A Novel Method For Transient Leakage Flow Rate Calculation of Gas Transmission Pipelines
A Novel Method For Transient Leakage Flow Rate Calculation of Gas Transmission Pipelines
A Novel Method For Transient Leakage Flow Rate Calculation of Gas Transmission Pipelines
A novel method for transient leakage flow rate calculation of gas transmission
pipelines
Qian Chen, Xiaokai Xing, Can Jin, Lili Zuo, Jianhang Wu, Weishuo Wang
PII: S1875-5100(20)30115-3
DOI: https://doi.org/10.1016/j.jngse.2020.103261
Reference: JNGSE 103261
Please cite this article as: Chen, Q., Xing, X., Jin, C., Zuo, L., Wu, J., Wang, W., A novel method for
transient leakage flow rate calculation of gas transmission pipelines, Journal of Natural Gas Science &
Engineering, https://doi.org/10.1016/j.jngse.2020.103261.
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transmission pipelines
Qian Chen1, Xiaokai Xing1*, Can Jin1, Lili Zuo1, Jianhang Wu1, Weishuo Wang2
1. National Engineering Laboratory for Pipeline Safety/Beijing Key Laboratory of Urban Oil and
2. China Sinopec Sales Co., Ltd. Beijing Oil Branch, Building 6, Guangqu Jiayuan, Dongcheng,
Beijing
Abstract
To objectively evaluate the consequences of the pipeline leakage and ensure the
safe operation and reliable gas supply of the gas pipeline, it is necessary to calculate
the leakage flow rate variations. A novel model for transient leakage flow rate
calculation of gas transmission pipelines is proposed in this paper. Based on the
pressure data collected at the upstream and downstream block valve rooms of the
leakage position, the time for alarm signal and closure signal of block valves can be
determined, and the leakage orifice can be calculated by iterative method based on the
collected data of the block valve rooms from alarm signal to closure signal. The
leakage process is divided into two stages according to the time when the leakage
occurred and two block valves were automatically closed, and the leakage flow rate at
each stage is calculated based on the characteristic line method. The proposed method
is applied to a real gas transmission pipeline in China, and the minimum detectable
leakage orifice at different locations is calculated and sensitivity analyses of leakage
location on leakage flow rate calculation are conducted in detail.
1
Keywords
Gas pipelines; Transient leakage flow rate; Pressure drop rate; Characteristic line
method; Leakage orifice calculation
Nomenclature
1. Introduction
4
Leakage flow rate calculation models of gas pipelines based on steady state are
mainly divided into three types: hole model, pipe model and Hole–pipe generalized
model, which are characterized by the assumption that the operation pressure in the
gas pipeline does not change with time after leakage.
Levenspiet (2014) was the first to give the calculation model of the leakage rate
of the tank–nozzle–pipe system. After that, Crowl et al. (2011) deduced the
calculation model of leakage flow rate at small orifice for gas pipeline based on
assumptions that the pressure in the pipeline does not change with time during
leakage process and the leakage process is an isentropic expansion process. Catin et al.
(1998) calculated the leakage flow rate of gas transmission pipelines based on fluid
mechanics and characteristic line method, and this model is only suitable for scenarios
that the pipeline was completely ruptured. Young et al. (2003) propose a simplified
model to estimate the leakage flow rate of the high-pressure gas pipeline, which
consists of a correction factor considering the pressure drop due to the wall friction
loss. The mode has some positive deviation from the theoretical complex equations
(ranges from about 0 up to 20%). Montiel (1998) proposed a new model based on
fundamental equations of fluid mechanics, this model is developed as a combination
of the classical ‘hole’ and ‘pipe’ models which can be applied to small hole in a tank
or a pipe and full-bore holes at medium and low pressures. Based on Montiel’s model,
Huo (2004) and Wang (2008) proposed a new model for the leakage hole diameter
that lies between the small hole and complete rupture for high-pressure gas pipelines.
