# Identification of Factors That Influence Energy Performance in Water Distribution System Mains

^{*}

## Abstract

**:**

_{HW}are not as influential as expected in distinguishing high-efficiency from low-efficiency pipes. Further, a comparison between the approach used in this paper and a simplified common-practice replacement strategy points out the difference energy considerations can make, if included in a bigger asset management landscape.

## 1. Introduction

- What hydraulic parameters have the largest influence on the energy performance for water mains data in distribution systems?
- What combinations of hydraulic parameters can better distinguish highly efficient water mains from those with low efficiency?
- How aligned are the simplified rehabilitation approaches, for example those based on pipe age or break rate, with energy efficiency in water mains?

## 2. Methods

#### 2.1. Pipe-Level Energy Metrics

_{HW}), pipe diameter (D), average unit headloss (UH), presssure (P), elevation (Elv) and hydraulic proximity to major components) and energy use in water mains of distribution systems (see Table 1). The pipe-level metrics and their parameters are defined in Equations (1)–(6). The reader can refer to [12] to obtain more details on these pipe-level metrics.

_{delivered}) to the energy supplied to that pipe (E

_{supplied}). Each energy components are defined in Table 1. NEE, net energy efficiency (Equation (2)), compares the energy delivered to users serviced by a pipe (E

_{delivered}) to the net energy in that pipe (E

_{supplied}− E

_{ds}), where net energy is the energy supplied to the pipe minus (E

_{supplied}) the energy supplied to users located downstream of the pipe and not directly serviced by the pipe (E

_{ds}). ENU, energy need by user (Equation (3)), compares the energy delivered to the users serviced by a pipe (E

_{delivered}) against the minimum energy needed by those users (E

_{need}). The minimum energy by a user is defined as E

_{need}= γ Q

_{min}H

_{min}Δt and is a function of the minimum water use needed by users (Q

_{min}) and the minimum pressure head required to deliver acceptable water service to users (H

_{min}). ELTF, energy lost to friction (Equation (4)), compares the magnitude of friction loss in the pipe (E

_{friction}to satisfy the demand and leakage at the end of the pipe, and demands downstream of the pipe) to the net energy supplied to the pipe (E

_{supplied}− E

_{ds}). ELTL, energy lost to leakage (Equation (5)), compares the sum of the energy lost directly to leakage and the frictional energy loss along the pipe required to meet the leakage flow, Q

_{l}, at the end of the pipe or E

_{leak}+ E

_{friction (leak)}relative to the net energy supplied to the pipe.

#### 2.2. Principal Components Analysis (PCA)

#### PCA Mono-Plots and Bi-Plots

_{i}score)

_{j}is the score of pipe

_{i}on the jth PC, [pipe

_{i}]

_{1}

_{×n}is the vector on the ith row on the matrix of pipes including the ranks of all n hydraulic variable values for pipe

_{i}and [PC

_{j}]

_{n}

_{×j}is the Eigenvector corresponding to the jth largest Eigenvalue (the jth PC), including the scores of all n hydraulic parameters. Therefore, each pipe or observation will be assigned one value on each of the new directions or PCs, which makes the visualization of the observation on the new/transformed coordinate system possible. Clusters of pipe scores on the PCA bi-plot can distinguish data groups with similar characteristics. The formation of clusters can help identify the factors that have the most impact on the similarities or dissimilarities in the observations.

## 3. Application of Multivariate Statistical Analyses in Large WDSs

## 4. Results

#### 4.1. Hierarchical Importance of Parameters in Energy-Based Decision Making

#### 4.1.1. Non-Leaky Ensemble

_{1}, describing the most variation in the pipe dataset (47.3%). The y-axis represents PC

_{2}, describing the second most variation in the data (16.9%). More influential parameters and metrics are mainly perceived to have scores higher than 0.3 on each PC. However, to narrow down the important parameters and metrics for decision making, higher alignment with the PCs will also be preferable. According to Figure 2, GEE and NEE track closely, meaning that higher values for one result in higher values for the other as well. The PC

_{1}values for these two metrics suggest that they are more influential in describing variance than parameters such as C

_{HW}, diameter and Elv. On the other hand, ELTF, Average flow (Ave. Q), headloss and proximity are clustered together. This not only means that they have similar effects on pipes, but also that high values of these parameters result in lower values of GEE and NEE. It is also noted that all parameters of GEE, NEE, ELTF, proximity, Ave Q and headloss are well represented with regard to PC

_{1}, as their respective vectors are first, much larger compared to parameters such as C

_{HW}and diameter and, second, closely aligned with the PC

_{1}axis.

