Study on the Leakage Diagnosis of a Chilled Water Pipeline Network System Based on Pressure Variation Rate Analysis for Climate Change Mitigation

Abstract

In the context of increasing climate variability and extreme weather, chilled water systems face mounting challenges due to amplified heating and cooling demands and prevalent pipe leakages. Such leakages reduce system lifespan, raise maintenance costs, and degrade operational efficiency. To overcome the limitations of current methods, such as insufficient interpretability and computational complexity in leak localization, this paper proposes a novel leakage diagnosis and localization scheme based on pressure variation rate analysis in closed chilled water pipeline networks. Hydraulic models under both normal and leakage conditions are established and experimentally validated. Work conditions under various leakage points and flow rates were simulated, and the results reveal that pressure variation rates systematically increase with the leakage flow rate and vary with the distance from the leakage point. Specifically, when a leakage flow rate reaches 20% of the total rated flow, the pressure variation rate is 12.27% at the water supply side of the leaking branch and 20.27% at the return side. Furthermore, other monitoring points can be categorized into three distinct levels with variation rates ranging from approximately 3.36% to 19.65%. Overall, as the leakage flow increases from 2% to 20% of the design flow, the maximum pressure variation rate rises from 0.411% to 20.27%. A threshold of 3% for this novel leakage diagnosis and localization scheme is used for prompt leakage detection. This scheme not only enhances leak localization accuracy but also contributes to more efficient and reliable system operation under the pressure imposed by climate change.

1. Introduction

With ongoing economic and social development, the demand for commercial buildings (CBs) has surged. The total floor area of CBs is expected to reach 1.247 billion square feet by 2050, marking a 34% increase from 2019 [1]. Consequently, energy consumption in commercial buildings accounts for approximately 40% of global energy demand and is projected to rise further in the coming years [2]. One of the primary challenges in energy conservation for commercial buildings is climate change. Monge-Barrio and Gutierrez have highlighted the significant impact of climate change on commercial buildings [3], as the heating and cooling requirements of such buildings are closely tied to temperature conditions and weather fluctuations [4]. On the one hand, temperature fluctuations and extreme weather events caused by climate change increase the operational burden of air-conditioning systems, making them more prone to faults [5]. On the other hand, air-conditioning system faults can reduce energy efficiency and increase energy consumption and greenhouse gas emissions, thereby exacerbating climate change [6]. The challenges posed by climate change have prompted engineers to adopt effective measures to maintain good operation performance for various facilities within buildings, including heating, ventilation, and air conditioning (HVAC) systems, etc., while considering costs. HVAC systems usually consume more than 30% of the total energy in commercial buildings [7]. Cho suggests that in large office buildings, HVAC systems can account for 40% to 50% of the total energy consumption [8]. Chilled water networks play a vital role in transporting cooling energy within HVAC systems. However, with extended operation, these networks inevitably experience aging and wear, leading to various faults [9]. Among these, pipeline leakage is one of the most common failures throughout the lifecycle of chilled water networks. Leaks not only accelerate the corrosion of buildings but also result in the waste of water resources, as the supply water is often high-cost softened cold or hot water. Moreover, pipeline leaks may cause the system to deviate from its optimal operating point, ultimately reducing the quality of life for occupants while increasing electricity costs for HVAC systems [10]. As a large amount of electricity is generated from fossil fuels, this leads to increased greenhouse gas emissions, which is harmful to climate change mitigation [6].

Numerous studies have been conducted on pipeline leakage diagnosis both domestically and internationally. Leakage diagnosis technologies can be classified into direct and indirect methods. Direct methods involve the use of detection equipment to directly identify leaks, including acoustic methods [11], infrared thermal imaging [12], fiber optic sensing [13], and laser remote sensing [14]. In contrast, indirect methods detect leaks through changes in the pressure and flow rate by utilizing hydraulic models or algorithms for analysis. Indirect methods are further divided into two categories: model-based methods and data-driven methods. Model-based methods include pressure point methods [15], pressure gradient methods [16], negative pressure wave methods [17], state estimation methods [18], and transient modeling [19], etc. Data-driven methods that leverage machine learning techniques [20,21], such as neural networks and support vector machines, use historical sensor data to learn patterns associated with leaks. These methods can identify anomalies in pressure and flow rates, enabling leak detection without the need for precise physical models of the pipeline system.