At present, the application scope of these three models has not formed a unified
conclusion. Among them, the most reliable method is the classification of natural gas
pipeline leakage accidents proposed by the European Gas pipeline Incident data
Group: The leakage orifice less than 20mm is a small hole leakage, the leakage orifice
larger than 20mm and smaller than the pipe diameter is a large hole leakage and the,
leakage orifice close to the pipe diameter is pipe broken leakage. Some authors
suggest that the ratio of the leakage orifice to the pipe diameter should be used to
classify of natural gas pipeline leakage accidents and calculate the leakage flow rate.
5
In short, the leakage flow rate calculation methods of gas pipelines based on
steady state are relatively mature. The modeling processes are also based on a series
of assumptions, and the definition of small holes or large holes needs further study
based on flow mechanism of leakage.
(2) Research status of leakage flow rate of gas pipelines based on transient state
At present, there are relatively few studies about leakage flow rate of gas
pipelines based on the transient state. When a leakage scenario is detected somewhere
in the pipeline, the block valves located upstream and downstream of the leakage
position will automatically closed, and the operational pressure in the leaking pipe
segment will decrease continuously, and the leakage rate will change accordingly.
Woodward et al. (1991) put forward the leakage flow rate calculation model of
the pressure vessel and gave the quantitative function of pressure variations in the
vessel. According to the relationship between the pressure of the gas pipeline and the
critical leakage pressure, the flow pattern at the orifice can be determined, and
leakage flow rate can be calculated based on corresponding formulas. Cui et al. (2010)
established a transient gas pipeline leakage rate calculation model. Like the model
based on the steady state, it only takes the flow characteristics of leakage hole into
consideration based on fluid mechanics, but does not take the transient gas flow in the
pipeline after leakage. Zhang et al. (2009) established the transient leakage flow rate
calculation model based on the continuity equation, and calculated the transient
leakage process of the gas pipeline after the gas source is cut off based on the
fourth-order Runge-Kuta method. Some more advanced and efficient semi-analytical
methods based on Adomian decomposition for solving these governing equations are
proposed by some researchers in recent years (Singh et al. 2016; Hasan et al. 2004;
Fatoorehchi et al. 2017; Fatoorehchi et al. 2019). Reza et.al (2014) proposed a mass
discharge function to simulate the dimensionless transient gas release rate parameters
in a ruptured gas pipeline.
The research on leakage flow rate calculation based on the transient state is
mainly carried out based on the process of venting processes of the gas in the pipeline
6
after the closure of the upstream and downstream block valves. The difficulty of
transient leakage flow rate calculation is to establish a mathematical model for a
specific leakage process and solve it by numerical algorithm.
In summary, many existing literatures often take the leakage orifice as a known
parameter when establishing the calculation model of leakage flow rate. In fact, when
the leakage occurs in the pipeline, it is difficult to get the actual leakage orifice in the
first time. And the steady-state leakage flow rate calculation cannot reflect the
variations of actual leakage flow rate. After the pipeline leakage, operation pressure in
the pipeline will decrease exponentially, so the leakage flow rate will show a trend of
decrease.
This paper proposes a new model for transient flow rate calculation of gas
transmission pipelines. In case that the block valves of gas transmission pipelines are
alarmed and automatically closed, the model proposed in this paper can calculate the
leakage flow rate based on transient pressure variations collected on the upstream and
downstream block valve rooms of the leakage point. The leakage process is divided
into two stages according to the time when the leakage occurred and block valves are
automatically closed, and the leakage flow rate at each stage is calculated based on
the characteristic line method.
The basic framework of the developed real-time leakage flow rate calculation
method is introduced in Section 2. The real-time leakage simulation model of gas
transmission pipelines based on the characteristic line method, the calculation method
of pressure drop rate, and the calculation method of leakage orifice and transient
leakage flow rate of gas transmission pipelines are proposed in Section 3. The
proposed method is applied to a real gas pipeline in China in Section 4, and the
minimum detectable leakage orifice at different locations are calculated and
sensitivity analysis of leakage location on leakage flow rate calculation are analyzed
in detail. This paper closes with some conclusions and future work in Section 5.
