Document Type : Research Paper
Authors
 Mehdi Mahmoodi ^{1}
 Mofid Gorji Bandpy ^{} ^{2}
^{1} Ph.D. Candidate, Babol Noshirvani University of Technology, Mazandaran, Iran
^{2} Professor, Babol Noshirvani University of Technology, Mazandaran, Iran
Abstract
When a natural gas pipeline ruptures, the adjacent upstream and downstream automatic control valves (ACV) should close quickly to prevent leakage or explosion. The differential pressure set point (DPS) at each valve location is the main criteria for value setting in ACV actions. If the DPS is not properly adjusted, the ACV may mistakenly close or it may not take any actions at a proper time. In this study, the effect of characteristic parameters such as pipeline operational pressure (POP) and pipeline pressure drop rate (ROD) due to rupture or a major leak was experimentally investigated on DPS. 25 different conditions with the double set of the mentioned typical characteristic parameters were chosen. In each condition, the differential pressure (DP) was measured over a period of 180 s by statistically analyzing the experimental results, so 25 maximum DP values (DPSs) were obtained. The DPS rises by an increase in ROD or a decrease in POP. Because of using nitrogen gas instead of natural gas for safety reasons and the uncertainties, the DPS results can be practically applied by adding a safety factor of 15%. Finally, the diagram of DPS with respect to ROD and that of nondimensional DPS (DOP) versus nondimensional ROD (RTP) were provided for different POP’s.
Keywords
Main Subjects
1. Introduction
Pipelines are used broadly all over the world for transportation and distribution of water, natural gas, and other light petroleum products. Natural gas and petroleum products are carried over long distances from oil and gas fields or refineries to customers. Rupture, explosion, or a large leak due to various reasons are hazardous problems affecting the safe operation of pipelines. Leak detection in pipeline systems carrying natural gas and other petroleum products is critically serious from the point of view of economic, environment, and safety aspects. The hardwarebased methods such as pigging, acoustic methods, gas tracer, and radar methods are difficult to install (Geiger et al., 2003) and the softwarebased methods for continuously monitoring leaks are so expensive. ACV’s are installed on oil and gas pipelines for these reasons. When a natural gas pipeline ruptures, the automatic control valves should close quickly to prevent significant gas leakage before the rupture causes a disastrous accident.
Various experimental studies have been performed on leak detection in liquid pipelines (Souza et al., 2000; Brunone and Ferrante, 2002) and gas pipelines (Mahmoodi et al., 2017), but relatively fewer studies have been presented on gas pipelines. Leak tests on gas pipeline simulator were conducted by acousticbased methods in laboratory (Watanabe and Himmelblau, 1980). A field study on a 150km long gas pipeline has also been reported (Billmann and Isermann, 1984). Several studies on leak detection (Noguerol, 2011; Harriott, 2011, Reddy et al., 2011, Yan et al., 2015; Ebrahimi, 2016, Chen et al., 2017; Mahmoodi et al., 2018) and rupture detection (Peekema, 2013; Richards, 2013) in gas pipelines have been reported. However, there are only a few studies on setting the differential pressure set point (DPS) value of automatic control valves (ACVs) (Lorusso, 2012; Doostaregan, 2013; Wang, 2013; Zuo, 2015), especially about how the value settings might differ between gas pipelines.
The DPS value is the important parameter that determines whether an ACV closes in time or not. The calculation of DPS values of ACV’s is complex owing to the changing operating conditions along a pipeline. The normal pressure drop rate is due to frictional losses in a piping system. The normal pressure drop should not cause an ACV to act. Actually, the differential pressure value between two sides (the right and left) of the diaphragm in a differential pressure switch (see Figure 1) is DP. When the DP value equals the DPS, the diaphragm moves to the right and changes the normally closed valve position. ACV will be regulated at a certain DPS in different conditions. The DP value depends on several parameters such as pipeline operating pressure (POP) and the rate of pressure drop due to rupture or a large leak (ROD). The orifice diameter (see Figure 1) is another important parameter of ACV’s. The orifice diameter is considered to be constant and equal to 0.5 mm in this study. As mentioned, the DPS’s of ACV’s are usually adapted based on experiments or the estimated values derived from the pipeline steady flow over a long time.
In this study, the effects of critical parameters such as POP and ROD on the DPS of ACV’s were experimentally studied. 25 different typical conditions were chosen with the double set of the mentioned parameters. Each condition was experimentally studied 3 times, so 75 tests were performed. The DP over a period of 180 s in each condition was depicted by the statistical analysis of the experimental results; therefore, 25 DPS’s with their occurrence times were obtained. A series of equations relating the DP value over 180 s to the time at different POP’s and ROD’s were developed. An uncertainty analysis was also performed, and finally a series of equations correlating the DOP with the RTP at different POP’s were extracted. The dimensionless DPS and ROD are named DOP and RTP respectively.