Direct leakage detection methods are often time-consuming and costly. For instance, acoustic methods require sensors at both ends of a pipe and are effective primarily for a single long-distance pipeline, making them unsuitable for complex pipe networks [22]. Similarly, infrared thermography typically uses drones and is mainly applied to under-ground heating systems [23], which makes it impractical for indoor chilled water pipe networks. In contrast, model-based and data-driven indirect methods offer enhanced functionality, maintainability, and adaptability and enable real-time continuous detection. As a result, these methods have received increasing attention in recent research [24]. Regarding model-based approaches, Brahami et al. [25] modeled leakage as an inverse source localization problem and proposed a hybrid genetic algorithm combined with matching field processing to optimize the search for leakage sources, improving performance over traditional exhaustive search methods. Manservigi et al. [26] developed a diagnostic method based on a digital twin model to correctly diagnose common faults in district heating networks, namely leaks, heat loss, and pressure loss. Buonomano et al. [27] pointed out that white-box modeling allows for high-precision analysis and fine control. Meseguer et al. [28] established a model-driven decision support system that implements an online leakage detection and localization method based on the pressure-point technique. It has been proven to be effective for various water distribution networks. Ozgener et al. [29,30] developed an energy and energy use model to monitor district heating systems located in Afyon and Salihli by calculating energy and energy use efficiency [31]. Guan et al. [32] constructed a pressure-driven leakage model that combines leakage and pressure relationships with a nonlinear genetic algorithm by using multi-population genetic algorithms for leak localization. Kaliatka et al. [33] also detected simulated pipeline ruptures by monitoring pressure waves triggered by pressure reduction in district heating networks. For data-driven approaches, Zhou et al. [34] developed a backpropagation (BP) leakage diagnostic model for heating pipe networks, achieving an accuracy of over 89.31%. They also introduced a multi-fault diagnosis methodology based on principal component analysis (PCA) and BP neural networks for timely fault diagnosis in district heating systems [35]. Li et al. [36] proposed a leakage detection method using improved wavelet denoising and short-time Fourier transform on pressure signals, which is used in water distribution, heating networks, and gas pipeline networks. Liu et al. [10] presented a two-phase leakage fault diagnostic methodology utilizing the Adam optimization BP neural network algorithm to locate leakage in air-conditioning water pipelines. Fan et al. [37] similarly used a deep confidence network for the two-stage fault diagnosis of district heating pipe networks, which could locate leaks in pipes with an average error of 17.3 m. Kammoun et al. [38] implemented a multivariate long short-term memory (LSTM) autoencoder to create an unsupervised recurrent neural network (RNN) model for leakage detection, achieving 97% sensitivity by using leakage pressure data and 100% sensitivity with flow rate data. Wang et al. [39] conducted experiments on gas pipeline leakages. They ultimately achieved a leakage identification rate of 96.87% by using an artificial neural network with detectors and specific frequency filters for enhancing accuracy.

Despite the advances in data-driven approaches in recent years due to technological improvements, challenges still remain in practical applications. Chen et al. [40] highlighted that the interpretability of data-driven HVAC troubleshooting approaches is often inadequate, and the complexity of these systems makes it difficult to communicate their value to building owners, thus limiting their broader adoption. In addition, recent studies have applied machine learning techniques to automate fault feature extraction for leakage detection and localization in pipeline networks [10,32,34]. Although these methods achieve high detection accuracy, their black-box nature reduces interpretability and limits insights into how different leakage locations and hydraulic changes influence the system. On the other hand, although model-based methods are generally interpretable, they often rely on optimization algorithms that require iterative, time-consuming, and expensive computation. These issues present significant barriers to real-time fault diagnosis and practical deployment in engineering applications. Therefore, improving both interpretability and computational efficiency is crucial for the advancement of leakage diagnostic technologies.

To address the above limitations, this study proposes a leakage diagnosis and localization scheme tailored for closed chilled water pipe networks to overcome the limitations of acoustic and infrared thermography methods commonly used in such systems. Unlike many existing approaches that rely on iterative optimization algorithms or machine learning models requiring extensive training data, this leakage diagnosis and localization scheme utilizes pressure variation rate analysis to detect and locate leaks. This scheme offers clear interpretability as the pressure response patterns caused by leakage can be directly associated with hydraulic changes in the system. Moreover, it does not require model training or complex iterative computation, significantly reducing both diagnostic time and computational cost.

In this paper, the proposed novel leakage diagnosis and localization scheme is evaluated by using a simulation model of the hydraulic pipe network, and this model is validated by using experimental tests. The simulation hydraulic model of the pipe network under normal conditions is first established and experimentally validated. Based on this validated model, various leakage scenarios with varying leakage locations and flow rates are simulated, and pressure variation rate analysis is carried out to evaluate the effectiveness of this leakage diagnosis and localization scheme. This paper is arranged as follows. Section 2 describes the closed chilled water system for a ship-shaped building with seven zones and several user branches in each zone. Section 3 presents the leakage diagnosis scheme of the pipe network system, which is based on pressure variation rate analysis. Section 4 outlines the hydraulic models of the closed chilled water network under normal and leakage conditions. The calculation results and the leakage diagnosis of this closed pipe network system are presented in Section 5, and Section 6 concludes this paper.

