Fast Detection of the Single Point Leakage in Branched Shale Gas Gathering and Transportation Pipeline Network with Condensate Water

: The node pressure and flow rate along the shale gas flow process are analyzed according to the characteristics of the shale gas flow pipe network, and the non‑leaking and leaking processes of the shale gas flow pipe network are modeled separately. The changes in pressure over time along each pipe segment in the network provide new ideas for identifying leaking pipe sections. This pa‑ per uses the logarithmic value of pressure as the basis for judging whether the flow pipe network is leaking or not, according to the process of varying flow parameters resulting in the regularity of leakage. A graph of the change in pressure of the pipe section after the leak compared to the pres‑ sure of the non‑leaking section of pipe over time can be plotted, accurately identifying the specific section of pipe with the leak. The accuracy of this novel method is verified by the leakage section and statistical data of the shale gas pipeline network in situ used in this paper.


Introduction 1.Background
Rapid identification of leakage accidents in shale gas gathering and transportation pipeline networks is crucial in preventing serious consequences.Most of the research on pipeline leakage is limited to single-point or multi-point leakage identification of single pipeline, where there are relatively few studies on leakage identification of pipeline networks [1].Existing studies have conducted a lot of research in the fields of the leak acoustic wave method [2], negative pressure wave method, optical fiber leakage identification method [3,4], pipeline real-time model method [5], most of which are applied to pipeline leakage identification and rarely applied to pipeline network leakage identification.Therefore, there is an urgent need for a rapid leak detection method to detect puncture leaks caused by corrosion or perforation in the shale gas gathering and transportation network.

Related Work
At present, there are many studies interested in the leakage problems of single-phase flow pipe networks and gas-liquid two-phase flow pipe networks, but there are very few studies on single-point leakage problems in multi-phase flow pipe networks.

Leak Detection and Location of Single-Phase Flow Pipe Network
In order to improve the accuracy of gas pipeline network leak location, Wu and Lee [6] proposed an improved leak location method based on AE signals and combined an improved generalized cross-correlation location method and an attenuation-based multi-layer This paper mainly studies the identification of the leaking pipe section after a singlepoint leakage in the dendritic shale gas gathering and transportation network.First, the pressure changes after the leak of the shale gas gathering pipeline network are analyzed, and then the leaking section of the shale gas flow pipe network is preliminarily assessed.Finally, based on the rate of pressure drop, a method is proposed to quickly identify leaking pipe sections.

Problem Description and Model Assumptions
This paper focuses on the leakage identification problem of shale gas containing condensate water gathering and transportation network.The topological structure diagram of shale gas gathering and transportation network, and the schematic diagram of leakage points, are shown in Figure 1.
The pipe length, pipe diameter, leakage aperture, temperature, pressure, flow rate, gasliquid ratio and other parameters of the trunk and branch lines of the shale gas gathering, and transportation network are known.Based on the calculation of the hydraulic and thermal energy of the pipe network, the changes in pressure, temperature, liquid holdup rate, and gas and liquid flow rate of the pipe network are analyzed.Based on the rate of change in these key fluid parameters, this research proposes a method for rapid leak detection.The pipe length, pipe diameter, leakage aperture, temperature, pressure, flow rate, gas-liquid ratio and other parameters of the trunk and branch lines of the shale gas gathering, and transportation network are known.Based on the calculation of the hydraulic and thermal energy of the pipe network, the changes in pressure, temperature, liquid holdup rate, and gas and liquid flow rate of the pipe network are analyzed.Based on the rate of change in these key fluid parameters, this research proposes a method for rapid leak detection.

Transient Model for Gas-Liquid Two Phase Pipe Network Flow and Single Point Leakage
The shale gas gathering and transportation network model is established by using the control equation set of one-dimensional flow in a two-phase gas-liquid pipeline network.Then, the different leakage situations of the pipeline network are simulated, where the effects of single-point leakage in different pipeline sections on the temperature, pressure, liquid holdup, and gas-liquid flow rate of the pipeline network are separately analyzed.A three-dimensional diagram of the change in the parameters of the entire pipeline network before and after the leakage is drawn to conduct in-depth research on the leakage identification of the pipeline network.
The two-fluid model [16,17] usually contains the following six equations: the mass equation, momentum equation, and energy equation of the gas and liquid phases, respectively.In this study, a two-fluid model is established based on the following three assumptions: (1) It is a one-dimensional flow; (2) there is no axial heat conduction or heat radiation along the pipe; and (3) the liquid and gas phases have the same pressure at the same cross section of the pipe.The two-fluid model is a set of quasi-linear partial differential equations, in which the main variables are P, g  , vg, vl, ul and ug, and other parameters can be calculated from the closed relationship.
The mass conservation equation is as follows: where the subscripts l and g represent the liquid and gas phases, respectively; t is for time, s; x is the distance, m;  is the density, kg/m 3 ; v is the velocity, m/s, g  is the vapor void

