# Cost–Benefit Analysis of Leakage Reduction Methods in Water Supply Networks

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{t}= cash flow in year t.

#### 2.1. Data

^{3}for surface water facilities, 0.56 kWh/m

^{3}for groundwater facilities, and 0.22 kWh/m

^{3}for water distribution. The average values were used for the around 60% of the utilities that did not report energy consumption. The cost of energy was estimated as electricity cost, even though a small part of the total energy consumption sometimes comes from other sources such as fuel oil. The cost of electricity was estimated based on the Finnish electricity price statistics [15] and was 0.07–0.12 euros/kWh. The unbilled authorized consumption was assumed to be 2% of the network input for all utilities. The average length of service lines was set to 22.5 m [16]. All customers, usually the property owner, are metered in Finland, and the water meters are located inside the buildings.

#### Water Supply in Finland

#### 2.2. Estimating the Leakage Reduction Potential

_{m}= length of mains (km), N

_{c}= number of service connections, L

_{s}= total length of service pipes (km), and h = average pressure head (m). The UARL can be used with the current leakage level to calculate the infrastructure leakage index (ILI) as

#### 2.3. The Leakage Reduction Methods

#### 2.3.1. District Metering

#### 2.3.2. Pressure Reduction

_{0}= initial leakage volume, L

_{1}= leakage volume after pressure change, P

_{0}= initial pressure, P

_{1}= pressure after change, and N1 = empirical exponent for the leakage–pressure relationship [24]. Based on previous assessments, values of 1.5 and 0.5 for the N1 exponent are often assumed for elastic and rigid materials, respectively [25]. We used the following values: ‘plastic’ N1 = 1.5, ‘other/unknown’ N1 = 1, and ‘metal’ N1 = 0.5.

#### 2.3.3. Renovations

#### 2.4. The Economic Level of Leakage

_{measure i}= the net present value of leakage reduction measure i. In calculating the NPVs, the leakage potential as well as the benefit gained from each measure are functions of the total leakage volume. In the case of renovations, the pipe failure rate is also a function of the total leakage volume, and it is assumed to increase or decrease in proportion to the leakage rate.

#### 2.5. Uncertainty and Sensitivity Analysis

#### 2.6. Limitations of the Method

## 3. Results

#### 3.1. Current Leakage Levels and Leakage Reduction Potential in Finland

^{3}/km/day according to the Portuguese classification [38] (p. 71) and almost all (97%) in the best category of less than 8 m

^{3}/km/day according to the Swedish classification [39] (p. 34). ILI values are very low for over half of the utilities.

#### 3.2. The Cost–Benefit Analysis of Leakage Reduction Measures

^{3}) of our utilities. The median NPV was −0.32 euros/billed m

^{3}for DMA, −0.34 euros/billed m

^{3}for DMA + P, and −0.36 euros/billed m

^{3}for renovations.

#### 3.3. The Economic Level of Leakage (ELL)

^{3}/km/day was 4.6, or 39% as leakage percentage, while the current median leakage levels are 1.6 m

^{3}/km/day and 17% in terms of percentage of water input. Naturally, it is not guaranteed that the systems would actually work with such high theoretical leakage levels.

#### 3.4. Uncertainty and Sensitivity Analysis

## 4. Discussion

#### 4.1. Context-Specific Findings: Mostly Low Water Loss Levels in Finland

^{3}/km/day) was wide (0.5–19), which means that no threshold value for the cost-benefit of leakage reduction measures could be identified in terms of this leakage indicator. In terms of leakage percentage, the ELLs were 10%–59%. The values are high but not necessarily unfeasible, since the current leakage level is at highest 49%. The highest ELL percentages resulted for utilities that have lower connection densities and lower burst rates.

^{3}, which is in the lower end compared to European case studies with costs between 0.09 and 0.51 euros/m

^{3}[40].

#### 4.2. Leakage Reduction Methods

#### 4.3. Leakage Indicators and Policies

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Steps of the analysis for calculating the net present value of three leakage reduction measures: (1) district metering areas, (2) district metering areas with pressure reduction, and (3) renovations.

**Figure 2.**The current leakage level, the minimum leakage level according to the unavoidable annual real losses (UARL) formula, and the devised minimum leakage level in terms of leakage volume in m

^{3}/km of the Finnish utilities plotted against the density of people per kilometre of network.

**Figure 3.**Net present values per volume of billed water (euros/m

^{3}) for the leakage reduction measures: (1) district metered areas (DMA), (2) district metered areas with pressure reduction (DMA + P), and (3) renovations plotted against the leakage reduction potential (m

^{3}/km/d).

**Figure 4.**The economic level of leakage in terms of leakage per network length per day for each utility against (

**a**) the current leakage level and (

**b**) the connection density. The markers show which leakage reduction measure is the most cost-beneficial for each utility.