2. Description of the Closed Chilled Water System

The closed chilled water system for a ship-shaped building comprises seven zones, each equipped with a pump (refrigeration unit) branch and several user branches. These user branches are distributed across the upper and lower floors, interconnected by a loop pipe, and separated by butterfly valves, allowing for an independent water supply to each zone. To simplify the analysis, this work focuses on the pipe network of Zone 1, illustrated in Figure 1. This zone includes two loops: the lower loop features six user branches, while the upper loop includes four. The pump has a flow rate of 50 m³/h and a head of 85 mH₂O. The designed flow rates for the upper and lower loops are 20.98 m³/h and 29.02 m³/h, respectively, with individual branch flow rates detailed in

Table 1. Pipe diameters and designed flow rates of the pipeline sections of the Zone 1 chilled water system.

Zone 1 Network	Branch No.	Pipe Diameter (mm)	Designed Flow Rate (m3/h)
Pump branch	B	80	50
Upper loop	S-Z1	20	2.60
	S-Z2	32	7.61
	S-Z3	32	5.71
	S-Z4	32	5.06
Lower loop	X-Z1	25	3.37
	X-Z2	25	4.91
	X-Z3	25	3.41
	X-Z4	20	2.92
	X-Z5	40	8.84
	X-Z6	32	5.57

. The pump inlet is equipped with a tank for pressure stabilization and water supply, and a balancing valve is included in the pump branch to ensure stable operation under varying conditions.

User branches are arranged in parallel, comprising two types of end users: ordinary user branches with variable loads and electromechanical equipment users with fixed loads. Pressure sensors (Pb-1 and Pb-2) are installed at both ends of the pump branch, and pressure measurement points (Ps-1, Ps-2, Px-1, and Px-2) are positioned on the upper and lower loop pipes. The upper loop branches are designated S-Z1 to S-Z6, while the lower loop branches are labeled X-Z1 to X-Z6, with each branch equipped with a pressure point at both ends to measure pressure drops. In total, 20 pressure measurement points (P1 to P20) are established at network nodes. Pressure sensors and water flow meters are used in experimental measurements. The pressure sensor has a full-scale range of 1 MPa with an accuracy of 0.5% FS. The maximum measurement error is 0.005 MPa. The water flow meter has 1.5 times the designed flow rate of each branch, with an accuracy of 0.5% FS. For the raw measured data processing, a signal filter was used to reduce the influence of random noise, and measurement uncertainty was controlled within 0.0029 MPa for pressure measurement. The accuracy and reliability of the proposed diagnostic methodology can be ensured because the pressure values observed during the tests were generally higher than 0.15 MPa, which is significantly above the error and uncertainty range. Additionally, globe valves and ball valves are installed in each user branch to facilitate switching and balancing adjustments.

3. Leakage Diagnosis Scheme of the Pipe Network System Based on Pressure Variation Rate Analysis

When the pipe network operates normally and no leakage occurs, the pressure at each node of the pipe network is constant and higher than atmospheric pressure. When a leak occurs somewhere, the negative pressure wave generated at the leakage point spreads to all parts of the system and causes changes in pressure at each node. The closer the node is to the leakage point, the greater the magnitude of the pressure variation. For a point where the measured pressure at the normal operation is p^A, the measured pressure is p^B at this point when leakage occurs at this point. The pressure variation rate at this point before and after the leakage is formulated as follows.

$$\sigma ={\displaystyle \frac{| p^{\mathrm{A}}-p^{\mathrm{B}} |}{p^{\mathrm{A}}}}$$

(1)

where σ is the pressure variation rate.

In order to better judge the occurrence of leakages in the pipe network system, it is necessary to set an appropriate and reasonable threshold for the pressure variation rate σ_Threshold. When σ < σ_Threshold, it is considered that there is no leakage in the pipeline. It is considered that a leakage has occurred in the pipeline when σ > σ_Threshold. The specific value of σ is related to the proximity to the leakage point, as well as the size of the pipeline and the flow rate.

Referring to the “design code of district heating networks” in China [41], the accidental supply water flow rate of the closed heat network should not be less than 4% of the circulating flow rate of the heat supply system. For the closed-loop chilled water pipe network system in this paper, when the leakage amount is 4% of the total rated flow rate of the pipe network, the range of pressure variation rates at each node is investigated. Based on the maximum pressure variation rates, the threshold value of the pressure variation rate for determining the occurrence of leakages in the pipe network is determined. In practice, when the maximum value of the pressure change rates is greater than this threshold, the leakage flow rate can be considered to be more than 4% of the total rated flow rate, which is then recognized as a leakage.