Transient Model for Gas-Liquid Two Phase Pipe Network Flow and Single Point Leakage
The shale gas gathering and transportation network model is established by using the control equation set of one-dimensional flow in a two-phase gas-liquid pipeline network.Then, the different leakage situations of the pipeline network are simulated, where the effects of single-point leakage in different pipeline sections on the temperature, pressure, liquid holdup, and gas-liquid flow rate of the pipeline network are separately analyzed.A three-dimensional diagram of the change in the parameters of the entire pipeline network before and after the leakage is drawn to conduct in-depth research on the leakage identification of the pipeline network.
The two-fluid model [16,17] usually contains the following six equations: the mass equation, momentum equation, and energy equation of the gas and liquid phases, respectively.In this study, a two-fluid model is established based on the following three assumptions: (1) It is a one-dimensional flow; (2) there is no axial heat conduction or heat radiation along the pipe; and (3) the liquid and gas phases have the same pressure at the same cross section of the pipe.The two-fluid model is a set of quasi-linear partial differential equations, in which the main variables are P, α g , v g , v l , u l and u g , and other parameters can be calculated from the closed relationship.
The mass conservation equation is as follows: where the subscripts l and g represent the liquid and gas phases, respectively; t is for time, s; x is the distance, m; ρ is the density, kg/m 3 ; v is the velocity, m/s, α g is the vapor void ratio; α 1 is the liquid void fraction; ∆ .m gl is the liquid mass transfer rate per unit volume, kg/(m 3 •s); ∆ .m lg is the mass transfer rate of gas per unit volume, kg/(m 3 •s).The momentum conservation equation is as follows: where the subscript i refers to the phase between the liquid and gas phases; P is the total pressure, Pa; S is the wall circumference in contact with the liquid or gas phase, 1/m; τ i is the shear stress between phases at the interface, Pa; τ wg and τ wl are respectively the gas phase and liquid phase shear stresses acting on the tube wall, Pa; θ is the Angle of the pipe, rad.
The energy conservation equation is as follows: where u is for inner energy; h is enthalpy, J/kg; q wg and q wl are the heat transferred from the tube wall to the liquid and gas phases, respectively, J/(m 2 •s); q i is the heat transfer exchanged at the interface, J/(m 2 •s).
Gas leakage in pipeline transportation is a complex process.After a leak occurs, the gas flows from the pipeline to the surrounding environment.During the flow process, the real gas undergoes a sudden reduction in cross-section, resulting in a Joule Thomson effect and a decrease in gas temperature.At the same time, the pressure at the leakage hole will attenuate and transmit pressure relief waves upstream and downstream of the pipeline.The huge pressure difference inside and outside the pipeline can easily generate a jet at the leakage point [18].Based on engineering practice, a pipeline large hole leakage model is selected [19], the leakage aperture size is set to 25 mm, and the backpressure at the leak hole is set at 1 atmosphere.The gas flow at the leakage hole is supersonic.At this time, the pressure, temperature, and density at various points on the same cross-section are not equal.The leakage rate of natural gas is as follows: (7) where C d is the flow coefficient of the gas at the leakage point; A h is the leakage area, m 2 ; P b is the pressure at the center point of the leak, Pa; M is the molecular weight of natural gas, kg/kmol; k is the Gas adiabatic index, dimensionless; Z is the Gas compressibility factor; T b is the temperature at the center point of the leak, K; R is the gas constant, usually taken as 8.314 kJ/(kmol k) for natural gas.
The flash method is used to calculate the physical properties of the fluid and the fluid flow inside the pipeline.Based on this, the fluid flowing process model is established, where the mutual influence of condensate and pressure is clarified.

Verification Method for the Effectiveness of Leak Detection Technology
The effectiveness of pipeline leak detection technology refers to its ability to continuously detect pipeline leaks.Currently, the most widely used and promising leak detection methods include the distributed fiber-optic method, the transient model method, and the acoustic wave method.
The distributed fiber-optic method detects leaks through the vibration and temperature changes of the soil around the leakage point.Currently, the temperature threshold method is commonly used to alert the leakage location.By using optical fibers laid along the pipeline to obtain temperature changes at various points, the difference T 0 between the temperature T and the average temperature along the pipeline is compared with the temperature threshold set by the distributed optical fiber monitoring system.If T − T 0 > 3σ, the system sounds an alarm indicating that a specific point in the pipework is leaking [20].
The temperature measurement accuracy of this method is around 1 • C, the positioning error range is within 5 m and the response time is within 5 s.
The transient model method is a method that combines flow rate and pressure to determine whether a pipeline has occurred the leakage.By simulating the changes in parameters such as temperature, pressure and flow rate at the start and end points and comparing them with the parameters before the leak.If the relative error between the two exceeds a certain threshold, it can be determined that the pipeline is leaking.Based on previous experience, a leakage rate of 4% of the internal flow rate was chosen as the flow rate threshold, and an empirical value of 0.15 MPa/min for the gas transmission main line shut-off valve was chosen as the pressure drop rate threshold [21].This method can control the leakage accuracy to about 1%.
The acoustic wave method receives and collects acoustic signals through acoustic sensors installed at both ends of the pipe.The acoustic signal is usually represented by the change in amplitude of the acoustic wave over time.After de-noising and extracting the collected wave signal, the acoustic wave amplitude without leakage is taken as the threshold value and compared with the real time acoustic signal, to determine whether leakage has occurred in the pipeline [22].When used for gas pipeline leak detection, the minimum detectable leak is 0.01% of the transported volume.For long distance pipelines, the positioning accuracy is approximately 50 m and the response time is less than 3 min.By comparing the above three pipeline leak detection technologies, the validity verification indexes, and threshold names of each detection technology are obtained as shown in Table 1.