2. Experimental test setup
A schematic of the experimental test setup is depicted in Figure 1, and the utilized facilities are illustrated in Figure 2. The gaseous fluid is transferred from pipeline to ACV through a connecting hose and tube (No. 19 and No. 20 in Figure 3)< which is divided into three branched tube routes; Route 1 is through the normally closed valve (NC Valve in Figure 1). The test setup is shown in Figure 2 and it includes: (1) pipeline, (2) a compressed nitrogen cylinder, (3) a pressure gauge, (4) a pressure diaphragm switch, (5) an electrical box, (6) a PT signal receiver, (7) a pressure transducer (PT), (8) a set of orifice and check valve, (9) a reference tank, (10) tubing, (11) a calibrated valve, and (12) a connecting hose. A closedends pipe was used as the pipeline (No. 1 in Figure 2). To avoid any hazardous conditions, nitrogen gas was used instead of natural gas. The pipeline pressure is attained at the desired POP by a compressed nitrogen cylinder (No. 2 in Figure 2). A calibrated valve (No. 11 in Figure 2) is attached to the pipeline to create an ROD by withdrawing gas and releasing it to the atmosphere.
Figure 1
A schematic of the experimental test setup.
Figure 2
The experimental test setup.
Nitrogen gas enters the reference tank by means of a set of orifice and check valves (No. 8 in Figure 2) installed in Route 3 (Figure 1). The pressure of the reference tank equals the pipeline pressure instantaneously. When a failure occurs in the pipeline, the reference tank pressure will be greater than the pipeline pressure. Now, the route with the check valve is closed. Therefore, all the fluid in the reference tank passes through the orifice. This creates a new pressure drop rate in the system which is lower than the ROD. The DP between the pipeline and the reference tank equals the DP between the two sides of the diaphragm in the differential pressure switch. The normally closed valve position changes when the DP attains the maximum value (i.e. DPS) at the time of t_{max,} and finally ACV acts.
The isolated pipeline is pressurized to a constant value, and the pressure is then reduced for 5 minutes by opening the valve (No. 11 in Figure 2) which is installed on the pipeline. The mean ROD (kPa/s) should be measured for this determined valve opening (in degree). To calculate the ROD, the pressure difference (kPa) between the initial time and 5 minutes after the valve opens was divided by 300 seconds. Therefore, the ROD was obtained for this determined valve opening. Consequently, the valve calibration was performed in all the conditions. Finally, the valve was calibrated for 9 ROD’s from 0.2 kPa/s up to 2 kPa/s. 25 different typical conditions are summarized in Table 1. Each condition was experimentally studied 3 times, so 75 experimental tests were carried out. The maximum and minimum limits of each range of ROD depend on POP and the chosen orifice diameter. 25 DPS’s with their occurrence times were obtained. The pieces of equipment used in this study are listed along with their uncertainties and measured parameters in Table 2.
Table 1
Experimental parameters and their values.
Parameter 
Unit 
Values 
POP 
kPa 
3500, 5000, 7500, 9000, and 10500 
ROD 
kPa/s 
0.2, 0.4, 0.6, 0.8, 1, 1.2, 1.4, 1.6, and 2 
Table 2
Pieces of equipment and their uncertainties
Equipment and model 
Accuracy 
Measured section 
Test range 
Uncertainty in experiment 
LCD digital stopwatch (SigmaAldrich, Germany) 
± 0.003% 
Time, ROD 
0180 s 
± 5.4×10^{3} s 
Pressure transducer, PXM01MD0160BARG5T (Omega, the UK) 
± 0.05% 
POP, DP, DPS, ROD 
206010500 kPa 
± 0.22% (± 8 kPa) 
3. Results and discussion
As mentioned above, the DPS can be determined according to the maximum DP values over a period of 180 s. Failure occurred at the initial time (t=0) by ROD. The DP increased with respect to time to a maximum value (i.e., DPS), and then it dropped in all the conditions. The DP with respect to time is depicted based on the transmitted data by two pressure transducers, namely PTS and PTR, for 180 s after linefailure in each condition as displayed in Figures 3 to 7; The DP has been measured every 10 s. The DP is determined as a function of the ROD and the POP parameters and predicted by Equation 2 over a period of 180 s in all the conditions. Each condition has its six unique constant coefficients tabulated in Tables 3, 5, 7, 9, and 11.
(1) 
Figure 3
DP versus time for a POP of 3500 kPa.
Table 3
Coefficients of Equation 1 for a POP of 3500 kPa.
ROD 
a 
b 
c 
d 
e 
f 
0.2 
1.56×10^{2} 
2.84×10^{6} 
3.8×10 
7.72×10 
1.31×10^{3} 
1.56×10^{2} 
0.4 
2.12×10^{2} 
2.84×10^{6} 
3.47×10 
1.04×10^{3} 
1.18×10^{3} 
2.12×10^{2} 
0.6 
1.29×10^{2} 
2.84×10^{6} 
2.71×10 
1.32×10^{3} 
9.2×10^{4} 
1.29×10^{2} 
0.8 
4.15×10^{2} 
2.84×10^{6} 
2.43×10 
1.83×10^{2} 
8.38×10^{4} 
4.15×10 
1 
3.9×10 
2.84×10^{6} 
1.97×10 
2.01×10^{3} 
6.81×10^{4} 
3.9×10 
Each row in these tables is the result in each condition after 3 times of repetition. For data x_{i}, deviation is defined by d_{i} (Equation 2). The standard deviation (SD) is calculated by Equation 3. For parameter x, the uncertainty of the experimental test repetition and the uncertainty of its measuring equipment are shown by U_{rep} and U_{tool} respectively. The total uncertainty of each experimental test (U_{tot}) is defined by Equation 4, where, h_{a} is the half measuring equipment accuracy.
(2) 