The response time of leak detection is closely related to the time required for the system to reach a steady state after a leak occurs. Once the leak happens, the system stabilizes quickly, and the sensor data also reach a stable state within a short period. Based on the experiments in this study, the sensor data typically stabilize within 8 min after the leak occurs. After the data stabilize, a period of time is selected to record sensor data as steady-state data. The length of the selected time period is closely related to the sensor data’s update frequency. In this study, the pressure sensors have a sampling frequency of 1 Hz, and the chosen time period (periods A and B in Figure 2) for steady-state data collection is 5 min.

Based on the above analysis, a leakage diagnosis scheme of the pipe network system is proposed, as shown in Figure 2. There are four main steps, i.e., baseline data establishment, leakage data collection, pressure variation rate calculation, and threshold comparison. They are described as follows.

Step 1: Baseline data establishment

Select a period (period A) of steady-state operation when the pipe network operates normally. Record and store the operation parameters of the pipe network, including pump frequency and valve ON/OFF states. Process all data with the time-averaged [p^A₁, ⋯, p^A_N] from all pressure sensors (N is the number of pressure sensors).

Step 2: Leakage data collection

Maintain the network in steady-state operation for a subsequent period (period B). Adjust the operating parameters during this period coincident with those recorded in period A, except that a valve is open to simulate the leakage. Obtain and store the time-averaged data [p^B₁, ⋯, p^B_N] from all pressure sensors.

Step 3: Pressure variation rate calculation

Calculate the pressure variation rates [σ₁, ⋯, σ_N] for all sensors during period B and identify the maximum value σ_Max among these pressure variation rates.

Step 4: Leakage Diagnosis

Compare the maximum pressure variation rate σ_Max with a predefined threshold σ_Threshold. If σ_Max < σ_Threshold, it is concluded that there is no leakage in the pipe network system. Otherwise, a leakage is detected if σ_Max > σ_Threshold. The leakage location is identified based on the sequence of pressure variation rates [σ₁, ⋯, σ_N] from all sensors.

4. Hydraulic Models of the Pipe Network and Validation

In this section, two hydraulic models of the pipe network are developed by using Modelica [42] to simulate the operation of the pipe network system. One hydraulic model (i.e., a hydraulic model for normal operation) is developed to simulate operation in normal operation conditions, and the other hydraulic model (i.e., a hydraulic model for leakage conditions) simulates operation when leakages occur in the closed chilled water pipe network. The hydraulic model for normal operations is validated against the experimental data from the in-field pipe network tests at various pump frequencies. Similarly, the hydraulic model for leakage conditions is also validated through experiments designed to assess the precision of the model under different leakage locations and flow rates.

4.1. Calculation Principle of the Pipe Network Components

In this section, the principle and mathematical models of the main components of the pipe network, i.e., the pipe, pump, valve, resistance components, and flow source, are briefly described since they are very important for developing the hydraulic models of the pipe network by using Modelica.

Pumps can be classified by their specific speed (N_s) based on their hydrodynamic properties. The specific speed [43] is a dimensionless number determined by the operation conditions of the pump, and the calculation is based on the performance index of the pump at the optimum efficiency point, with a mathematical expression as shown in Equation (2).

$$N_S={\displaystyle \frac{N{Q}^{1/2}}{H^{3/4}}}$$

(2)

where N is the pump speed, r/min; Q is the pump flow, m³/s; and H is the pump head, Pa.

A cylindrical rigid pipe is used as the pipe element. The fluid dynamics calculations for this pipe type are based on the Colebrook–White equation [44], as shown in Equations (3)–(6).

When Re ≤ 2000, the fluid is in laminar flow:

$$f=f_l={\displaystyle \frac{64}{Re}}$$

(3)

When 2000 < Re ≤ 4000, the fluid is in transition:

$$f=x{f}_t+(1-x)f_l$$

(4)

$$x={\displaystyle \frac{Re-2000}{2000}}$$

(5)

When Re ≥ 4000, the fluid is in a turbulent state:

$$f=f_t={\displaystyle \frac{0.25}{{\left[\log \left(\frac{k}{3.7D}+\frac{5.74}{R{e}^{0.9}}\right)\right]}^2}}$$

(6)

where f is the friction coefficient; f_l is the friction coefficient of laminar flow state; f_t is the friction coefficient of the turbulent flow state; Re is the Reynolds number; D is the inner diameter of the pipe, m; and k is the absolute roughness of the inner wall of the pipe, mm.