Identification Method for Single Point Leakage in Gas-Liquid Two-Phase Flow Pipeline Network Based on Pressure Drop Rate
The NPW (negative pressure wave) produced by the leakage propagating up and down simultaneously at the speed a.The produced NPW is detected by the sensors at t and t + ∆t time, respectively, with pressure signals p u (t + ∆t) and p d (t) when l 1 > l 2 .According to the leakage data, the ∂p ∂t in the upstream and downstream are functions related to t, and the shapes of line A and B are very similar.
The sum of the pressure node values of pipe section i in the non-leaking pipe network is ∑ P 0 (i), while in the leaking pipe network, it is ∑ P t (i).The average value of the pressure node value of pipe section i in the non-leaking pipe network is ∑ P 0(i) , while in the leaking pipe network, it is ∑ P t(i) .Therefore, when the leakage time is t, the pressure drop in pipe section i in the pipe network is: where i represents a certain pipe section in the pipe network; t represents the leakage time of the pipe network; N t (i) represents the pressure change range of the pipe section i after the leakage time t.After the sum of the pressure node values of pipe section i with different leakage time t being simulated, the pressure change range N t (i) of pipe section i is then calculated.The leakage time log(t) and N t (i) are applied to plot the pressure variation amplitude curve of the pipe section with leaked point after leakage.Then, the change amplitude curve is shown in Figure 2.
where i represents a certain pipe section in the pipe network; t represents the leakage time of the pipe network; Nt(i) represents the pressure change range of the pipe section i after the leakage time t.After the sum of the pressure node values of pipe section i with different leakage time t being simulated, the pressure change range Nt(i) of pipe section i is then calculated.The leakage time log(t) and Nt(i) are applied to plot the pressure variation amplitude curve of the pipe section with leaked point after leakage.Then, the change amplitude curve is shown in Figure 2.

Application Example of Leaking Pipe Segment Identification Method Based on Pressure Drop Rate
The non-leakage pipeline network and single-point leakage pipeline network models of gas-liquid two-phase flow are established.The selected block is a gathering and transportation network consisting of seven pipelines.The basic parameters of the network are shown in Table 2.The annual average surface temperature of this block is 273 K and the initial conditions of the pipe network are shown in Table 3.The boundary conditions and initial conditions used for establishing the pipeline model are shown in the Table 4.

Application Example of Leaking Pipe Segment Identification Method Based on Pressure Drop Rate
The non-leakage pipeline network and single-point leakage pipeline network models of gas-liquid two-phase flow are established.The selected block is a gathering and transportation network consisting of seven pipelines.The basic parameters of the network are shown in Table 2.The annual average surface temperature of this block is 273 K and the initial conditions of the pipe network are shown in Table 3.The boundary conditions and initial conditions used for establishing the pipeline model are shown in the Table 4. 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 Table 4. Boundary conditions and initial conditions.

Parameter Equation
Energies 2024, 17, 2464 The transmission fluid of the pipeline network is shale gas and water.Two single point leakage models of pipe section 4 and pipe section 7 are constructed using the given initial conditions and basic parameters of the pipe network (shown in Figure 3), respectively.Both pipe section 4 and pipe section 7 leak at 500 m, where the leak hole diameter is 25 mm, and the leak time is 10 min.The one-dimensional flow control equations are used to calculate the two leakage conditions of the pipe network, giving the changes in pressure, temperature, liquid holdup, and gas-liquid flow rate of the leaking pipe section and the entire pipe network before and after the leakage.

Export Boundary Conditions
, , ) The transmission fluid of the pipeline network is shale gas and water.Two singl point leakage models of pipe section 4 and pipe section 7 are constructed using the give initial conditions and basic parameters of the pipe network (shown in Figure 3), respec tively.Both pipe section 4 and pipe section 7 leak at 500 m, where the leak hole diamete is 25 mm, and the leak time is 10 min.The one-dimensional flow control equations ar used to calculate the two leakage conditions of the pipe network, giving the changes i pressure, temperature, liquid holdup, and gas-liquid flow rate of the leaking pipe sectio and the entire pipe network before and after the leakage.The pressure changes in pipe section 4 and pipe section 7 before and after the leak occurred are shown in Figures 4 and 5, respectively.The pressure in the pipe sections before and after the leak is reduced, and the pressure after the leak is lower than before the leak.The pressure of pipe section 4 decreases from 0.69 MPa to 0.45 MPa before the leak, and the pressure decreases from 0.65 MPa to 0.45 MPa after the leak.The pressure in pipe section 7 drops from 0.44 MPa to 0.36 MPa before the leak, and from 0.43 MPa to 0.35 MPa after the leak.
Energies 2024, 17, x FOR PEER REVIEW