7
2. Methodology
This paper presents a novel method for transient leakage flow rate calculation of
gas pipelines based on data of the pressure variations collected at the upstream and
downstream block valve rooms of the leakage point. This method can address two
stage transient leakage rate calculations based on the iterations of the equivalent
leakage orifice and characteristic line method. Based on the recommended threshold
of the pressure drop rate in the block valve rooms and closure time of block valves,
the leakage process is divided into two stages according to the time when the leakage
occurred and block valves were automatically closed. The first stage is the process
from the leakage of the pipeline to the closure of one block valve. The second stage is
the process from the closure of one block valve to the closure of both upstream and
downstream block valves.
After the closure of both upstream and downstream block valves, assuming an
equivalent leakage orifice, the pressure data can be simulated based on the
characteristic line method, leakage calculation model and corresponding boundary
conditions. Compare the pressure data obtained from the SCADA system to the
simulation data. The actual leakage orifice can be obtained through a number of
iterations until the error between these two data set are within the allowable range.
Then transient leakage flow rate of the two stages can be calculated based on the
closure time recommended by Line Guard 2100. The basic framework is shown in Fig.
1.
8
Fig. 1. Framework of the developed methodology.
The gas pipeline between two compressor stations is divided into several pipe
segments according to block valve rooms. Based on the continuity equation, the
momentum equation, the gas state equation and thermodynamic equations, the
transient simulation model of gas pipeline leakage is established to calculate the
pressure variations at each valve rooms and compressor stations.
The characteristic line method (CLM) is adopted to solve the continuity equation
and the momentum equation. The knot space for hydraulic simulations is set as 1000
meters. Divide all nodes of the gas pipeline into three categories, namely general
nodes, leakage nodes and boundary nodes (including the left boundary and the right
boundary). The boundary conditions and legal or physical constraints of these nodes
are described as follows:
9
Fig.2. Hydraulic simulation of leakage scenarios based on CLM.
10
Based on gas composition and the BWRS equation in equation (3), gas
compressibility factor can be calculated at given temperature and pressure.
A0 C D E a d α d 5 c ρ0 2 (3)
Z = 1 + ( B0 − − 0 3 + 04 − 0 5 ) ρ0 + (b − − ) ρ 0
2
+ ( a + ) ρ0 + (1 + γρ02 )exp(−γρ0 2 )
RT RT RT RT RT RT 2 RT T RT 3
Where denotes the Moore gas density, kmol/m3; R denotes the gas constant,
8.314 kJ/ ∙ ; Z denotes the gas compressibility factor; A0, B0, C0, D0, E0, a, b,
c, d, α, γ are the parameters related to the gas composition; the detailed calculation
process of these parameters can be seen in the reference (Li and Yao, 2009).
Considering the gas state equations (3) and (4) and the velocity equation of
pressure wave (5), equations (6) and (7) can be obtained by taking equations (3)∽(5)
P = ρ ZRg T (4)
∂P
a= (5 )
∂ρ s
∂P a 2 ∂M
+ = 0 (6 )
∂t A ∂x
∂P 1 ∂M P λa2
+ + 2 g sin θ + M M = 0 (7 )
∂x A ∂t a 2dA2 P
a λ a 2 ∆x M D + M A g
F1 = PD − PA + ( D A)
M − M + M D + M A + 2 ( PD + PA )sin θ = 0 (8)
A 4 DA2 PD + PA 2a
a λ a 2 ∆x M D + M B g
F2 = PB − PD + (MD − MB ) + M D + M B + 2 ( PD + PB ) sin θ = 0 (9)
A 4 DA 2
PD + PB 2a
11
The pressure and flow rate of node D can be calculated based on the binary
nonlinear equations (8) and (9). To solve the binary nonlinear equations (8) and (9),
the Newton iteration method can be used, the initial value of the pressure and flow
rate of node D in the first iteration can take the average of the pressure and flow of
node A and node B. The iterative formula is as follows:
∂F2 ∂F1
F1 − F2
PD k +1 = PD k + ∂QD ∂QD (10)
∂F2 ∂F1 ∂F1 ∂F2
−
∂PD ∂QD ∂PD ∂QD
∂F1 ∂F2
F2 − F1
∂PD ∂PD
QD k +1 = QD k + (11)
∂F2 ∂F1 ∂F1 ∂F2
−
∂PD ∂QD ∂PD ∂QD
Assume that the flow rate before and after the leakage node G is )* and ) **
respectively, and the leakage flow rate at node G is . The discrete form of the
continuity equation and the momentum equation at the leakage node are shown as
equations (15) and (16), and the node flow balance equation is shown as equation
(17).