_{2}axis, ENU and Pressure (P) are clustered together and have high vector magnitudes compared to other parameters. Therefore, it can be inferred that these two vectors are highly correlated/aligned to each other, and that they have higher importance compared to D and C

_{HW}. However, ENU and P have lower importance or influence compared to those with higher values along the PC

_{1}axis (ELTF, GEE, NEE, headloss, etc.). This is mainly because PC

_{2}describe less variance (16.9%) compared to PC

_{1}(47.3%).

_{HW}and D vectors are not situated close to any other parameters or to each other, which means that they will not affect the dataset in the same way as the other parameter. In addition, these vectors are not well represented on either the PC

_{1}or PC

_{2}axes, both in their magnitude and in their direction, which explains less importance in the variance of the ensemble. The Elv vector points away from other parameters, implying that it has a different effect on the variance of the pipe dataset. It can also be inferred that higher elevations cause lower pressure, since the Elv and P vectors point in opposite directions.

#### 4.1.2. Leaky Ensemble

_{2}in Table 2 as the largest distribution network). PCA for this includes the same variables as in the non-leaky ensemble plus daily leakage and ELTL, which comes to the total of 13 variables as opposed to 11 in the non-leaky ensemble. Even though the percentage of leakage in this system is fairly small (almost 8%), Figure 3 shows slightly different results to those of Figure 2 which could illustrate the importance of considering leakage. As shown by the axes, PC

_{1}describes 36.5% and PC

_{2}20% of the variance. The sum of these contributions is slightly smaller compared to that of the previous mono-plot mainly because more parameters (including daily leakage and ELTL) are now included in the PCA, which makes each parameter less descriptive with regard to the total variance in the ensemble. According to Figure 3, influential parameters are GEE, ELTF, proximity, Ave Q and headloss as they all hold comparatively higher scores along PC

_{1}(above absolute values of over 0.3 on both axes). Diameter is now more influential and closer to the cluster of ELTF, headloss, proximity, and Ave Q compare to the non-leaky ensemble results. This difference in the relative importance of the parameters may emphasize the importance of considering leakage and larger networks. Further, ELTL, leakage and NEE are the next most influential vectors, with high PC

_{2}scores (absolute value over 0.40). Elv in the leaky ensemble is a fairly important parameter compared to C

_{HW}, pressure, and even ENU, because of the length of the corresponding vector in Figure 3. As in the results for the non-leaky ensemble, C

_{HW}is a less important parameter—its vector points away from other parameters and has a small magnitude. Compared to the non-leaky ensemble, although ENU and P still track closely, their importance is dwarfed by ELTL and leakage along the PC

_{2}axis. This implies that in systems with leakage, the impact of pressure may be lower compared to leakage on the energy dynamics of the system.

_{1}). It is also observed that average unit headloss and diameter can potentially have similar effects on the dataset, which was not captured originally by correlation analysis. It could also be interpreted as larger pipes being generally located near the major components, and thus may bear inherently higher unit headloss rates. This is also corroborated by the fact that water main sizes decrease moving away from major components in a system.

#### 4.2. Clusters of High Efficiency Versus Low Efficiency Pipes

_{1}and PC

_{2}axes. This would suggest that the mono-plots represent energy dynamics landscape in the two ensembles. Therefore, the energy metrics values can be used to characterize high/low-efficiency pipes throughout the whole dataset.

#### 4.2.1. Non-Leaky Ensemble

_{1}, therefore, based on Equation (6) pipes with similar ELTF values (pipe

_{i,n}) will have similar products of these values and ELTF score on PC

_{n,1}(pipe

_{i,n}× PC

_{n,1}). As Figure 2 indicated ELTF as one of the most influential hydraulic factors (with high score along PC

_{1}), the product of pipe parameter values and the ELTF score, based on Equation (6), will then be higher and form bands on the direction shown in Figure 4. Based on Table 4, threshold values of Figure 4 are chosen to distinguish high efficiency pipes in green, low efficiency in red and other values in between in light blue. Further, it is seen that the direction on which the colors of bands change in Figure 4 is the same as the direction of the ELTF vector in Figure 2, i.e., higher values of ELTF, that is tantamount to low efficiency pipes in terms of ELTF, cause these pipes to form a band on the left side of Figure 4 (based on ELTF vector in Figure 2). Similarly, NEE and GEE display clusters of low values (close to zero) on the left hand side and the cluster of higher values (close to 1) on the right hand side. However, because of similar visual result as the ELTF cluster, they are not presented. As general rule, pipes with similar values of metrics expressed with larger vectors (GEE, NEE, ENU and ELTF) tend to cluster more visibly in certain areas of the bi-plots.