The Law of Pressure Change
The pressure changes in pipe section 4 and pipe section 7 before and after occurred are shown in Figures 4 and 5, respectively.The pressure in the pipe before and after the leak is reduced, and the pressure after the leak is lower tha the leak.The pressure of pipe section 4 decreases from 0.69 MPa to 0.45 MPa be leak, and the pressure decreases from 0.65 MPa to 0.45 MPa after the leak.The pre pipe section 7 drops from 0.44 MPa to 0.36 MPa before the leak, and from 0.43 MP MPa after the leak.

The Law of Temperature Change
The temperature changes in pipe section 4 and pipe section 7 before and leakage occurred are shown in Figures 6 and 7, respectively.The temperature a pipe network before and after the leak is reduced, and the temperature after th lower than before the leak.The temperature of pipe section 4 dropped from 31.8 ° °C before the leak and from 31.7 °C to 26.2 °C after the leak.The temperature section 7 dropped from 26.7 °C to 23.9 °C before the leak and from 26.3 °C to 23.1 the leak.

The Law of Temperature Change
The temperature changes in pipe section 4 and pipe section 7 before and after the leakage occurred are shown in Figures 6 and 7, respectively.The temperature along the pipe network before and after the leak is reduced, and the temperature after the leak is lower than before the leak.The temperature of pipe section 4 dropped from 31.The changes in liquid holdup of the pipe sections before and after the leak in section 4 and pipe section 7 are shown in Figures 8 and 9, respectively.The liquid hol  The changes in liquid holdup of the pipe sections before and after the leak in section 4 and pipe section 7 are shown in Figures 8 and 9, respectively.The liquid ho The changes in liquid holdup of the pipe sections before and after the leak in pipe section 4 and pipe section 7 are shown in Figures 8 and 9, respectively.The liquid holdup of the pipe section before and after the leak shows a general downward trend, and the liquid holdup after the leak is lower than before the leak.

Change Law of Liquid Holdup
The changes in liquid holdup of the pipe sections before and after section 4 and pipe section 7 are shown in Figures 8 and 9, respectively.Th of the pipe section before and after the leak shows a general downward liquid holdup after the leak is lower than before the leak.

The Law of Gas Flow Rate Change
The changes in gas flow velocity in the pipe sections before and afte section 4 and pipe section 7 are shown in Figures 10 and 11, respectively. of the pipe network before and after the leak shows an overall upwar velocity increases from 23.5 m/s to 36.2 m/s before the leak in pipe sectio from 25.4 m/s to 29.6 m/s after the leak, with a sudden change at the 50 velocity increases from 26.7 m/s to 32.8 m/s before the leak in pipe sectio from 27.5 m/s to 32.1 m/s after the leak, which also shows a sudden cha leak.

The Law of Gas Flow Rate Change
The changes in gas flow velocity in the pipe sections before and after the leak in pipe section 4 and pipe section 7 are shown in Figures 10 and 11, respectively.The gas flow rate of the pipe network before and after the leak shows an overall upward trend.The gas velocity increases from 23.5 m/s to 36.2 m/s before the leak in pipe section 4 and increases from 25.4 m/s to 29.6 m/s after the leak, with a sudden change at the 500 m leak.The gas velocity increases from 26.7 m/s to 32.8 m/s before the leak in pipe section 7 and increases from 27.5 m/s to 32.1 m/s after the leak, which also shows a sudden change at the 500 m leak.
velocity increases from 23.5 m/s to 36.2 m/s before the leak in pipe section 4 and incre from 25.4 m/s to 29.6 m/s after the leak, with a sudden change at the 500 m leak.The velocity increases from 26.7 m/s to 32.8 m/s before the leak in pipe section 7 and incre from 27.5 m/s to 32.1 m/s after the leak, which also shows a sudden change at the 5 leak.

The Law of Change in Liquid Flow Rate
The changes in liquid flow rate in the pipe sections before and after the leak in section 4 and pipe section 7 are shown in Figures 12 and 13  velocity increases from 23.5 m/s to 36.2 m/s before the leak in pipe section 4 and incre from 25.4 m/s to 29.6 m/s after the leak, with a sudden change at the 500 m leak.Th velocity increases from 26.7 m/s to 32.8 m/s before the leak in pipe section 7 and incre from 27.5 m/s to 32.1 m/s after the leak, which also shows a sudden change at the 5 leak.