For resistance components, the resistance can be calculated by Equation (7).

$$p_1-p_2={\displaystyle \frac{K{m}_2\left|m_2\right|}{2A^2\rho }}$$

(7)

where P₁ and P₂ are the inlet and outlet pressure values, Pa; K is the resistance coefficient; m₂ is the mass flow rate through the outlet, kg/s; A is the resistance pieces of the circulation cross-section area, m²; and ρ is the density of the fluid, kg/m³. By adjusting the resistance coefficient K, it is possible to change the pipe’s resistance and thus distribute and adjust the flow in the pipe network.

The valve resistance calculation formula is the same as (6). However, for the resistance coefficient K, the resistance of the valve is not a preset constant value but is affected by a variety of factors such as the valve opening, fluid properties, etc. The calculation of K is shown in Equation (8).

$$K=C_{Re}{K}_v$$

(8)

where C_Re is the Reynolds correction factor and K_v is the valve opening factor.

In order to simulate pipe leakage, the leakage flow is simplified to a negative flow source component. The equation for the flow source model is shown in Equation (9). By setting m_in, the flow rate can be controlled. If it is used to model leakage, m_in can be set to a negative value.

$$m_{\mathrm{flow}}=m_{\mathrm{in}}$$

(9)

where m_flow is the flow rate of the flow source (kg/s) and m_in is the flow rate of the artificially set flow source (kg/s).

4.2. Hydraulic Model of the Pipe Network System for Normal Operation

The hydraulic model of the pipe network system is coded using Modelica. This hydraulic model for the closed chilled water system is developed based on the physical topology of the pipe network, i.e., the length, pipe diameter, number of valve components (including valves, tees, and elbows), and locations of pressure measurement points for each pipe section, etc. To simplify the piping system, only the pump is provided in the pump branch, and a branch resistance component is used to simulate the total resistance of the other components in the pump branch (chillers, filters, piping, etc.). In addition, a constant pressure point is provided at the pump inlet to ensure a steady water supply pressure. The model of the Zone 1 chilled water system pipe network is illustrated in Figure 3.

4.3. Validation of the Hydraulic Model for Normal Operation

To ensure that the hydraulic model of the pipe network for normal operation accurately represents the hydraulic characteristics of the actual system under normal operation conditions, model validation was conducted using the measured in situ operation parameters in Zone 1. Based on the measured pressure and flow rates, the branch resistance coefficient was estimated, and the resistance coefficients of each component, together with the pipe roughness and other parameters, were adjusted to align the simulated values of the coincident point with the actual measurement. The hydraulic parameters of the pipe network were further evaluated under different pump operation frequencies in the simulation. Taking Zone 1 as an example, Figure 4 presents the errors between the simulation results by using the hydraulic model for normal operation and the actual measurements. The comparison results show that the errors between the simulation and the measurements are all within 5%. It indicates that the hydraulic model for normal operation conditions can accurately represent the actual system and effectively reflect the hydraulic characteristics of the real closed chilled water network system under normal operation conditions.

4.4. Hydraulic Model of the Pipe Network System for Leakage Conditions

In practical engineering, a pipe network leakage initiates a transient dynamic process. If the damage does not worsen, the system will quickly reach a steady state. Given the numerous branches in the Zone 1 pipe network, which more accurately reflect the pressure changes in each branch, this work focuses on the leakage diagnosis of the Zone 1 pipe network under steady-state conditions, where the leakage flow rate remains constant. A flow source component (shown in Figure 5) is utilized to represent the hydraulic state during leakage. The simulation of pipe network leakages is achieved by applying a negative flow rate, with leakage points located on branches X-Z3 and X-Z6. Four leakage flow rates, denoted as ƒ₁, ƒ₂, ƒ₃, and ƒ₄, were established, accounting for 2%, 4%, 10%, and 20% of the total designed flow rate of the Zone 1 pipe network, respectively. The leakage conditions are summarized in

Table 2. Description of leakage branches and leakage flow rates.

Branch No.	Leakage Flow f1 for 2% (m3/h)	Leakage Flow f2 for 4% (m3/h)	Leakage Flow f3 for 10% (m3/h)	Leakage Flow f4 for 20% (m3/h)
X-Z3	1	2	5	10
X-Z6	1	2	5	10

.

4.5. Validation of the Hydraulic Model for Leakage Conditions

To ensure that the hydraulic model of the pipe network system accurately reflects the hydraulic characteristics of the actual system under leakage conditions, model verification was conducted using measured hydraulic parameters from the pipe network in Zone 6, as illustrated in Figure 6. This zone is equipped with a pump (refrigeration unit) branch and several user branches, comprising two circuits with five user branches in the lower loop and three in the upper loop. The water pump has a flow rate of 50 m³/h and a head of 80 mH₂O, with designed flow rates of 16.38 m³/h for the upper loop and 33.62 m³/h for the lower loop, as detailed in

Table 3. Pipe diameters and designed flow rates of pipeline sections in the Zone 6 chilled water system.