a λ a 2 ∆x M G ' + M E g
PG ' − PE + ( MG' − M E ) + M G ' + M E + 2 ( PG ' + PE ) sin θ = 0 (15)
A 4 DA PG ' + PE
2
2a
a λ a 2 ∆x M G '' + M F g
PF − PG '' + ( M G '' − M F ) + M G '' + M F + 2 ( PF + PG '' ) sin θ = 0 (16)
A 4 DA PG '' + PF
2
2a
Based on the pressure and flow at node E and F at the previous time step 1,
four parameters of )* , ) ** , ) and can be calculated based on equations (13)
~ (17) and Newton iteration method. The initial values for iteration and the iterative
formula is similar to the methods introduced in general nodes.
14
and 1.6), the right boundary is usually constrained by the minimum operational
pressure. If the pressure calculated through step (a) is lower than the minimum
operational pressure, the boundary condition is converted to the minimum pressure
control, and the flow rate variations of the right boundary can be calculated according
to the left characteristic line and the minimum pressure of the right boundary.
(c) If the flow rate calculated in step (b) is lower than 0, it is necessary to switch
the boundary condition to flow rate control (equal to 0) in order to prevent backflow.
And the pressure variations of the right boundary can be calculated according to the
left characteristic line and the flow rate (equal to 0) of the right boundary.
As shown in Fig. 3, pressure collection devices are equipped at each block valve
rooms. After the pipeline leaks, the pressure at each block valve room will decrease.
When the pressure drop rate at the block valve room of the gas pipeline is greater than
0.15 MPa/min (Zuo et al., 2015; Phan et al., 2012;), the block valve room will send an
alarm signal. And if the alarm signal lasts more than 120s, then the block valve will be
automatically closed. The calculation method of the pressure drop rate in this paper is
the method recommended by the Line Guard 2100 system.
15
Fig. 3. Pressure variations at block valve rooms after leakage.
The pressure signal is extracted every 5 second from the SCADA system.
Assuming that the pressure of a block valve room at the 5th, 10th, ..., 80th second are
+, , … and +, respectively, then the average pressure of the block valve room at
the 20th and 80th second is as follows:
1/ 2/ 3/ 4
'-$ = (18)
3
13 / 14 / 15 / 16
'-$ 4 = (19)
3
Then the average value of the pressure drop rate at the 80s block valve room is:
1 9 13 / 2 9 14 /: 3 9 15 ;/ 4 9 16
#78 = '-$ '-$ 4 = 3
(20)
Pressure collection devices are generally installed in each block valve room and
compressor station of the gas transmission pipeline. Assuming an equivalent leakage
orifice, compare the pressure data obtained from the SCADA system (pressure data
from the alarm of pressure drop rate to the closure of the block valve) to the pressure
data simulated based on the assumed equivalent leakage orifice. If the error between
these two data is within the allowable range, the actual leakage orifice is equal to the
assumed equivalent leakage orifice, otherwise the equivalent leakage orifice can be
calculated by iterations. As shown in equation (21), ERR is adopted as the error
indicator between simulation data and collection data.
'AB CDE FG 9CHE FG 'AB CDJ FG 9CHJ FG
<## = <##= + <##? = ∑KL3 I
+ I
(21)
Where <## is the total error between simulation results and collection data,
MPa; <##= is the error of the upstream block valve between simulation results and
collection data, MPa; <##? is the error of the downstream block valve between
simulation results and collection data, MPa; BM is the real-time pressure data
collected from the upstream block valve of the leakage pipe segment, MPa; NM is the
16
real-time pressure data collected from the downstream block valve of the leakage pipe
segment, MPa; BO is the real-time pressure data of the upstream block valve of the
leakage pipe segment calculated by simulation model, MPa; NO is the real-time
pressure data of the downstream block valve of the leakage pipe segment calculated
by simulation model, MPa.