_{2}axis than the PC

_{1}axis, as seen in Figure 5. The direction on which the color of bands changes is the same as the direction of the ENU vector in Figure 2. Values of ENU > 113% that correspond to low efficiency pipes tend to stratify on the bottom (indicated in the color of red) while those that correspond to 100% < ENU < 105% form a horizontal band closer to the top and indicated in green. Other pipes indicated in blue pertain to the other pipes ranging between high efficiency and low efficiency pipes. ENU obtains higher score along PC

_{2}, which indicates, first, lower importance compared to GEE, NEE and ELTF (that merit high scores on PC

_{1}) and, second, no correlation between the two set of variable. This implies the direction on which the ENU values change has no correlation to that of GEE, NEE and ELTF, as PC

_{1}and PC

_{2}are orthogonal. In other words, efficiency in terms of ENU does not seem to have an effect on efficiency in terms of GEE, NEE and ELTF.

_{1}) and horizontal bands (from the metrics with high scores on PC

_{2}) forms smaller clusters of high or low efficiency pipes. High-efficiency pipes are defined as summarized in Table 4. However, the purpose of setting thresholds for the metrics is to approximately locate the cluster of high-efficiency pipes on the PCA bi-plots, and not to suggest threshold values for rehabilitation and replacement in practice, as this would be a complex decision task involving multiple factors such as budgetary limitations, risk assessment, water quality, pipe age and break rates, along with energy considerations. The selected thresholds lead to a cluster formed on the top right area of the plot in Figure 6. Similarly, low efficiency pipes cluster are also defined as per summarized in Table 4. The mentioned thresholds create a cluster on the left hand side of the bi-plot. To the extent that stricter values of metrics are desired, the clusters can be smaller or larger, however, the location of clusters will remain the same.

#### 4.2.2. Leaky Ensemble

_{1}and PC

_{2}axes, which makes this set of results different from non-leaky set of pipes. Thresholds of high versus low-efficiency pipes are considered based on Table 4.

_{2}axis (value of 0.42) and its corresponding vector is closely aligned with the PC

_{2}axis. This is reflected in the bi-plot in Figure 8, where ELTL values change almost along PC

_{2}. High efficiency pipes regarding ELTL (based on Table 4) are clustered at the top (indicated in green), while low-efficiency pipes, on the bottom (indicated in red) and other value ranges (indicated in light blue) are situated in between. Stratifications of metrics values for GEE, NEE and ENU for the leaky ensemble resemble those of the non-leaky ensemble considering the same thresholds, and therefore are not presented here.

#### 4.3. Examining Current-Practice Pipe Rehabilitations

## 5. Discussion

_{HW}would not serve as suitable guides to identify high/low efficiency pipes. Although C

_{HW}is considered as an influential factor for pipe replacement in practice, the results indicate that this parameter alone is not a suitable representative of energy efficiency.

_{1}. The next best set of hydraulic parameters includes leakage and pressure, which have relatively less importance in identifying high/low efficiency pipes, because of their alignment with the second most important principal component, PC

_{2}. At the same time, the leakage flow itself seems to be more important compared to pressure because of its vector size. Therefore, leakage in pipes, if well characterized, would be a better indicator than pressure for identifying energy efficiency in pipes. Similar to the case for the non-leaky pipe ensemble, Elv, C

_{HW}and diameter play a less significant role in characterizing energy dynamics in pipes. In addition, in the leaky ensemble, diameter seemingly has gained more importance due to a longer vector along PC1 in Figure 3. This perhaps corresponds to the correlation of larger pipe sizes and higher flows (not clearly shown in the non-leaky ensemble), due to more accurate model calibration compared to the KY systems, which are the majority of the non-leaky ensemble. However, since diameter does not point directly towards the clusters of high/low efficiency pipes on the bi-plot of Figure 9, they would not be nominated among the most influential parameters in the energy dynamic landscape.