(3) 

(4) 
The mean and maximum values of the standard deviation are 1.65 and 4.49 kPa respectively. Furthermore, the mean and maximum values of the DP estimation error are 1.03% and 5.74% respectively. The mean and maximum values of the DP total uncertainty are also 0.928 and 1.39 kPa, and the mean estimation error of t_{max} is 13.19% at a POP of 3500 kPa.
Table 4
t_{max} at a POP of 3500 kPa.
ROD 
0.2 
0.4 
0.6 
0.8 
1 
Estimated value 
122 
123 
126 
120 
120 
Estimation error 
12.86% 
12.14% 
10% 
14.29% 
16.67% 
The percent error of the DP estimation is defined using Equation 5. Its maximum and average values are presented in any conditions in Table 13. In any conditions, the estimated value of the DP is in good agreement with its obtained experimental value.
(5) 
According to the experimental tests, the required time to attain the maximum DP (t_{max}) is 140 seconds. The estimated value of t_{max} is calculated by solving Equation 6 which is the derivation of Equation 5. The estimated values of t_{max} and their errors are presented in Tables 4, 6, 8, 10, and 12 for each condition.
(6) 
When the POP is constant, the only variable parameter is ROD. An increase in ROD raises the DP when other parameters are kept constant (POP) in all the conditions. A more mass of compressed nitrogen gas in the pipeline ( ) is discharged to atmosphere by increasing the ROD. The pressure of ACV equals the pipeline pressure at the initial time before pipeline failure. The pressure drop rate on the right side of the diaphragm in differential pressure switch (Figure 1) equals the ROD due to the direct connection. However, the pressure drop rate on the left side of the diaphragm in differential pressure switch differs from the ROD owing to the compressed nitrogen gas passing through the orifice. The mean and maximum values of the standard deviation are 1.72 and 3.36 kPa respectively; the mean and maximum values of the DP estimation error are 0.86% and 3.2% respectively.
Figure 4
The DP versus time at a POP of 5000 kPa.
Table 5
Coefficients of Equation 1 at a POP of 5000 kPa.
ROD 
a 
b 
c 
d 
e 
f 
0.2 
2.53×10^{2} 
2.84×10^{6} 
3.55×10 
2×10^{3} 
1.25×10^{3} 
2.53×10^{2} 
0.4 
2.04×10^{2} 
2.84×10^{6} 
3.16×10 
2.01×10^{3} 
9.92×10^{4} 
2.04×10^{2} 
0.6 
1.52×10^{2} 
2.84×10^{6} 
2.75×10 
2.01×10^{3} 
8.55×10^{4} 
1.52×10^{2} 
1 
1.37×10^{2} 
2.84×10^{6} 
2.72×10 
2.01×10^{3} 
8.77×10^{4} 
1.37×10^{2} 
1.2 
7.3×10 
2.84×10^{6} 
2.24×10 
2.01×10^{3} 
5.81×10^{4} 
7.3×10 
The mean and maximum values of the DP total uncertainty are 1.19 and 1.94 kPa, and the mean estimation error of t_{max} is 7% at a POP of 5000 kPa.
Table 6
t_{max} at a POP of 5000 kPa.
ROD 
0.2 
0.4 
0.6 
1 
1.2 
Estimated value 
119 
134 
133 
126 
139 
Estimation error 
15% 
4.29% 
5% 
10% 
0.71% 
The is always equal to or greater than the discharged mass flow rate of the reference tank . The value of rises by an increase in the ROD; in fact, the difference between and grows which consequently raises the DP. The DP rises to a maximum value (DPS) and then drops due to the mass reduction of compressed gas inside the reference tank. The mean and maximum values of the standard deviation are 1.84 and 3.95 kPa respectively. The mean and maximum values of the DP estimation error are 0.8% and 6.1% respectively, and the mean and maximum values of the DP total uncertainty are 1.1 and 2.3 kPa respectively.