Table 1 Boundary conditions and constraints for the transient leakage rate calculation.
Unit Boundary condition Legal or physical constraints
Leakage diameter
Leakage point /
Atmospheric pressure
18
4. Case study
Fig. 4 shows the topology and configurations of the tested gas pipeline model
which is based on a real gas pipeline system in China. The designed pressure of the
gas pipeline is 10 MPa, the diameter and the wall thickness are 1016 mm and 17.4
mm respectively. The total length between these two compressor stations is 160km.
There are four centrifugal compressors in CS1, and two centrifugal compressors in
CS2. The gas pipeline system often operates under high pressure to reduce energy
consumption, so the control mode for each compressor station is outlet setpoint
pressure which is close to the designed pressure. The outlet setpoint pressure is 9.7
MPa since a certain margin should be left to ensure operational safety. If the outlet
pressure of the compressor station cannot reach 9.7 MPa even at the maximum
rotational speed, then the boundary condition for the compressor station is converted
to maximum rotate speed to ensure the highest outlet pressure as much as possible.
The minimum required inlet pressure for compressor station CS2 is 5.5MPa. The
transmission flow rate of the gas pipeline is 50 mcm/d.
19
the operational gas pipeline because of privacy policy, in order to obtain operational
data close to the actual scenario, the international commercial software TGNET is
adopted to simulate the leakage scenario in this paper, and the pressure variations and
pressure drop rate variations at block valve rooms BV4 and BV5 are obtained as
shown in Fig. 5.
8.5
0.8
8.0
Pressure (MPa)
0.6
ROD (MPa/min)
7.5
0.4
7.0
6.5 0.2
6.0
0.0
5.5
1600 1700 1800 1900 2000 2100 2200 2300 2400
Time (s)
Fig. 5 Pressure and pressure drop rate variations of BV4 and BV5 under the specified
leakage scenario.
Based on data in Fig. 5 and the control logic of block valves, the pressure drop
rate of the block valve BV5 and BV4 are detected to be greater than 0.15MPa/min at
the 1820s and 1890s respectively, and the block valve BV5 and BV4 are fully closed
automatically at the 1940s and 2010s respectively after the pressure drop rate exceeds
the threshold for 120s.
Assuming that the location of the leakage location can be accurately determined
by existing methods, such as the negative pressure wave method or the acoustic wave
method, then the equivalent leakage orifice can be calculated iteratively based on the
20
pressure variations collected on the block valve room by the SCADA system. As
shown in Fig. 6, the equivalent leakage orifice can be calculated through 9 iterations.
The equivalent leakage orifice obtained by iterative calculation is 398.9mm, the <##=
and <##? are 0.019 MPa and 0.016 MPa respectively under this equivalent leakage
orifice.
0.7 550
0.6 500
0.4
400
ERR3
0.3
350
0.2
300
0.1
250
0.0
200
0 2 4 6 8 10
Number of iterations
Fig. 6 Errors and number of iterations for calculating the leakage orifice.
According to the leakage orifice obtained above and the closure time of upstream
and downstream block valves of the leakage point, assuming that the closure action of
block valve is completed instantly, then the leakage flow rate variations during these
two stages are calculated as shown in Fig. 7. At the beginning of leakage process, the
operation pressure in the gas pipeline is high, so the leakage flow rate is higher. As the
leakage process continues, the operation pressure and the leakage flow rate will
decrease gradually, and the leakage rate will decrease further after the closure of one
block valve. Comparisons have been made between the simulations results by
TGNET and calculation results by CLM. The time step selected by TGNET
simulation is automatically calculated by this software according to the simulation
error in each iteration, but the CLM method adopts a constant time step in this paper,
21
and the relative error of the accumulative leakage flow rate variations by these two
methods is within 1.109%. The line pack after these two processes are calculated by
equation (22). After these two processes, some practical venting processes will be
adopted by dispatchers to release the gas in the pipeline as soon as possible. The error
of accumulative leakage flow rate calculation based on transient flow and steady flow
is 39.593%, so it is necessary to consider the transient flow after leakage to calculate
the leakage flow rate of the high-pressure gas pipeline.
