level range [m] | [0, 10] | |
Initial level [m] | 10 |
Link ID | Diameter [mm] | Length [m] | Link ID | Diameter [mm] | Length [m] |
---|---|---|---|---|---|
1 | 132.7600 | 204 | 21 | 83.9600 | 368 |
2 | 374.6800 | 80 | 22 | 49.8200 | 511 |
3 | 119.7400 | 80 | 23 | 78.5000 | 450 |
4 | 312.7200 | 80 | 24 | 99.2700 | 368 |
5 | 289.0900 | 130 | 25 | 82.2900 | 307 |
6 | 336.3300 | 80 | 26 | 147.4900 | 163 |
7 | 135.8100 | 80 | 27 | 197.3200 | 204 |
8 | 201.2600 | 80 | 28 | 83.3000 | 511 |
9 | 132.5300 | 80 | 29 | 113.8000 | 450 |
10 | 144.6600 | 80 | 30 | 80.8200 | 307 |
11 | 175.7200 | 102 | 31 | 340.9700 | 130 |
12 | 112.1700 | 163 | 32 | 77.3900 | 80 |
13 | 210.7400 | 257 | 33 | 112.3700 | 80 |
14 | 75.4100 | 102 | 34 | 37.3400 | 204 |
15 | 181.4200 | 92 | 35 | 108.8500 | 257 |
16 | 146.9600 | 736 | 36 | 182.8200 | 80 |
17 | 162.6900 | 450 | 37 | 136.0200 | 80 |
18 | 99.6400 | 368 | 38 | 56.7000 | 80 |
19 | 52.9800 | 204 | 39 | 124.0800 | 80 |
20 | 162.9700 | 204 | 40 | 234.6000 | 80 |
41 | 203.8300 | 204 | 51 | 215.0500 | 163 |
42 | 248.0500 | 80 | 52 | 144.4400 | 80 |
43 | 65.1900 | 163 | 53 | 34.7400 | 257 |
44 | 210.0900 | 163 | 54 | 59.9300 | 368 |
45 | 147.5700 | 204 | 55 | 165.6700 | 163 |
46 | 103.8000 | 80 | 56 | 119.9700 | 102 |
47 | 210.9500 | 163 | 57 | 83.1700 | 163 |
48 | 75.0800 | 257 | 59 | 100.0000 | 80 |
49 | 180.2900 | 80 | 60 | 100.0000 | 80 |
50 | 149.0500 | 80 |
Node ID | Base Demand [CMH] | Node ID | Base Demand [CMH] |
---|---|---|---|
1 | 7.055916 | 19 | 27.071680 |
2 | 14.975824 | 20 | 13.391844 |
3 | 14.687828 | 21 | 13.823836 |
4 | 11.663864 | 22 | 13.967836 |
5 | 9.071892 | 23 | 12.383856 |
6 | 11.375868 | 24 | 9.647888 |
7 | 3.743956 | 25 | 11.087868 |
8 | 8.351900 | 26 | 24.335712 |
9 | 7.775908 | 27 | 20.447760 |
10 | 15.983812 | 28 | 4.319948 |
11 | 25.199703 | 29 | 8.927896 |
12 | 13.103844 | 30 | 7.775908 |
13 | 16.703804 | 31 | 12.959848 |
14 | 7.775908 | 32 | 14.831824 |
15 | 15.839812 | 33 | 11.087868 |
16 | 17.423796 | 34 | 10.655876 |
17 | 18.287785 | 35 | 16.703804 |
18 | 29.087656 | 36 | 6.767920 |
Component | Attribute | Value |
---|---|---|
Sources | Elevation [m] | 0 |
Nodes | Elevation [m] | 0 |
Service pressure [m] | 30 | |
Pumps | Efficiency [%] | 85 |
Curve coefficients | [1 × 10−5, 200] | |
Rotation speed range [rpm] | [0, 50] | |
Elevation [m] | 40 | |
Cross-section area [m2] | 19.635 | |
Level range [m] | [0, 10] | |
Initial level [m] | 10 |
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Shmaya, T.; Ostfeld, A. Employing Tank Constraints to Present Total Cost and Water Age Trade-Offs in Optimal Operation of Water Distribution Systems. Water 2024, 16, 1637. https://doi.org/10.3390/w16121637
Shmaya T, Ostfeld A. Employing Tank Constraints to Present Total Cost and Water Age Trade-Offs in Optimal Operation of Water Distribution Systems. Water. 2024; 16(12):1637. https://doi.org/10.3390/w16121637
Chicago/Turabian StyleShmaya, Tomer, and Avi Ostfeld. 2024. "Employing Tank Constraints to Present Total Cost and Water Age Trade-Offs in Optimal Operation of Water Distribution Systems" Water 16, no. 12: 1637. https://doi.org/10.3390/w16121637
APA StyleShmaya, T., & Ostfeld, A. (2024). Employing Tank Constraints to Present Total Cost and Water Age Trade-Offs in Optimal Operation of Water Distribution Systems. Water, 16(12), 1637. https://doi.org/10.3390/w16121637