Table 7
Coefficients of Equation 1 at a POP of 7500 kPa.
ROD 
a 
b 
c 
d 
e 
f 
0.2 
9.25×10 
3.57×10^{2} 
2.8 
1.37×10^{9} 
2.3×10^{4} 
9.25×10 
0.4 
9.45×10 
3.11×10^{2} 
3.11 
1.37×10^{9} 
4.65×10^{4} 
9.45×10 
0.6 
9.44×10 
3.35×10^{2} 
3.29 
1.37×10^{9} 
3.32×10^{4} 
9.44×10 
1 
9.49×10 
3.84×10^{2} 
3.45 
1.37×10^{9} 
1.96×10^{4} 
9.49×10 
1.4 
1.1×10^{2} 
3.55×10^{2} 
3.58 
1.37×10^{9} 
3.76×10^{4} 
1.1×10^{2} 
Figure 5
The DP versus time at a POP of 7500 kPa.
Table 8
t_{max} at a POP of 7500 kPa.
ROD 
0.2 
0.4 
0.6 
1 
1.4 
Estimated value 
122 
123 
126 
120 
120 
Estimation error 
12.86% 
12.14% 
10% 
14.29% 
14.29% 
The mean estimation error of t_{max} is 12.7% at a POP of 7500 kPa.
Table 9
Coefficients of Equation 1 at a POP of 9000 kPa.
ROD 
a 
b 
c 
d 
e 
f 
0.2 
9.74×10 
3.97×10^{2} 
2.44 
1.35×10^{9} 
2.74×10^{4} 
9.74×10 
0.6 
9.78×10 
3.87×10^{2} 
2.69 
1.3×10^{9} 
2×10^{4} 
9.78×10 
0.8 
1.04×10^{2} 
4.02×10^{2} 
2.72 
1.39×10^{9} 
1.97×10^{4} 
1.04×10^{2} 
1.2 
1.15×10^{2} 
3.68×10^{2} 
1.41 
1.36×10^{21} 
2.29×10^{4} 
1.15×10^{2} 
1.6 
1.18×10^{2} 
3.86×10^{2} 
1.6 
9.58×10^{19} 
2.45×10^{4} 
1.18×10^{2} 
The mean and maximum values of the standard deviation are 2 and 3.5 kPa respectively. The mean and maximum values of the DP estimation error are also 0.62% and 1.92% respectively. Moreover, the mean and maximum values of the DP total uncertainty are 1.16 and 1.73 kPa, and the mean estimation error of t_{max} is 5.14% at a POP of 9000 kPa.
Figure 6
The DP versus time at a POP of 9000 kPa.
Table 10
t_{max} at a POP of 9000 kPa.
ROD 
0.2 
0.6 
0.8 
1.2 
1.6 
Estimated value 
129 
134 
135 
127 
139 
Estimation error 
7.8% 
4.29% 
3.6% 
9.3% 
0.71% 
Figure 7
The DP versus time at a POP of 10500 kPa.
Table 11
Coefficients of Equation 1 at a POP of 10500 kPa.
ROD 
a 
b 
c 
d 
e 
f 
0.2 
9.75×10 
4.6×10^{2} 
7.36×10^{1} 
1×10^{30} 
6.48×10^{5} 
9.75×10 
0.8 
1.03×10^{2} 
3.89×10^{2} 
1.08 
3.7×10^{23} 
1.62×10^{4} 
1.03×10^{2} 
1.2 
1.07×10^{2} 
3.82×10^{2} 
1.19 
3.89×10^{22} 
1.53×10^{3} 
1.07×10^{2} 
1.6 
1.16×10^{2} 
3.34×10^{2} 
1.03 
1×10^{30} 
3.24×10^{4} 
1.16×10^{2} 
2 
1.17×10^{2} 
3.43×10^{2} 
1.15 
1×10^{30} 
2.84×10^{4} 
1.17×10^{2} 
The mean and maximum values of the standard deviation are 1.9 and 3.16kPa respectively. The mean and maximum values of the DP estimation error are also 0.7% and 2.5% respectively. Moreover, the mean and maximum values of the DP total uncertainty are 1.15 and 1.82 kPa respectively, and the mean estimation error of t_{max} is 9.71% at a POP of 10500 kPa.
Table 12
t_{max} at a POP of 10500 kPa.
ROD 
0.2 
0.8 
1.2 
1.6 
2 
Estimated Value 
130 
122 
127 
132 
121 
Estimation Error 
7.14% 
12.86% 
9.29% 
5.71% 
13.57% 