[ [ \ ]
TUVW X Y = Z ! ! =Z ! ! = 1.289 × 10, e (22)
3 3 ^_ `a
4000
Calculation results by CLM
Start leaking
Simulation results by TGNET
3500 Calculation results by steady state model
Leakage flow rate (Nm3/s)
3000
Closure of BV5
2500
2000
Closure of BV4
1500
1000
500
1800 1850 1900 1950 2000
Time (s)
Fig. 7 Comparisons of two-stage leakage flow rate variations by CLM, TGNET and
steady state model.
At present, the closure threshold of block valves is set based on the two
parameters (larger than 0.15 MPa/min and last for more than 120s) in the gas
transmission trunk pipeline of PetroChina. There is a critical leakage orifice at
22
different locations of the gas transmission pipeline, the block valves at the upstream
and downstream of the leakage point can automatically alarm and be closed only
when the actual equivalent leakage orifice is larger than the critical equivalent leakage
orifice.
In this paper, the calculation of the minimum detectable equivalent leakage
orifice between BV4 and BV5 block valves are carried out. As shown in Fig. 8, the
closer to the downstream block valve BV5, the larger the minimum detectable leakage
orifice. The minimum detectable leakage orifices at the upstream and downstream of
the pipe segment between block valves BV4 and BV5 are about 300mm and 440mm
respectively.
If the leakage point is located upstream of the pipe segment between block
valves BV4 and BV5, the BV4 block valve can easily detect the abnormal pressure
drop rate because of the smaller attenuation of the pressure wave, and the minimum
detectable leak hole diameter depends on the pressure drop rate at the block valve
BV5. Due to the high operating pressure at the upstream of the gas pipeline, the
negative pressure wave which is generated because of the leakage occurred at the
upstream of the gas pipe segment is larger, so the minimum detectable leakage orifice
is relatively small at the upstream of the pipe segment. On the contrary, if the leakage
point is located downstream of the pipe segment between block valves BV4 and BV5,
the block valve BV5 can easily detect the abnormal pressure drop rate, and the
minimum detectable leak hole diameter depends on the pressure drop rate at the block
valve BV4. The negative pressure wave generated because of the leakage occurred at
the downstream of the pipe segment is smaller, and the propagation direction of the
pressure wave is opposite to the gas flow direction, which to some extent prevents the
propagation of pressure wave from the leakage point to the block valve BV4. As a
result, the minimum detectable leakage orifice is relatively larger at the downstream
of the pipe segment.
23
700
500
400
300
200
100
0 5 10 15 20
Distance from BV4 (km)
Fig. 8 The minimum detectable leakage orifice at different locations between BV4
and BV5
Because the frequency of data collection of the SCADA system on the block
valve room is relatively slow, it is difficult to accurately calculate the actual leakage
position of the gas transmission pipeline based on existing methods, such as the
acoustic wave method and the negative pressure wave method (Jin et al., 2014; Li et
al., 2019;). Therefore, it is necessary to study the relationship between the error of the
leakage flow rate and the error of the leakage position.
According to different leakage position in the first column of Table 2 and the
collected pressure data of BV4 and BV5, the leakage orifices are calculated based on
methods proposed in Section 3.3. It can be seen that the more the calculated leakage
position deviates from the actual leakage position, the more the calculated leakage
orifice and leakage flow rate will deviate from the actual leakage orifice and leakage
flow rate. If the leakage position is located upstream of the actual leakage point, the
24
calculated leakage orifice and the accumulative leakage flow rate will be larger than
the actual leakage orifice and the accumulative leakage flow rate. On the contrary, if
the leakage position is located downstream of the actual leakage point, the calculated
leakage orifice and the accumulative leakage flow rate will be smaller than the actual
leakage orifice the actual accumulative leakage flow rate. So, if the calculation error
of the accumulative leakage flow rate needs to be controlled within ∓15%, the
precondition is that the calculation error of the leakage position needs to be controlled
within ∓3km.
