711E AMERICAN SOCIETY OF MECHANICAL ENGINEERS 345 E. 47th St.. New York, N.Y. 10017 974A-81 The Society shall not be responsible for statements or opinions advanzed in papers or crieussion at meetings of the Society or of its Divisions or Sections, or printed In its publications. Discussion is printed only if the paper is published in an ASME Journal. Authorization to photocopy material for Internal or personal use under circumstance not falling within the fair useprovisions of the Copyright Act is grantedby ASME to. libraries and other users registered with the Copyright Clearance Center (CCC)Transactional Reporting Service provided that the base fee of $0.30 per page is paid directly to the CCC, 27 Congress Street Salem MA 01970. Requests for special pemiesion or bulk reproduction should be addressed to the ASME Technical Pubfishing Department CopyrigM 0 1997 by ASME An Rights Reserved. Printed In U.S.A LEAKAGE EFFECTS ON THE RATE OF CHANGE OF PRESSURE AT THE PIPELINE EXIT Seungyong Chang Korea Gas Corporation, R&D Training Center 111111111111111111111 ABSTRACT This paper investigates leak effect on the outlet pressure at pipeline exit. A modified Weymouth equation (includes inclination effect) was used as a governing equation for this study. First, a brief summary of the modified Weymouth equation was reviewed. Next, predicted results by the equation were compared to those by field data for checking discrepancy. Then, to investigate leak effect, outlet pressure and ratio of outlet to inlet pressure were compared between no leak and leak conditions for horizontal, upward, and downward flows, respectively. Finally, effects of leak location as well as leak rate on the outlet pressure were also investigated for all pipeline inclinations. Keyword: leakage effect, outlet pressure, Weymouth equation, inclination effect, leak location, leak rate INTRODUCTION In gas industry, safe and efficient operations of piping systems are very important. To ensure such operations, a pipeline integrity monitoring system is frequently introduced. The pipeline Safety Code divides the integrity monitoring into three categories as follows (Tumer,I991). (I) Corrosion Monitoring (2) Damage Detection (3) Leak Detection As shown above, leak detection is a category of the pipeline integrity monitoring system. According to a Report of GRI, 800,000 cases of main and service leaks are detected and repaired annually at a cost of more than $450 million (GRID,I 99511996). A leak can be defined as an undesirable escape of fluid from the pipe. Thus, knowing leak location and leak effect on the gas pipeline operations can be very important in gas industry. Especially, leak detection in large diameter long marine pipelines is a major concern. There have been many studies regarding leak detection techniques. As an example of the studies, Turner (1991) reviewed several techniques for pipeline leak detection monitoring. In this study; a method of investigating leak effect on the outlet pressure is suggested and results from the method are analyzed. As mentioned above, many techniques for the leak detection have been developed and used in gas industry. Most techniques, however, require a lot of detection equipments and procedures. It results in considerable inconvenience and cost to use the techniques. On the other hand, the leak detection using the rate of change of pressure at the pipeline exit requires only pipe exit pressure monitoring and is very easy to use. Only standard pressure sensors are required for this technique provided the telemetry/scada system is able to scan them at a suitable rate. A modified Weymouth equation including inclination effect is used as a governing equation. The Weymouth equation is used most often for designing high-pressure, horizontal gas transmission systems because it generally maximizes pipe diameter requirements for a given flow rate and pressure drop. Because the most gas transmission lines have gradual slopes, only slight modification of the equation for including inclination effect is necessary to describe the gas flow behaviors in the pipeline. To investigate leak effect, the outlet pressure and ratio of outlet to inlet pressure are compared between no leak and leak conditions for horizontal, upward, and downward flow, respectively. Finally, effects of leak location as well as leak rate on the outlet pressure are also investigated and analyzed. Presented at the ASME ASIA '97 Congress & Exhibition Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ Singapore on 07/13/2018 September Terms 3D-October of Use: http://www.asme.org/about-asme/terms-of-use 2,1997
A MODIFIED WEYMOUTH EQUATION A well-known Weymouth equation used for gas flow is as follow (Beggs,1984). q. = 433.50E 03 2 667 ( PTbil [ PC---2Lti r s (t) d. where, (I) q. = cu ft/day measured at standard condition Tt, Pb E = Pipeline efficiency lb = 520 R Pb --- 14.7 psia T = p = psia L = miles, and d = inches The Eq.(1), however, is derived for horizontal flow condition and, thus, the equation cannot be used for inclined flow conditions. Thus, Eq.(I) should be modified in order to investigate terrain effect. Considering a Bowline is laid on the surface as Fig. I. To account for the difference in elevation between the inlet and outlet (AZ), one of the approach is to modify the outlet pressure. Let pi be the inlet pressure, and p2 the outlet pressure. Then, the outlet pressure p2 must be corrected as follows (Kumar,1987). p2 = e sl2 p2 where (2) (0.0375r,42) ( Z Note that GI Z is positive if the outlet is higher than the inlet (upward flow) and negative if the inlet is higher than the outlet (downward flow). Thus, s is positive for upward flow, negative for downward flow. From Fig. 1, the flowline is equivalent to a horizontal line with an inlet pressure equal to pi, and an outlet pressure equal to ev2p2 This correction can be incorporated into any horizontal flow correlations to give the flow through such a flowline. The Weymouth equation for this condition can be written as: = 433.50E ( Tb [ T Pb Z T es L 17 05 ( -9 5 d2 66 7g (3) This is a modified Weymouth equation for inclined flow applications (Kumar,I987). Rearranging Eq.(3) for outlet pressure p 2 gives: 2