The Law of Change in Liquid Flow Rate
The changes in liquid flow rate in the pipe sections before and after the leak in section 4 and pipe section 7 are shown in Figures 12 and 13

The Law of Change in Liquid Flow Rate
The changes in liquid flow rate in the pipe sections before and after the leak in pipe section 4 and pipe section 7 are shown in Figures 12 and 13 respectively.The liquid flow rate before and after the leak shows an overall downward trend, and the liquid flow rate after the leak is lower than before the leak.
Energies 2024, 17, x FOR PEER REVIEW 11 o rate before and after the leak shows an overall downward trend, and the liquid flow after the leak is lower than before the leak.

The Law of Pressure Changes along the Pipeline
The changes in the network pressure before and after the leakage of pipe section and pipe section 7 are shown in Figures 14 and 15.The pressure of all pipe sections befor and after the leakage decreased, and the pressure after the leak was lower than that befor the leak, especially the pressure drop of the leaking pipe section is greater than that of th other non-leaking pipe sections.Numbers 1-7 represent the numbering of each pipe seg ment in the pipeline network.Same as Figures 15-23   The changes in the network pressure before and after the leakage of pipe section 4 and pipe section 7 are shown in Figures 14 and 15.The pressure of all pipe sections before and after the leakage decreased, and the pressure after the leak was lower than that before the leak, especially the pressure drop of the leaking pipe section is greater than that of the other non-leaking pipe sections.Numbers 1-7 represent the numbering of each pipe segment in the pipeline network.Same as Figures 15-23

The Law of Pressure Changes along the Pipeline
The changes in the network pressure before and after the leakage of pipe section 4 and pipe section 7 are shown in Figures 14 and 15.The pressure of all pipe sections before and after the leakage decreased, and the pressure after the leak was lower than that before the leak, especially the pressure drop of the leaking pipe section is greater than that of the other non-leaking pipe sections.Numbers 1-7 represent the numbering of each pipe segment in the pipeline network.Same as Figures 15-23  The temperature changes in the pipe network before and after the leak in pipe section 4 and pipe section 7 are shown in Figures 16 and 17.The temperature of all pipe sections decreased before and after the leak, and the temperature decrease trend after the leak is

The Law of Temperature Changes along the Pipeline
The temperature changes in the pipe network before and after the leak in pipe section 4 and pipe section 7 are shown in Figures 16 and 17.The temperature of all pipe sections decreased before and after the leak, and the temperature decrease trend after the leak is the same as before the leak.

The Law of Temperature Changes along the Pipeline
The temperature changes in the pipe network before and after the leak in pipe section 4 and pipe section 7 are shown in Figures 16 and 17.The temperature of all pipe sections decreased before and after the leak, and the temperature decrease trend after the leak is the same as before the leak.

The Law of Liquid Holdup Changes along the Pipeline
The change rule of the liquid holdup of the pipe network before and after the leak of pipe section 4 and pipe section 7 is shown in Figures 18 and 19.The liquid holdup rate

The Law of Temperature Changes along the Pipeline
The temperature changes in the pipe network before and after the leak in pipe section 4 and pipe section 7 are shown in Figures 16 and 17.The temperature of all pipe sections decreased before and after the leak, and the temperature decrease trend after the leak is the same as before the leak.

The Law of Liquid Holdup Changes along the Pipeline
The change rule of the liquid holdup of the pipe network before and after the leak of pipe section 4 and pipe section 7 is shown in Figures 18 and 19.The liquid holdup rate

The Law of Liquid Holdup Changes along the Pipeline
The change rule of the liquid holdup of the pipe network before and after the leak of pipe section 4 and pipe section 7 is shown in Figures 18 and 19.The liquid holdup rate before and after the leak showed a downward trend, and the liquid holdup rate after the leak is slightly lower than before the leak.
Energies 2024, 17, x FOR PEER REVIEW 13 of 17 before and after the leak showed a downward trend, and the liquid holdup rate after the leak is slightly lower than before the leak.

The Gas Flow Rate Changes along the Pipeline
The change rule of the gas flow rate of the pipe network before and after the leakage of pipe section 4 and pipe section 7 is shown in Figures 20 and 21.The gas flow rate before and after the leak showed an upward trend.The gas flow rate at the leak point of the leaking pipe section shows a sudden change.The gas flow rate before the leak is higher than without the leak and the gas flow rate after the leak is lower than without the leak.

The Gas Flow Rate Changes along the Pipeline
The change rule of the gas flow rate of the pipe network before and after the leakage of pipe section 4 and pipe section 7 is shown in Figures 20 and 21.The gas flow rate before and after the leak showed an upward trend.The gas flow rate at the leak point of the leaking pipe section shows a sudden change.The gas flow rate before the leak is higher than without the leak and the gas flow rate after the leak is lower than without the leak.

The Gas Flow Rate Changes along the Pipeline
The change rule of the gas flow rate of the pipe network before and after the leakage of pipe section 4 and pipe section 7 is shown in Figures 20 and 21.The gas flow rate before and after the leak showed an upward trend.The gas flow rate at the leak point of the leaking pipe section shows a sudden change.The gas flow rate before the leak is higher than without the leak and the gas flow rate after the leak is lower than without the leak.