## 6. Conclusions

_{HW}and Elv, which are not well-represented on any of the principal components. However, since leakage and C

_{HW}could change throughout the time, it would be a worthwhile study to consider time-based degradation of the leakage and C

_{HW}in other efforts.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 10.**Bi-plot of high/low efficiency clusters compared to common-practice replacement plan by Prosser et al. [16].

**Table 1.**Summary of energy components and metrics by [12].

Item | Definition |
---|---|

E_{supplied} | Energy supplied to the upstream end of the pipe |

E_{delivered} | Energy delivered to the user to satisfy downstream demand Q_{d} at pressure head H_{d} |

E_{ds} | Energy flowing out of the pipe to meet downstream user demands |

E_{leak} | Energy directly lost to leakage |

E_{friction} | Friction energy loss incurred along the pipe |

E_{local} | Local energy losses through valves, appurtenances, and blockages |

E_{need} | Energy needed/required by the downstream node according to standards |

E_{friction (leak)} | Friction energy loss incurred along the pipe as a result of leakage |

GEE | Gross Energy Efficiency |

NEE | Net Energy Efficiency |

ENU | Energy Needed by User |

ELTF | Energy Lost to Friction |

ELEL | Energy Lost to Leakage |

Proximity | Hydraulic proximity to major components of the network based on pressure head and pipe flow |

Q | Pipe flow (m^{3}/s) |

H_{s} | Head supplied at the upstream node of a pipe |

Network | State/Province | No. of Pipes | Pipes Length (km) | No. of Model Junctions | Difference in Elevations (m) ^{a} | No. of Pumps | No. of Tanks | Average Daily Demand (MLD) | Average Daily Pressure (m) |
---|---|---|---|---|---|---|---|---|---|

1 | ON_{1} ^{b} | 12,189 | 627 | 11,177 | 50 | 31 | 10 | 69.07 | 44.86 |

2 | ON_{2} | 405 | 56 | 349 | 46 | 6 | 3 | 3.54 | 46.71 |

3 | KY_{1} ^{c} | 984 | 67 | 856 | 37 | 1 | 2 | 7.52 | 33.07 |

4 | KY_{2} | 1124 | 152 | 811 | 29 | 1 | 3 | 7.92 | 46.07 |

5 | KY_{3} | 366 | 91 | 271 | 43 | 5 | 3 | 15.19 | 41.76 |

6 | KY_{4} | 1156 | 260 | 959 | 75 | 2 | 4 | 5.65 | 48.02 |

7 | KY_{5} | 496 | 96 | 420 | 75 | 9 | 3 | 8.58 | 134 |

8 | KY_{6} | 644 | 123 | 543 | 96 | 2 | 3 | 6.19 | 60.2 |

9 | KY_{7} | 603 | 137 | 481 | 70 | 1 | 3 | 5.80 | 55.32 |

10 | KY_{8} | 1614 | 247 | 1325 | 135 | 4 | 5 | 9.32 | 54.15 |

11 | KY_{9} | 1270 | 972 | 1242 | 138 | 17 | 15 | 5.07 | 94 |

12 | KY_{10} | 1043 | 435 | 920 | 96 | 13 | 13 | 8.18 | 68 |

13 | KY_{11} | 846 | 464 | 802 | 248 | 21 | 28 | 6.61 | 97.11 |

14 | KY_{12} | 2426 | 655 | 2347 | 145 | 15 | 7 | 5.18 | 111 |

15 | KY_{13} | 940 | 155 | 778 | 95 | 4 | 5 | 8.92 | 50.78 |

16 | KY_{14} | 548 | 105 | 377 | 65 | 5 | 3 | 3.94 | 53.9 |

17 | OH_{1} ^{d} | 1183 | 166 | 956 | 100 | 15 | 4 | 10.13 | 57 |

18 | OH_{2} ^{e} | 27,231 ^{f} | 5500 | 19,618 | 154 | 28 | 27 | 531.49 | 53 |

^{a}: Difference in Elevations = maximum junction elevation (excluding elevated storages) minus minimum junction elevation;

^{b}: ON = Ontario;

^{c}: KY = Kentucky;

^{d}: OH = Ohio;

^{e}: OH

_{2}system includes total leakage equivalent to 8% of the total daily demand for nodes;

^{f}: Not all the pipes in all systems participate in the statistical analysis.

