Improving the Performance of Water Distribution Networks Based on the Value Index in the System Dynamics Framework
Abstract
:1. Introduction
2. Materials and Methods
2.1. Environmental Assessment
2.1.1. Goal and Scope Definition
2.1.2. Life Cycle Inventory
2.1.3. Life Cycle Impact Assessment
2.1.4. Environmental Performance Index
2.2. Hydraulic Assessment
2.2.1. Leakage Estimation
2.2.2. Hydraulic Performance Index
2.3. Value Index
2.4. System Dynamics
- Pipe roughness coefficient: hydraulic capacity of pipes decreases over time. In general, reducing hydraulic capacity is the result of increasing roughness in pipes. As roughness of a pipe increases, roughness coefficient decreases. Thus, according to the Hazen–Williams Equation (14), overall head loss increases and pressure decreases as a result. Therefore, the pipes’ roughness coefficients are directly related to the pressure of WDNs. In the SD model, Equation (15) is used to consider the changes in Hazen–Williams coefficient in each pipe [44]. Average roughness coefficient of a network (CHWt) as the representative of the whole system roughness is calculated by weighting the coefficient of each diameter based on its length.
- Demand changes: The pressure independent discharge (demand) is the second variable on which the pressure and velocity of WDNs are dependent. Increasing the demand results in increasing the consumption which reduces the pressure of the nodes and increases the flow velocity in the pipes.
- Adjusted pressure of pressure-reducing valves (PRV): adjusted pressure of PRV valves can have a significant effect on the pressure and velocity of the system.
- Discharge of the background losses and unreported bursts: it is considered as the function of the average pressure and average age of the system (Equation (18)).
- Discharge of the reported bursts: regarding the guidelines [41], it is considered as the function of total breaks, the flow rate of burst, the average pressure of the system, and the duration of the total breaks (Equation (19)). The break rate of the pipes is calculated based on Equations (20) and (21) [45]. According to the previous studies and guidelines [41,46], the flow rate of burst () is considered 12 . The parameters of A, B, C in Equation (18) and t (the total break duration) in Equation (19) are determined by calibration of these equations with the leakage calculated based on MNF method. For this purpose, OptQuest calibration module [47,48] in AnyLogic software is used. This module minimizes the difference between the simulated and observed leakage. This process is basically an optimization process which its objective function is defined in accordance with Equation (22).
3. Case Study
4. Results and Discussion
4.1. Environmental Impacts Assessment
4.2. Calibration of the Leakage Equation
4.3. Correlation between the Simulated and Observed Inflow
4.4. Evaluation of the Leakage, Pressure, and Inflow of the WDN
4.5. Evaluation of the Leakage, Pressure, and Inflow of the WDN
4.6. Evaluating VI of the System
4.7. Scenarios for Improvement of VI
4.7.1. Scenario 1: Reducing the Per Capita Water Demand
4.7.2. Scenario 2: Reducing the Average Pressure
4.7.3. Scenario 3: Reducing the Age of the System by Renewing Pipe
4.7.4. Scenario 4: Reducing the Per Capita Water Demand and Average Pressure
4.7.5. Comparing the Best Scenarios
5. Summary and Conclusions
Supplementary Materials
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Factors | Empirical Equations | Equation | |
---|---|---|---|
Head loss (H) | , | (14) | |
Remark | H is head loss (m), is flow rate (), L is length of pipe (m), D is diameter (m), and CHW is Hazen–Williams coefficient. | ||
Roughness coefficient () | , [44] | (15) | |
Remark | is Hazen–Williams coefficient in pipe p at year t, is initial roughness at the installation time (unit of length), is roughness growth rate in pipe p (unit of length per year), is the diameter of pipe p (unit of length), is the age of pipe p at the present time (year) and t is annual time. , and are calculated using Equations (16) and (17). | ||
Initial roughness | , | (16) | |
roughness growth rate () | , | (17) | |
Remark | is Hazen–Williams coefficient in pipe p at the installation time. | ||
Background losses + unreported bursts | , | (18) | |
Remark | is the average pressure in the SD model (m), is the average age (year), A, B, and C are undetermined coefficients. | ||
Reported bursts | , [41] | (19) | |
Remark | is the total bursts of pipes in each time step, is the flow rate of burst in the pressure of 50 m (), is the average pressure (m), is the power term of pressure, and is the total time of break (h). | ||
Break rate of ductile iron and steel pipes | , [45] | (20) | |
Break rate of plastic pipes | , [45] | (21) | |
Remark | is the rate of break (), is the length of pipe (m), is the age of pipe (year), and S is pipe diameter (mm). | ||
Objective function of the calibration module | (22) | ||
Remark | is the leakage which is calculated based on the MNF, is the leakage which is obtained from the sum of Equations (18) and (19). | ||
Factors | Regression Equations | Equation | |
Per capita demand | , | 0.943 | (23) |
Remark | All the variables are calculated based on the average monthly amount. | ||
Average pressure | , | 0.997 | (24) |
Average velocity | , | 0.992 | (25) |
Remark | is the average monthly demand (), is the average roughness coefficient and is adjusted pressure of the PRV valves (m). | ||
Pressure performance index (PIP) | , | 0.993 | (26) |
Velocity performance index (PIV) | , | 0.951 | (27) |
Remark | is total inflow to the network (), is the average roughness coefficient, and is the pressure of the PRV valves (m). |
Parameters | Remark | Optimum Value |
---|---|---|
A | Coefficient of the average pressure | 4.472 |
B | Coefficient of the average age | 0.507 |
C | Constant number | 99.939 |
T | Total breaks duration (h) | 24 |
Simulated Phase | R | RS | |
---|---|---|---|
After calibration | 0.9516 | 0.97 | 24.4 |
Validation | 0.9073 | 0.94 | 27.5 |
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Hajibabaei, M.; Nazif, S.; Sitzenfrei, R. Improving the Performance of Water Distribution Networks Based on the Value Index in the System Dynamics Framework. Water 2019, 11, 2445. https://doi.org/10.3390/w11122445
Hajibabaei M, Nazif S, Sitzenfrei R. Improving the Performance of Water Distribution Networks Based on the Value Index in the System Dynamics Framework. Water. 2019; 11(12):2445. https://doi.org/10.3390/w11122445
Chicago/Turabian StyleHajibabaei, Mohsen, Sara Nazif, and Robert Sitzenfrei. 2019. "Improving the Performance of Water Distribution Networks Based on the Value Index in the System Dynamics Framework" Water 11, no. 12: 2445. https://doi.org/10.3390/w11122445