When the ROD parameter is constant, the only variable parameter is the POP. An increase in the POP intensifies collision between fluid molecules, which results in a rise in ; in fact, the velocity of the discharged compressed nitrogen gas through orifice grows when the POP rises. Therefore, the local pressure drops in orifice and the rate of the pressure drop in Route 3 approaches the rate of pressure drop in Route 2 (ROD). Thus, the difference between and decreases, and consequently the DP falls.
Figure 8 depicts the variation of the DPS versus ROD at different POP’s. The rate of pressure drop in normal operating conditions is lower than the ROD at the same POP. Therefore, it is necessary to select an ROD higher than the rate of the pipeline pressure drop during a normal operation and lower than all the possible ROD’s to regulate the ACV. The DPS results can be practically employed by applying a safety factor of 15% since nitrogen gas is used instead of natural gas and we have some uncertainties. In the case of a real gas pipeline rupture in which the ROD and the pipeline operating pressure (POP) are different from the experimental values obtained herein, new values can be found by applying interpolation to Figure 8.
Figure 8
The DPS versus ROD at different POP’s; gray continuous curves are estimations.
The maximum and the average percent of error of the DP estimation are 6.1% and 0.86% respectively in all the conditions. Furthermore, the maximum and average percent of error of the DPS estimation are 1.89% and 1.15% respectively in all the conditions. Equation 7 was developed for the DPS value estimation based on the ROD and POP. The constant parameters of a, b, and c of Equation 7 are presented in Table 13.
(7) 
For example, the DPS and ROD can be determined at a specified POP. Each curve is denoted for a specified POP. A value can be selected for ROD bigger than the designed rate of the normal pipeline pressure drop. Finally, the DPS is determined by the indicated values of the POP and the ROD. For example, at a designed rate of the normal pipeline pressure drop equal to 0.65 kPa/s, the ROD can be selected as 0.85 kPa/s. At a POP of 5000 kPa and an ROD of 0.85 kPa/s, the DPS is determined to be 177 kPa. Accordingly, the spring of NC valve can be loaded for 150.45 kPa by adding a safety factor of 15%. The mentioned safety factor is based on the limited available data related to the practical conditions of ACV installation in gas transportation pipelines of Iran. The data confirm that a safety factor of 15% is sufficient and reliable for applying the findings of this paper to practical applications. The comparison between natural gas and nitrogen is presented in Table 15.
Table 13
Data analysis of the DPS estimation.
POP 
a 
b 
c 
R^{2} 
3500 
6.43 
21.99 
20.8 
1 
5000 
9.71 
15.11 
30.2 
0.989 
7500 
6.04 
18.14 
47 
0.992 
9000 
3.76 
22.47 
59 
0.992 
10500 
3.58 
17.81 
70.7 
0.999 
This safety factor is mainly related to the mass density; the mass density of natural gas and nitrogen in standard conditions (0 °C and 101.325 kPa) are 0.9 kg/m^{3} and 1.2 kg/m^{3} respectively.
Table 14
Data analysis of the DPS estimation.
POP 
ROD 
DPS 
Estimated 
Error 
POP 
ROD 
DPS 
Estimated 
Error 
3500 
0.2 
173.1 
172.02 
0.63% 
5000 
0.2 
168.2 
167.37 
0.5% 
0.4 
178.1 
177.59 
0.29% 
0.4 
174.1 
172.84 
0.79% 

