A Framework for Improving Reliability of Water Distribution Systems Based on a Segment-Based Minimum Cut-Set Approach
Abstract
:1. Introduction
2. Methods
2.1. WDS Reliability Assessment Using A Segment-Based Minimum Cut-Set Approach
2.1.1. Unintended Isolation
2.1.2. Minimum Cut-Sets
- What: suspension of water supply and/or low pressure at any node
- Where: node(s), segment(s) and unintended isolation(s)
- When: a pipe failure
2.1.3. Success Mode Approach
2.2. Proposed Framework for Improving WDS Reliability
2.2.1. General Criteria for Installing Valves and Increasing Pipe Durability
- The WDS reliability increases by replacing existing pipes in the minimum cut-sets with more durable (i.e., larger diameters) ones represented by even with the same construction cost.
- Even though the WDS reliability linearly increases in proportion to the construction cost, the increasing rate is not significant. It means that structural modification or installing additional valves to the WDS is required to efficiently improve the WDS reliability.
- It is not necessary to install valves on a pipe which does not belong to minimum cut-sets. This is because the pipe does not cause any top events when broken.
- Even though some nodes can be free from a suspension of water by installing valve(s) around a broken pipe, in case the pipe breaking still causes any top event in the system, it is better to increase the durability of the pipe than installing valves.
- For a segment consisting of two or more pipes, valves should be installed for the weakest pipe. However, if the pipe with the additional valve is broken, no top event should occur in the system. If the top event still occurs due to the pipe breakage, the durability of the pipe should be increased rather than installing the valves.
2.2.2. Proposed Framework for Improving WDS Reliability
Proposed Three Types of Reinforcement
Proposed Rules for Improving WDS Reliability
3. Results and Discussion
3.1. Application Results of Rules 1 and 2
3.2. Caveats and Follow-Up Studies
4. Summary and Conclusions
Supplementary Materials
Author Contributions
Funding
Conflicts of Interest
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Case | Install Location | Pipes in Minimum Cut-Sets | WDS Reliability | Total Cost |
---|---|---|---|---|
1 | × | P1, P2, P4, P5, P6 | 0.849 | 0 |
2 | (1) | P1, P4, P5, P6 | 0.903 | 1 |
3 | (2), (6) | P1, P2, P4, P5 | 0.866 | 2 |
4 | (3) | P1, P2, P4, P5, P6 | 0.849 | 1 |
5 | (4), (5) | P1, P2, P4, P6 | 0.894 | 2 |
6 | (7) | P1, P2, P4, P5, P6 | 0.849 | 1 |
Rule | Case | WDS Reliability | Number of Pipes in MC | Number of Segments | Number of Valves Installed | Cost (USD, ×106) | Total EN |
---|---|---|---|---|---|---|---|
- | Initial | 0.137 | 90 | 80 | - | - | 286 |
1 | 1 | 0.178 | 86 | 86 | 6 | 0.868 | 254 |
2 | 0.231 | 80 | 94 | 8 | 0.371 | 227 | |
3 | 0.273 | 74 | 101 | 7 | 0.305 | 221 | |
4 | 0.314 | 68 | 108 | 7 | 0.279 | 203 | |
5 | 0.359 | 61 | 118 | 10 | 0.170 | 182 | |
6 | 0.401 | 55 | 127 | 9 | 0.197 | 109 | |
7 | 0.431 | 51 | 131 | 4 | 0.220 | 105 | |
8 | 0.463 | 45 | 140 | 9 | 0.152 | 68 | |
9 | 0.483 | 40 | 149 | 9 | 0.112 | 57 | |
2 | 1 | 0.157 | 80 | 98 | 18 | 0.020 | 162 |
2 | 0.181 | 73 | 111 | 13 | 0.130 | 119 | |
3 | 0.206 | 69 | 116 | 5 | 0.492 | 95 | |
4 | 0.236 | 65 | 121 | 5 | 0.492 | 83 | |
5 | 0.269 | 58 | 130 | 9 | 0.226 | 75 | |
6 | 0.311 | 54 | 135 | 5 | 0.394 | 69 | |
7 | 0.379 | 49 | 140 | 5 | 0.412 | 62 | |
8 | 0.446 | 42 | 147 | 7 | 0.156 | 58 | |
9 | 0.483 | 40 | 149 | 2 | 0.351 | 57 | |
- | - | 69 | 2.674 |
Item | From | To | |
---|---|---|---|
Rule-Based | Practical | ||
Cost (USD, ×106) | - | 2.674 | 0.549 |
WDS reliability | 0.137 | 0.483 | 0.423 |
Total EN | 286 | 57 | 64 |
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Kim, S.; Jun, H.D.; Yoo, D.G.; Kim, J.H. A Framework for Improving Reliability of Water Distribution Systems Based on a Segment-Based Minimum Cut-Set Approach. Water 2019, 11, 1524. https://doi.org/10.3390/w11071524
Kim S, Jun HD, Yoo DG, Kim JH. A Framework for Improving Reliability of Water Distribution Systems Based on a Segment-Based Minimum Cut-Set Approach. Water. 2019; 11(7):1524. https://doi.org/10.3390/w11071524
Chicago/Turabian StyleKim, Seokhyeon, Hwan Don Jun, Do Guen Yoo, and Joong Hoon Kim. 2019. "A Framework for Improving Reliability of Water Distribution Systems Based on a Segment-Based Minimum Cut-Set Approach" Water 11, no. 7: 1524. https://doi.org/10.3390/w11071524