The Law of Liquid Flow Rate Change along the Pipeline
The change rule of the liquid flow rate of the pipe network before and after the leakage of pipe section 4 and pipe section 7 is shown in Figures 22 and 23.The liquid flow rate before and after the leak shows a downward trend, and the total change trend of the liquid flow rate after the leak is the same as before the leak.

The Law of Liquid Flow Rate Change along the Pipeline
The change rule of the liquid flow rate of the pipe network before and after the leakage of pipe section 4 and pipe section 7 is shown in Figures 22 and 23.The liquid flow rate before and after the leak shows a downward trend, and the total change trend of the liquid flow rate after the leak is the same as before the leak.

Identify Leaking Pipe Section Based on Pressure Changes
After a pipeline leak occurs, the parameters of the pipeline network will change accordingly.According to the pressure changes in the pipeline network, it can be seen that the pressure changed in the leaking pipe section are significantly higher than those of other non-leaking pipe sections.And the gas flow rate of the leaking pipe section will

The Law of Liquid Flow Rate Change along the Pipeline
The change rule of the liquid flow rate of the pipe network before and after the leakage of pipe section 4 and pipe section 7 is shown in Figures 22 and 23.The liquid flow rate before and after the leak shows a downward trend, and the total change trend of the liquid flow rate after the leak is the same as before the leak.

Identify Leaking Pipe Section Based on Pressure Changes
After a pipeline leak occurs, the parameters of the pipeline network will change accordingly.According to the pressure changes in the pipeline network, it can be seen that the pressure changed in the leaking pipe section are significantly higher than those of other non-leaking pipe sections.And the gas flow rate of the leaking pipe section will

Identify Leaking Pipe Section Based on Pressure Changes
After a pipeline leak occurs, the parameters of the pipeline network will change accordingly.According to the pressure changes in the pipeline network, it can be seen that the pressure changed in the leaking pipe section are significantly higher than those of other non-leaking pipe sections.And the gas flow rate of the leaking pipe section will undergo an obvious sudden change after pipe section 4 or pipe section 7 leaks.This allows a preliminary assessment of the leaking section of pipe.
It can be seen from Figure 24 that pipe section 4 intersects the horizontal axis first, indicating that the pressure of pipe section 4 decreases the fastest with time, which also verifies that pipe section 4 is a leaking pipe section.The amplitude of the pressure changes of pipe section 7 before and after the leak is the same as that of pipe section 4, which verifies the accuracy of identifying the leaking pipe section based on the pressure change amplitude.
It can be seen from Figure 24 that pipe section 4 intersects the horizontal axis first, indicating that the pressure of pipe section 4 decreases the fastest with time, which also verifies that pipe section 4 is a leaking pipe section.The amplitude of the pressure changes of pipe section 7 before and after the leak is the same as that of pipe section 4, which verifies the accuracy of identifying the leaking pipe section based on the pressure change amplitude.It can be seen from Figure 25 that the pipe section 7 and the horizontal axis intersect first, indicating that the pipe section 7 is a leaking pipe section, which also verifies that the leaking pipe section can be identified based on the speed of pressure change with time before and after the leak.At the same time, from the intersection of each pipe section with the abscissa, it can be seen that when pipe section 4 leaks, the pressure starts to drop 31.5% earlier than the other non-leaking pipe sections.When pipe section 7 leaks, the pressure starts to drop 20.7% earlier than other non-leaking pipe sections.It can be concluded that the time at which the pressure of the leaking pipe section starts to drop is more than 20% earlier than that of the non-leaking pipe section according to the analysis.It can be seen from Figure 25 that the pipe section 7 and the horizontal axis intersect first, indicating that the pipe section 7 is a leaking pipe section, which also verifies that the leaking pipe section can be identified based on the speed of pressure change with time before and after the leak.At the same time, from the intersection of each pipe section with the abscissa, it can be seen that when pipe section 4 leaks, the pressure starts to drop 31.5% earlier than the other non-leaking pipe sections.When pipe section 7 leaks, the pressure starts to drop 20.7% earlier than other non-leaking pipe sections.It can be concluded that the time at which the pressure of the leaking pipe section starts to drop is more than 20% earlier than that of the non-leaking pipe section according to the analysis.
It can be seen from Figure 24 that pipe section 4 intersects the horizontal axis first, indicating that the pressure of pipe section 4 decreases the fastest with time, which also verifies that pipe section 4 is a leaking pipe section.The amplitude of the pressure changes of pipe section 7 before and after the leak is the same as that of pipe section 4, which verifies the accuracy of identifying the leaking pipe section based on the pressure change amplitude.It can be seen from Figure 25 that the pipe section 7 and the horizontal axis intersect first, indicating that the pipe section 7 is a leaking pipe section, which also verifies that the leaking pipe section can be identified based on the speed of pressure change with time before and after the leak.At the same time, from the intersection of each pipe section with the abscissa, it can be seen that when pipe section 4 leaks, the pressure starts to drop 31.5% earlier than the other non-leaking pipe sections.When pipe section 7 leaks, the pressure starts to drop 20.7% earlier than other non-leaking pipe sections.It can be concluded that the time at which the pressure of the leaking pipe section starts to drop is more than 20% earlier than that of the non-leaking pipe section according to the analysis.