0.6 
183.8 
182.1 
0.93% 
0.6 
178.7 
177.11 
0.89% 

0.8 
190.3 
188.43 
0.99% 
1 
188.5 
186.7 
0.95% 

1 
196.7 
194.4 
1.17% 
1.2 
198.7 
196.48 
1.11% 

7500 
0.2 
163.2 
160.15 
1.87% 
9000 
0.2 
157.8 
155 
1.77% 
0.4 
167.1 
164.89 
1.32% 
0.6 
165.6 
163.17 
1.46% 

0.6 
174.4 
172.56 
1.05% 
0.8 
172.4 
170.54 
1.08% 

1 
182.3 
180.21 
1.15% 
1.2 
186.8 
184.97 
0.98% 

1.4 
197.2 
194.65 
1.29% 
1.6 
197.1 
194.23 
1.45% 

10500 
0.2 
152.4 
150.56 
1.2% 
10500 
1.6 
187.3 
184.89 
1.28% 
0.8 
165.1 
162.9 
1.33% 
2 
198.1 
199.1 
1.46% 

1.2 
174.4 
171.1 
1.89% 




Table 15
Comparison of the DPS of natural gas with that of nitrogen.
POP 
ROD 
DPS (Nitrogen) 
DPS (Natural gas) 
Safety factor 
5000 
1 
188.5 
166.7 
11.6% 
7500 
1.4 
197.2 
170 
13.8% 
The DOP and RTP parameters are calculated by Equations 8 and 9 respectively using the experimental results in Table 14. The variation of the DOP versus the RTP at different POP’s is delineated in Figure 9. The DOP can be defined by a linear equation (Equation 10) as a function of RTP at each POP. The constant parameters of a and b of Equation 10 are presented in Table 16.
(8) 

(9) 

(10) 
Table 16
Data analysis of the DOP estimation.
POP 
Mean DOP 
Error 
a 
b 
R^{2} 

Average 
Maximum 

3500 
0.053 
0.33% 
1.07% 
0.215 
0.048 
0.987 
5000 
0.04 
0.62% 
2.53% 
0.179 
0.033 
0.954 
7500 
0.024 
0.6% 
1.92% 
0.205 
0.021 
0.981 
9000 
0.019 
0.73% 
2.4% 
0.223 
0.016 
0.984 
10500 
0.017 
0.69% 
1.63% 
0.181 
0.14 
0.991 
Figure 9
The DOP versus RTP at different POP’s.
4. Conclusions
In the current work, the effect of parameters such as POP and ROD on the DPS of an automatic control valve was studied by performing 75 experimental tests, and statistical and uncertainty analyses were conducted. The compressed nitrogen gas was used instead of natural gas to avoid the hazardous conditions in presence of pressurized natural gas. The following conclusions are drawn based on our findings:
 The DP over a duration of 180 s is affected by the POP and the ROD. The DPS was increased by raising the ROD or decreasing the POP.
 The variation of DP with respect to time can be calculated using proposed Equation 1. The coefficients of this equation are presented in Tables 3, 5, 7, 9, and 11 in any conditions. In all the conditions, the mean of the maximum and average percent error of the DP estimation are 6.1% and 0.86% respectively.
 Equation 6 is proposed to estimate t_{max}. The mean percent error of this estimation is 7.35% in all the 25 conditions.
 The mean error of the DPS estimation using Equation 5 is 1.15%, and the maximum error is 1.89% at a POP of 10500 kPa and an ROD of 1.2 kPa/s.
 The DPS recommended herein can be practically employed by applying a safety factor of 15% to the experimental values in Figure 8.
The results in Figure 8 can be used for the value setting of automatic control valves installed on gas pipelines by applying a safety factor. Finally, the value setting (DPS) is determined by knowing the POP and the possible ROD in any specific condition in pipelines.
Acknowledgements
The authors acknowledge the financial support of the Research and Technology Center of the National Iranian Gas Company [Grant No. 950436 (2015)], Kiasa Company, and Ghaed Bassir Petrochemical Product Company.
Nomenclature
ACV 
Automatic control valve 
DOP 
Nondimensional DPS 
DP 
Differential pressure 
DPS 
Maximum DP value 
NC Valve 
Normally closed valve 
POP 
Pipeline operating pressure 
ROD 
Pipeline pressure drop rate 
RTP 
Nondimensional 
SD 
Standard deviation 
U 
Uncertainty 