**Figure 5.**Net present values (euros) per total billed volume of water in m

^{3}for: (

**a**) District metering; (

**b**) District metering with pressure reduction; and (

**c**) Renovations in relation to the leakage reduction potential. The simulated 10th to 90th percentile values are indicated by the error bars. Note that the scale of the x-axes changes at 3 m

^{3}/km/day.

**Figure 6.**Median net present values for baseline (horizontal line) and the median of the 90th percentile (blue bar) and 10th percentile (red bar) results for: (

**a**) District metering; (

**b**) District metering with pressure reduction; and (

**c**) Renovations.

**Table 1.**The estimated pipe failure rates (failures/100 km/year) for different material groups for ‘old’ and ‘new’ pipes, the ratio between the average failure rate and the failure rate of ‘old’ pipes, and the leakage rate of different material groups compared to the metal group.

Age Category | Pipe Failure Rate (Failures/100 km/year) | ||
---|---|---|---|

Metal | Plastic | Other/Unknown | |

Old (≥50 or ≥40 years old) | 16 | 10 | 6 |

New (≤15 years old) | 1 | 1 | 0 |

Average of all ages | 9 | 1 | 3.3 |

Ratio of old to average pipe failure rate | 1.8 | 7.1 | 1.8 |

Leakage rate compared to metal pipes (based on the average pipe failure rates) | 1 | 0.15 | 0.36 |

Variable | Unit | Distribution | Estimated Mean (µ) | Standard Deviation (σ) | Uniform Dist. Bounds |
---|---|---|---|---|---|

The total length of service lines | m | normal | 22.5 | 5 | - |

Unbilled authorized consumption | % of network input | uniform | 2 | - | [0.5, 3.5] |

Average pressure | m | uniform | 50 | - | [35, 65] |

Discount rate | % per year | normal | 3.5 | 0.8 | - |

Marginal cost of water | euros/m^{3} | truncated normal | varies by utility (median 0.11) | 0.1 µ (min. value 0.04) | - |

DMA effectiveness | % of the total leakage reduction potential | uniform | 30 | - | [20, 100] |

DMA cost | euros/DMA area | normal | 48,000 | 10,000 | - |

DMA lifetime | years | normal | 20 | 2 | - |

N1 (leakage–pressure exponent) | - | uniform | varies by utility | - | [0.5, 1.5] |

Average pressure reduction | m | uniform | 5 | [1, 10] | |

Cost of pressure management | euros/station | normal | 9000 | 2000 | - |

Burst repair cost | euros | truncated normal | 5500–14,500 (varies by utility size) | 0.25 µ (min. value 2000) | - |

Renovation cost | euros/metre | truncated normal | 94–628 (varies by utility size) | 0.25 µ (min. value 50) | - |

Pipe lifetime | years | normal | 70 | 15 | - |

**Table 3.**Median, minimum and maximum values for key leakage level characteristics for the 92 Finnish water utilities grouped by size, and the share of utilities with leakage reduction potential in the size groups in 2015–2017.

^{1}ILI: Infrastructure Leakage Index.

Utility Size (Sample Size) | Figure | Service Conn/km | No. of People/km | Leakage % ^{2} | Leakage m^{3}/km/d | ILI |
---|---|---|---|---|---|---|

Small (n = 43), | ||||||

3000–10,000 pop., | Median | J | F | J | J | J |

900–3700 conn. | Min–Max | 4–21 | 7–67 | 4–49 | 0.2–7 | 0.2–4.4 |

Medium (n = 39), | ||||||

10,000–60,000 pop., | Median | J | M | J | J | J |

2000–16,000 conn. | Min–Max | 5–31 | 17–198 | 6–28 | 0.4–5 | 0.3–2.2 |

Large (n = 10), | ||||||

60,000–1200,000 pop., | Median | J | M | J | J | J |

11,000–73,000 conn. | Min–Max | 13–27 | 70–365 | 6–20 | 1–13 | 0.6–5.2 |

^{1}Data from 2015 were used for most utilities, but if unavailable, data from 2016 or 2017 were used.

^{2}Percentage of water input to the network.

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**MDPI and ACS Style**

Ahopelto, S.; Vahala, R.
Cost–Benefit Analysis of Leakage Reduction Methods in Water Supply Networks. *Water* **2020**, *12*, 195.
https://doi.org/10.3390/w12010195

**AMA Style**

Ahopelto S, Vahala R.
Cost–Benefit Analysis of Leakage Reduction Methods in Water Supply Networks. *Water*. 2020; 12(1):195.
https://doi.org/10.3390/w12010195

**Chicago/Turabian Style**

Ahopelto, Suvi, and Riku Vahala.
2020. "Cost–Benefit Analysis of Leakage Reduction Methods in Water Supply Networks" *Water* 12, no. 1: 195.
https://doi.org/10.3390/w12010195