Conclusions
As this shale gas is a water-bearing (wet) shale gas, it flows in a gas-liquid two-phase flow in the pipeline network.As the gas pipeline is a very complex, non-linear, timevarying system, it is difficult to achieve satisfactory results using traditional methods for leak detection in pipeline networks.The use of the single-point leakage parameter change law of the pipe network to identify the leaking pipe sections in the pipe network is of great importance for maintaining pipeline safety, protecting human life and property safety, saving energy and reducing environmental pollution.Therefore, the accuracy of the pipe network leakage identification method based on the pressure drop rate model is effective to Energies 2024, 17, 2464 16 of 17 achieve the desired effect.Based on detailed theoretical research and actual field conditions, the following main conclusions can be drawn: (1) By analyzing the law of change before and after leakage of these parameters such as pressure, temperature, liquid holdup, and gas-liquid flow rate, it is found that the pressure at the leak point in the leaking section of pipe changes suddenly.In addition, the pressure of the leaking section of pipe changes more than other non-leaking sections of pipe, which can help to identify leaking sections of pipe in the network early on.
(2) Based on the example of gas-liquid two-phase flow pipe network, the pressure change rate model is used to make the pressure change amplitude curve after leakage, which can identify the leakage pipe section more quickly and accurately.
(3) The statistical data of the shale gas gathering and transportation network verified the correctness of the method of identifying the leaking pipe section using the proposed method, where the start time of the pressure drop of the leaking pipe section is more than 20% earlier than the non-leaking pipe section.

Figure 1 .
Figure 1.Topological structure diagram of shale gas gathering and transportation pipeline network and leakage schematic diagram of pipeline section 1.

Figure 1 .
Figure 1.Topological structure diagram of shale gas gathering and transportation pipeline network and leakage schematic diagram of pipeline section 1.

Figure 2 .
Figure 2. Pressure variation amplitude curve of the pipe section with leaked point after leakage.

Figure 2 .
Figure 2. Pressure variation amplitude curve of the pipe section with leaked point after leakage.

Figure 3 .
Figure 3. Single point leakage model of pipe section 4 or pipe section 7.

Figure 3 .
Figure 3. Single point leakage model of pipe section 4 or pipe section 7.

3. 1 .
Change Rule of Pipeline Parameters before and after Leakage 3.1.1.The Law of Pressure Change

Figure 4 .
Figure 4. Law of pressure change before and after leakage of pipe section 4.

Figure 4 .
Figure 4. Law of pressure change before and after leakage of pipe section 4.

Figure 4 .
Figure 4. Law of pressure change before and after leakage of pipe section 4.

Figure 5 .
Figure 5. Law of pressure change before and after leakage of pipe section 7.

Figure 5 .
Figure 5. Law of pressure change before and after leakage of pipe section 7.

9 Figure 6 .
Figure 6.Temperature changes before and after leakage in pipe section 4.

Figure 7 .
Figure 7. Temperature changes before and after leakage in pipe section 7.

Figure 6 .Figure 6 .
Figure 6.Temperature changes before and after leakage in pipe section 4.

Figure 7 .
Figure 7. Temperature changes before and after leakage in pipe section 7.

Figure 7 . 3 .
Figure 7. Temperature changes before and after leakage in pipe section 7.

Figure 7 .
Figure 7. Temperature changes before and after leakage in pipe section 7.

Figure 8 .
Figure 8. Changes in liquid holdup before and after leakage in pipe section 4.

Figure 8 .Figure 9 .
Figure 8. Changes in liquid holdup before and after leakage in pipe section 4.

Figure 9 .
Figure 9. Changes in liquid holdup before and after leakage in pipe section 7.

Figure 10 .
Figure 10.Changes in gas flow velocity before and after leakage in pipe section 4.

Figure 11 .
Figure 11.Changes in gas flow velocity before and after leakage in pipe section 7.

Figure 10 .
Figure 10.Changes in gas flow velocity before and after leakage in pipe section 4.

Figure 10 .
Figure 10.Changes in gas flow velocity before and after leakage in pipe section 4.

Figure 11 .
Figure 11.Changes in gas flow velocity before and after leakage in pipe section 7.

Figure 11 .
Figure 11.Changes in gas flow velocity before and after leakage in pipe section 7.

Figure 12 .
Figure 12.Changes in liquid flow velocity before and after leakage in pipe section 4.

Figure 12 . 17 Figure 12 .
Figure 12.Changes in liquid flow velocity before and after leakage in pipe section 4.

Figure 13 .
Figure 13.Changes in liquid flow velocity before and after leakage in pipe section 7. .

Figure 14 .Figure 13 .
Figure 14.Changes in pressure in pipeline network before and after the leakage happened in pip section 4.

3. 2 .
Changes in the Parameters of the Entire Pipeline Network before and after the Leak 3.2.1.The Law of Pressure Changes along the Pipeline .