Zone 6 Network	Branch No.	Pipe Diameter (mm)	Designed Flow Rate (m3/h)
Pump branch	A6-B	32	50
Upper loop	A6-S-Z1	25	5.89
	A6-S-Z2	32	3.17
	A6-S-Z3	25	7.32
Lower loop	A6-X-Z1	32	3.74
	A6-X-Z2	25	5.96
	A6-X-Z3	32	4.05
	A6-X-Z4	50	6.22
	A6-X-Z5	32	13.65

.

The inlet of the water pump is connected to a supply pipe leading to a tank, which stabilizes the pressure and provides water during the leakage experiment. This supply pipe includes a supply pump and a flow sensor. Additionally, pressure sensors are installed at both ends of the pump branch (i.e., pressure point B-P1 on the water supply side and B-P2 on the return side). The upper loop branches are labeled S-Z1 to S-Z3, while the lower loop branches are labeled X-Z1 to X-Z5. Each branch is equipped with a pressure point and a flow sensor to measure the pressure and flow rates at both the supply and return ends.

The leakage conditions for the site experiment are outlined in

Table 4. Tests on different leakage locations and leakage flow rates.

Leakage Test No.	Leakage Test 1	Leakage Test 2	Leakage Test 3	Leakage Test 4
Leakage branch	S-Z2	X-Z2	S-Z2	X-Z2
Leakage position	Supply side	Supply side	Return side	Return side
Leakage flow (m3/h)	0.2	0.58	0.2	0.3

, detailing leakage locations and flow rates. The model validation process is as follows. First, a simulation model of the Zone 6 pipe network was established (see Figure 7), and the resistance coefficients, pipe roughness, and other parameters were adjusted based on measured values during normal operating conditions, as described in Section 2. Hydraulic calculations were then performed under various leakage scenarios. The leakage simulation model is depicted in Figure 8.

As shown in Figure 9, the errors between the simulation results and actual measurements are all within 4%, indicating that the model closely aligns with the actual system and accurately reflects the hydraulic state under leakage conditions.

5. Calculations Results and Leakage Diagnosis of the Closed Pipe Network System

Zone 1 of the closed chilled water pipe network system was used to simulate the leakage and validate the leakage diagnosis scheme since this zone has a higher density and a greater number of branches. This zone allows for a more comprehensive analysis of pressure variation rates at each measurement point when a leakage occurs. The selected leakage locations are depicted in Figure 5. A leakage point is set up on the water supply side (supply side of branch X-Z3) and on the return side (return side of branch X-Z6) of the different branches, respectively. This arrangement enables us to analyze the distinct patterns of leakages occurring on the water supply side versus the water return side. It is worth noting that only one leakage point occurrence at a time is considered since two or more leakages rarely occur simultaneously in typical scenarios. Therefore, the diagnosis and analysis are confined to examining one point leakage at a time to ensure the clarity of the results.

5.1. Leakage Diagnosis at the Supply End of the Branch

The leakage is imposed on the water supply side of the X-Z3 branch at the entrance of the terminal user, as shown in Figure 5. Following the approach outlined in Section 4.4, a negative flow source is used to simulate the leakage.

Figure 10 illustrates the variation rate of the pressure monitoring point when the leakage point is positioned near the water supply end of the X-Z3 branch and different leakage levels are imposed. Four leakage flow levels are considered, as shown in Table 2, representing 2%, 4%, 10%, and 20% of the total rated flow of the pipe network. It shows that there is a corresponding pressure decrease at both the supply end (pressure points P1, P3, etc.) and the return end (pressure points P2, P4, etc.) of all branches in the system. For the leakage flow rate f₁ of 1 m³/h, the pressure variation rate at the monitoring point P6 (located at the water supply end of X-Z3) is the highest at 1.18%, followed closely by adjacent branches (P8, P10, and P12) with rates of approximately 1.16%. When the flow rate increases to f₂ (2 m³/h), P6 again shows the highest variation rate at 2.25%, with adjacent branches displaying rates around 2.23%. At a flow rate f₃ of 5 m³/h, P6 records a variation rate of 5.86%, while the adjacent branches show rates of about 5.73%. For a flow rate f₄ of 10 m³/h, P6 reaches a peak variation rate of 12.27%, followed by adjacent branches with rates near 11.86%.