**Table 3.**Correlation matrix of energy metrics and pipe hydraulic factors [11].

C_{HW} | D (mm) | P (m) | Avg. Q (L/s) | Avg. Unit Headloss (m/km) | Prox (m^{4}/s) | Elv. (m) | GEE (%) | NEE (%) | ENU (%) | ELTF (%) | |
---|---|---|---|---|---|---|---|---|---|---|---|

C_{HW} ^{1} | 1 | −0.20 | 0.05 | 0.05 | −0.13 | 0.05 | −0.10 | 0.11 | 0.06 | 0.05 | −0.10 |

D (mm) ^{2} | −0.20 | 1 | −0.07 | 0.53 | 0.09 | 0.55 | 0.26 | −0.57 | −0.30 | −0.01 | 0.29 |

P (m) ^{3} | 0.05 | −0.07 | 1 | −0.02 | −0.08 | −0.05 | −0.24 | 0.10 | 0.08 | 0.66 | −0.10 |

Avg. Q (MLD) ^{4} | 0.05 | 0.53 | −0.02 | 1 | 0.73 | 0.96 | 0.16 | −0.75 | −0.81 | −0.13 | 0.73 |

Avg. Unit Headloss (m/km) ^{5} | −0.13 | 0.09 | −0.08 | 0.73 | 1 | 0.69 | 0.10 | −0.64 | −0.88 | −0.14 | 0.82 |

Prox (m^{4}/s) ^{6} | 0.05 | 0.55 | −0.05 | 0.96 | 0.69 | 1 | 0.18 | −0.73 | −0.78 | −0.08 | 0.71 |

Elv. (m) ^{7} | −0.10 | 0.26 | −0.24 | 0.16 | 0.10 | 0.18 | 1 | −0.09 | −0.08 | −0.41 | 0.06 |

GEE (%) ^{8} | 0.11 | −0.57 | 0.10 | −0.75 | −0.64 | −0.73 | −0.09 | 1 | 0.80 | 0.04 | −0.76 |

NEE (%) ^{9} | 0.06 | −0.30 | 0.08 | −0.81 | −0.88 | −0.78 | −0.08 | 0.80 | 1 | 0.10 | −0.92 |

ENU (%) ^{10} | 0.05 | −0.01 | 0.66 | −0.13 | −0.14 | −0.08 | −0.41 | 0.04 | 0.10 | 1 | −0.07 |

ELTF (%) ^{11} | −0.10 | 0.29 | −0.10 | 0.73 | 0.82 | 0.71 | 0.06 | −0.76 | −0.92 | −0.07 | 1 |

^{1}: C

_{HW}= Hazen–Williams “C” factor;

^{2}: D = Pipe diameter;

^{3}: P = Average daily pressure of a pipe;

^{4}: Avg. Q = Average daily flow of a pipe. However, it is noted that the energy metrics are evaluated based on hourly flows [12];

^{5}: Avg. Unit Headloss = Average daily unit headloss in a pipe;

^{6}: Prox = Hydraulic proximity of each pipe to major components such as elevated storages and/or pump stations [11,12];

^{7}: Elv = Arithmetic Average of upstream and downstream nodes of a pipe;

^{8}: GEE = Gross Energy Efficiency (in percent);

^{9}: NEE = Net Energy Efficiency (in percent);

^{10}: ENU = Energy Needed by the User (in percent);

^{11}: ELTF = Energy Lost to Friction (in percent).

Energy Metric | Threshold Value to Define Low Efficiency Pipes (%) | Threshold Value to Define High Efficiency Pipes (%) |
---|---|---|

GEE | GEE < 15 | GEE > 20 |

NEE | NEE < 99.4 | NEE > 99.9 |

ENU | ENU > 113 | 100 < ENU < 105 |

ELTF | ELTF > 0.3 | ELTF < 0.0018 |

ELTL * | ELTL > 3 | ELTL < 0.8 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Hashemi, S.; Filion, Y.; Speight, V.
Identification of Factors That Influence Energy Performance in Water Distribution System Mains. *Water* **2018**, *10*, 428.
https://doi.org/10.3390/w10040428

**AMA Style**

Hashemi S, Filion Y, Speight V.
Identification of Factors That Influence Energy Performance in Water Distribution System Mains. *Water*. 2018; 10(4):428.
https://doi.org/10.3390/w10040428

**Chicago/Turabian Style**

Hashemi, Saeed, Yves Filion, and Vanessa Speight.
2018. "Identification of Factors That Influence Energy Performance in Water Distribution System Mains" *Water* 10, no. 4: 428.
https://doi.org/10.3390/w10040428