Figure 12 .
Figure 12.Changes in liquid flow velocity before and after leakage in pipe section 4.

Figure 13 .
Figure 13.Changes in liquid flow velocity before and after leakage in pipe section 7. .

Figure 14 .Figure 14 . 17 Figure 15 .
Figure 14.Changes in pressure in pipeline network before and after the leakage happened in pipe section 4.

Figure 15 .
Figure 15.Changes in pressure in pipeline network before and after the leakage happened in pipe section 7.

Figure 15 .
Figure 15.Changes in pressure in pipeline network before and after the leakage happened in pipe section 7.

Figure 16 .
Figure 16.Change in temperature in pipeline network before and after leakage happened in pipe section 4.

Figure 17 .
Figure 17.Change in temperature in the pipeline network before and after the leakage happened in pipe section 7.

Figure 16 .
Figure 16.Change in temperature in pipeline network before and after leakage happened in pipe section 4.

Figure 15 .
Figure 15.Changes in pressure in pipeline network before and after the leakage happened in pipe section 7.

Figure 16 .
Figure 16.Change in temperature in pipeline network before and after leakage happened in pipe section 4.

Figure 17 .
Figure 17.Change in temperature in the pipeline network before and after the leakage happened in pipe section 7.

Figure 17 .
Figure 17.Change in temperature in the pipeline network before and after the leakage happened in pipe section 7.

Figure 18 .
Figure 18.Changes in liquid holdup in pipeline network before and after the leakage happened in pipe section 4.Figure 18. Changes in liquid holdup in pipeline network before and after the leakage happened in pipe section 4.

Figure 18 .
Figure 18.Changes in liquid holdup in pipeline network before and after the leakage happened in pipe section 4.Figure 18. Changes in liquid holdup in pipeline network before and after the leakage happened in pipe section 4.

Figure 18 .
Figure 18.Changes in liquid holdup in pipeline network before and after the leakage happened in pipe section 4.

Figure 19 .
Figure 19.Changes in liquid holdup in pipeline network before and after the leakage happened in pipe section 7.

Figure 20 .
Figure 20.Changes in gas flow rate in pipeline network before and after the leakage happened in pipe section 4.

Figure 19 .
Figure 19.Changes in liquid holdup in pipeline network before and after the leakage happened in pipe section 7.

Figure 18 .
Figure 18.Changes in liquid holdup in pipeline network before and after the leakage happened in pipe section 4.

Figure 19 .
Figure 19.Changes in liquid holdup in pipeline network before and after the leakage happened in pipe section 7.

Figure 20 .
Figure 20.Changes in gas flow rate in pipeline network before and after the leakage happened in pipe section 4.Figure 20.Changes in gas flow rate in pipeline network before and after the leakage happened in pipe section 4.

Figure 20 . 17 Figure 21 .
Figure 20.Changes in gas flow rate in pipeline network before and after the leakage happened in pipe section 4.Figure 20.Changes in gas flow rate in pipeline network before and after the leakage happened in pipe section 4. Energies 2024, 17, x FOR PEER REVIEW 14 of 17

Figure 21 .
Figure 21.Changes in gas flow rate in pipeline network before and after the leakage happened in pipe section 7.

Figure 21 .
Figure 21.Changes in gas flow rate in pipeline network before and after the leakage happened in pipe section 7.

Figure 22 .
Figure 22.Change in liquid flow rate in pipeline network before and after leakage happened in pipe section 4.

Figure 23 .
Figure 23.Change in liquid flow rate in pipeline network before and after leakage happened in pipe section 7.

Figure 22 .
Figure 22.Change in liquid flow rate in pipeline network before and after leakage happened in pipe section 4.

Figure 21 .
Figure 21.Changes in gas flow rate in pipeline network before and after the leakage happened in pipe section 7.

Figure 22 .
Figure 22.Change in liquid flow rate in pipeline network before and after leakage happened in pipe section 4.

Figure 23 .
Figure 23.Change in liquid flow rate in pipeline network before and after leakage happened in pipe section 7.

Figure 23 .
Figure 23.Change in liquid flow rate in pipeline network before and after leakage happened in pipe section 7.

Figure 24 .
Figure 24.Pressure variation amplitude of each pipe segment in the pipeline network with time after leakage of pipe segment 4.

Figure 25 .Figure 24 .
Figure 25.Pressure variation amplitudes of each pipe segment in the pipeline network with time after leakage of pipe segment 7.

Figure 24 .
Figure 24.Pressure variation amplitude of each pipe segment in the pipeline network with time after leakage of pipe segment 4.

Figure 25 .
Figure 25.Pressure variation amplitudes of each pipe segment in the pipeline network with time after leakage of pipe segment 7.

Figure 25 .
Figure 25.Pressure variation amplitudes of each pipe segment in the pipeline network with time after leakage of pipe segment 7.

Table 1 .
Threshold value of validity verification method of leakage detection technology.

Table 2 .
Parameters of the pipe network.

Table 3 .
Initial conditions of the pipe network.