Figure 10 also shows that of the four leakage levels for different flow rates, pressure point P6 at the water supply end of the leakage branch always has the highest pressure variation rate. The pressure variation rates at monitoring points other than P6 can be categorized into three levels according to their magnitude. The first level includes the pressure monitoring points at the water supply end of the loop, where the leakage branch is located, except for the leakage branch (P8, P10, and P12); the second level includes the pressure monitoring points at the water supply end of each branch in the loops, except for the loop where the leakage branch is located (P1, P3, P13, P15, P18, and P20); and the third level includes the pressure monitoring points at the return end of all branches (P2, P4, P5, P7, P9, P11, P14, P16, P17, and P19).

The above pattern can be used to locate leakage. We sorted the pressure variation rates of all the pressure points and found that the pressure variation rates of the monitoring points located in water supply monitoring are generally greater than the pressure variation rates of the monitoring points on the return side, which can be determined to be caused by a leakage in the water supply side. The branch with the highest possibility of leakage is the branch with the largest pressure variation rate, P6. This is followed by P8, P10, and P12, which are located at the water supply end of the loop in which the leakage branch is located, except for the leakage branch. In fact, the location of the leakage is indeed the water supply end of the branch where P6 is located.

5.2. Leakage Diagnosis at the Return End of the Branch

The leakage is imposed on the return side of the X-Z6 branch, at the outlet of the terminal user, as shown in Figure 5. Following the methodology outlined in Section 4.4, a negative flow source was employed to simulate the leakage.

Figure 11 illustrates the variation rate of the pressure monitoring point when the leakage point is positioned near the return end of the branch of X-Z6 and different leakage levels are imposed. Four leakage flow levels are considered, as shown in Table 2, representing 2%, 4%, 10%, and 20% of the total rated flow of the pipe network. It shows there is a corresponding pressure decrease at both the supply end (pressure points P1, P3, etc.) and the return end (pressure points P2, P4, etc.) of all branches in the system. For the leakage flow rate f₁ of 1 m³/h, the pressure variation rate at the monitoring point P11, situated at the return end of branch X-Z6, is the highest at 1.89%, followed closely by the pressure variation rates at the return ends of adjacent branches (P9, P7, and P5), which are approximately 1.80%. When the leakage flow rate f₂ is 2 m³/h, P11 again exhibits the largest variation rate at 4.25%, with adjacent branches showing rates around 4.10%. At a flow rate f₃ of 5 m³/h, the pressure variation rate at P11 rises to 10.41%, while adjacent branches have rates of about 10.07%. For a flow rate f₄ of 10 m³/h, P11 records the highest variation rate at 20.27%, with adjacent branches displaying rates near 19.65%.

Figure 11 also shows that of the four leakage levels for different flow rates. Pressure point P11 at the return end of the leakage branch always has the highest pressure variation rate. The pressure variation rates at the other monitoring points can be categorized into three levels according to their magnitude. The first level includes the pressure monitoring points at the return end of the loop where the leakage branch is located, except for the leakage branch (P5, P7, and P9); the second level includes the pressure monitoring points at the return end of each branch in the loops, except for the loop where the leakage branch is located (P2, P4, P14, P16, P17, and P19); and the third level includes the pressure monitoring points at the supply end of all branches (P1, P3, P6, P8, P10, P12, P13, P15, P18, and P20).

The above pattern can be used to locate leakage. We sorted the pressure variation rates of all the pressure points and found that the pressure variation rates of the monitoring points located in the return monitoring are generally greater than the pressure variation rates of the monitoring points on the supply side, which can be determined to be from a leakage in the return side. The branch with the highest possibility of leakage is the branch with the largest pressure variation rate, P11. This is followed by P5, P7, and P9, which are located at the return end of the loop in which the leakage branch is located, except for the leakage branch. In fact, the location of the leakage is indeed the return end of the branch where P11 is located.

5.3. Discussion of the Threshold Selection of the Pressure Variation Rate

According to Section 3, with reference to the “design code of district heating networks” in China [41], it is generally accepted in engineering that leakage is identified when the leakage volume exceeds 4% of the total designed flow of the pipe network. For instance, in the examined pipe network, a leakage flow rate of 2 m³/h (representing 4% of the rated designed flow) results in a pressure variation rate of approximately 3% at the monitoring point. When the leakage flow rate exceeds 2 m³/h (e.g., rates f₃ and f₄, with leakage flow rates of 5 m³/s and 10 m³/s, respectively), the pressure variation rate at the measurement point increases significantly beyond 3%. Thus, a pressure variation rate of 3% can be used as the threshold for detecting the occurrence of leakage within the closed chilled water pipe network system. When the maximum variation rate of the pressure measurement points in the pipe network is found to be more than 3%, it can be determined that there is a leakage in the pipe network. When leakage is detected in the pipe network, the pressure variation rates of all pressure monitoring points are ranked in order of magnitude. If the pressure variation rate of the pressure monitoring points located on the water supply side (return side) is generally greater than that on the return side (water supply side), then it can be determined that leakage has occurred on the water supply side (return side) of the pipe network. The branch where the pressure monitoring point with the largest pressure variation rate is located is most likely to be the leakage branch, from which the leakage location can be realized.