Table 2 Sensitivity analysis of leakage location on leakage orifice and leakage flow
rate.
This paper presents a novel method for transient leakage flow rate calculation of
gas pipelines. The transient leakage flow rate variations of the gas pipeline are
calculated based on the pressure data collected at the upstream and downstream block
valve rooms from the leakage point. The main conclusions are as follows:
(1) It is necessary to consider the transient flow after leakage to calculate the
25
leakage flow rate of the gas pipeline. The error of accumulative leakage flow rate
calculation based on transient flow and steady flow is 39.593%.
(2) The minimum detectable leakage orifices at the upstream and downstream of
the pipe segment between block valves BV4 and BV5 are about 300mm and 440mm
respectively. The closer to the downstream block valve, the larger the minimum
detectable leakage orifice.
(3) The more the calculated leakage position deviates from the actual leakage
position, the more the calculated leakage orifice and leakage flow rate will deviate
from the actual leakage orifice and leakage flow rate. If the leakage position is located
upstream of the actual leakage point, the calculated leakage orifice and the
accumulative leakage flow rate will be larger than the actual leakage orifice and the
accumulative leakage flow rate, and vice versa.
(4) If the calculation error of the accumulative leakage flow rate needs to be
controlled within ∓15%, the precondition is that the calculation error of the leakage
position needs to be controlled within ∓3km.
The accuracy of the leakage flow rate calculation depends on the accuracy of the
leak position calculation. In the case of low frequency of data collection, it is
necessary to find a more robust algorithm to calculate the leakage position of the gas
pipeline. Combined with the practical operations and venting processes of the gas
pipeline, the leakage flow rate variations from the process of the closure of the
upstream and downstream block valves to the complete venting of the natural gas in
the pipeline also need to be calculated in the future.
Acknowledgement
The authors acknowledge the financial support from National Key Research and
Development Plan of China [2016YFC0801500]. The Pipeline Studio (TGNET)
software is used in this paper, thanks to the ESI company. The authors are also
thankful to all the reviewers for their insights and constructive comments.
26
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Table 1 Boundary conditions and constraints for the transient leakage rate calculation.
Unit Boundary condition Legal or physical constraints
Leakage diameter
Leakage point /
Atmospheric pressure
8.5
0.8
8.0
Pressure (MPa)
0.6
ROD (MPa/min)
7.5
0.4
7.0
6.5 0.2
6.0
0.0
5.5
1600 1700 1800 1900 2000 2100 2200 2300 2400
Time (s)
Fig. 5 Pressure and pressure drop rate variations of BV4 and BV5 under the specified
leakage scenario.
0.7 550
0.6 500
0.4
400
ERR3
0.3
350
0.2
300
0.1
250
0.0
200
0 2 4 6 8 10
Number of iterations
Fig. 6 Errors and number of iterations for calculating the leakage orifice.
4000
Calculation results by CLM
Start leaking
Simulation results by TGNET
3500 Calculation results by steady state model
Leakage flow rate (Nm3/s)
3000
Closure of BV5
2500
2000
Closure of BV4
1500
1000
500
1800 1850 1900 1950 2000
Time (s)
Fig. 7 Comparisons of two-stage leakage flow rate variations by CLM, TGNET and
steady state model.
700
500
400
300
200
100
0 5 10 15 20
Distance from BV4 (km)
Fig. 8 The minimum detectable leakage orifice at different locations between BV4
and BV5
1. The leakage orifice is calculated by iterative method based on collected
2. The leakage process is divided into two stages according to the time
when the leakage occurred and two block valves were automatically
closed.
The authors acknowledge the financial support from National Key Research and
Development Plan of China [2016YFC0801500]. The Pipeline Studio (TGNET)
software is used in this paper, thanks to the ESI company. The authors are also
thankful to all the reviewers for their insights and constructive comments.