5.4. Discussion of the Practical Feasibility and Scalability of the Diagnosis Scheme

To ensure the practical feasibility of this novel leakage diagnosis and location scheme, the relationship between sensor measurement errors and the overall diagnostic accuracy is investigated and evaluated. Many studies have indicated that sensor accuracy exerts only a minor influence on leakage diagnosis [22]. In addition, data preprocessing and noise filtering techniques can effectively reduce the impact of sensor noise on system measurement data, thereby enhancing the reliability of the measurements [45]. In this study, the novel leakage diagnosis and location scheme hinges solely on quantitative comparisons of the relative magnitude of sensor data, rather than on absolute pressure measurement. As a result, minor measurement errors do not obviously influence the data ranking of the pressure variation rate or the leak localization process. Specifically, when the detected pressure change rate exceeds 3%, a leakage is deemed to have occurred. The threshold of 3% is substantially higher than the sensor’s accuracy of 0.5% FS, which typically corresponds to leakage rates above 2 m³/h. Notably, the small sensor error does not materially affect the final determination of the leak.

The response time of the diagnosis scheme is also a key factor in its practical implementation. The response time mainly depends on the data transmission speed of the monitoring system and the computational speed of the diagnosis model. In practice, the data acquisition and transmission system operates with minimal delay (usually within a few milliseconds), ensuring real-time data availability. Meanwhile, the proposed diagnosis scheme utilizes a non-iterative algorithm with low computational complexity, which avoids the time-consuming iterative computation common to other schemes. As a result, the proposed scheme allows for rapid leakage diagnosis.

In terms of scalability, the proposed scheme relies on the relative magnitude of pressure variation rates between sensors rather than complex global data fitting or absolute precision. Additionally, it does not require iterative or training computations. As a result, the scheme can be transferred to other pipe networks without the need for re-modeling or re-training, offering a certain degree of scalability. However, to ensure effective deployment, a reasonable sensor layout is still required to capture the key pressure variation relationships.

6. Conclusions

Efficient leakage diagnosis is crucial for the timely management of faults in chilled water pipe systems, minimizing damage and ensuring the safe and stable operation of the network. This paper proposes a leak diagnosis and localization scheme based on the analysis of pressure variation rates. Hydraulic models of the pipeline network under both normal and leakage conditions are established and validated by experimental tests. By simulating the operation of the pipe network under various leakage points and flow rates, the relationship between the pressure variation rate at each node (branch end) and different leakage conditions is identified. This analysis allows for the determination of the leakage point (branch) based on the observed pressure variation rate patterns. Moreover, to accurately assess leakage, a reasonable threshold for the pressure variation rate must be established. Using a 4% leakage flow rate as a benchmark, a range of pressure variation rates is derived for each node, and a threshold is set to recognize the occurrence of leakage. The key conclusions are as follows.

(1). Taking the case of a 20% leakage flow rate of the total rated flow rate as an example, when a leak occurs at the water supply end (return end) of a branch, the pressure variation rate at the measurement point at the water supply end (return end) of the affected branch is the highest, measuring 12.27% (20.27%). This indicates the branch location of the leak. The pressure variation rates of the remaining measurement points can be categorized into three levels. The first level includes the pressure monitoring points at the water supply end (return end) of the loop where the leakage branch is located, except for the leakage branch, with rates around 11.86% (19.65%); the second level includes the pressure monitoring points at the water supply end (return end) of each branch in the loops, except for the loop where the leakage branch is located, with rates around 10.22% (16.83%); and the third level includes the pressure monitoring points at the return end (water supply end) of all branches, with rates around 9.06% (3.36%).

(2). The pressure variation rate at each node of the pipe network increases with the leakage flow rate. In this study, as the proportion of leakage flow increases from 2% to 20% of the total design flow, the maximum pressure change rate at the measurement points rises from 0.411% to 20.27%. Referring to the guidelines from the “design code of district heating networks” in China, a pressure variation rate of 3% can be used as the threshold for detecting the occurrence of leakage within the closed chilled water pipe network system.

(3). When leakage is detected in the pipe network, the pressure variation rates of all pressure monitoring points are ranked in order of magnitude. If the pressure variation rate of the pressure monitoring points located on the water supply side (return side) is generally greater than that on the return side (water supply side), then it can be determined that leakage has occurred on the water supply side (return side) of the pipe network. The branch where the pressure monitoring point with the largest pressure variation rate is located is most likely to be the leakage branch, from which the leakage location can be realized.