P2 {PI II" ( 433.50E) ( P7'61,) (vs' 77L)13 5 ( -.1(1) 2 61 2 I 2 e5 (4) Eq.(4) is used for this study to calculate outlet pressure for given conditions. Considering a flowline with a gas leak as Fig.2. Assuming a leak occurs at a position at a rate of q2. Applying a node to the position where the leak occurs and mass balance to the node gives: Etvi = Dm) = o (5) As shown above, a mass flow rate is a product of volumetric flow rate and density. In case of standard condition, density is equivalent for every mass flow rate. Thus, Eq.(5) can be expressed as follow: nt2x0 = 0 (6) Removing density term in Eq.(6), Eq.(5) in terms of mass flow rate can be expressed in terms of volumetric flow rate only as: E,(4) = 0. q i =.2 2 + Q3 (7) AS shown in Fig.2, the flowline can be divided into two sections, upstream and downstream sections prior and posterior to the leak position, respectively. These sections are represented as XI and X2 in Fig.2. First, the outlet pressure at upstream section can be calculated using flow rate qi Over a distance of Xl. Because a fraction of gas q2 escapes from the leak position, the gas flow rate at downstream section reduces to q3 and it flows through the remaining pipeline. Then, the outlet pressure at upstream section can be used as an inlet pressure at downstream section. The outlet pressure at pipe exit is, then, calculated using the reduced gas flow rate q3 and the inlet pressure at downstream section which is equivalent to the outlet pressure at upstream section. RESULTS AND DISCUSSIONS Fig.3 shows a comparison between measured and predicted pressures. The measured field parameters (T, pi, 13 2..,4) needed for the comparison are given in Ref. 4 (Tian and Adewumi, 1994). The parameters and predicted values are listed in Table I. In this table, the pipeline length is 10.678 miles for tests I through 6 and 63.068 miles for tests 7 through 16, respectively. These field tests were conducted with a wide range of gas flow rates and pressures, as well as different pipe sizes, lengths, and elevations. Therefore, the limitation of range of pressure and/or diameter is not critical. In this table, di represents % error for each test. It is noted that predicted results tend to underpredict compared to measured results, thus, all the % errors show negative values. However, 3
the % errors show acceptable condition. Figs. 4 through 6 show comparison of outlet pressure between no leakage and leakage conditions according to flow rate for horizontal, upward, and downward flow, respectively. The pipeline length used is 63.07 miles. The leakage rates are assumed to be I, 2, and 3% of total flow rate, in other words, small leak rates. In case of horizontal flow, outlet pressures are almost equivalent between no leak and leak conditions. Thus, for horizontal flow, leak effect is almost negligible for given leak rates in this study. For upward and downward flows, however, leakage effect is considerable compared to horizontal flow. A leak will induce a decrease and an increase in outlet pressure for upward and downward flow, respectively. For gas flow rate, a flow rate increase will cause a decrease in outlet pressure irrespective of inclinations. Tables 2 through 4 represent the results for Figs. 4 through 6 in addition to ratio of outlet to inlet pressure. Figs.7 through 9 show the effect of change of leak rate as well as leak location for horizontal, upward, and downward flow, respectively. For horizontal and downward flows, an increase in leakage location from the pipe inlet and a decrease in leak rate will cause an outlet pressure decrease. However, in case of downward flow, outlet pressure changes more rapidly compared to horizontal flow. For upward flow, outlet pressure change for 3% of leak rate shows similar trend with horizontal and downward flow, but more smooth variation. For 1% leakage, however, an increase in leak location will cause an increase in outlet pressure. For the case of 2% leakage, outlet pressure is almost equivalent irrespective of leak location. Tables 5 through 7 show the results for Figs.7 through 9 in addition to ratio of outlet to inlet pressure. CONCLUSIONS The following results are derived from this study. I. A study on the leak effect on the pressure at the pipeline exit has been conducted using a modified Weymouth equation. 2. For horizontal flow, outlet pressures are almost equivalent between no leak and leak conditions. Thus, leak effect is almost negligible for given leak rates in this study. 3. For upward and downward flows, on the contrary, leak effect is considerable compared to horizontal flow. A leak will induce a decrease and an increase in outlet pressure for upward and downward flow, respectively. 4. For gas flow rate, a flow rate increase will cause an outlet pressure decrease irrespective of inclinations. 5. For leak rate variations, an increase in leak location from the pipe inlet and a decrease in leak rate will cause a decrease in outlet pressure for horizontal and downward flows. However, the outlet pressure for downward flow changes more rapidly compared to horizontal flow. 6. For upward flow, outlet pressure change for 3% of leak rate shows similar trend with horizontal and downward flows, but more smooth variation. 7. For I% leakage, however, an increase in leak location will cause an outlet pressure increase. In case of 2% of leak rate, outlet pressure is almost equivalent irrespective of leak location. As shown, the modified Weymouth equation reveals explicit relations between inlet, outlet, and flow rate. Thus, the results in this study would considerably enhance gas pipeline design in terms of both ease of use and accuracy. It would have applications for detecting leak locations in case of pipeline networks also where many repetitive calculations are required. REFERENCES 1. Beggs, H.D.,1984,"Gas Production Operations," OGCI Publications, Tulsa, pp.108-109. 2. GRID, Winter,I995/1996."Leak Detection: Inside & Out,"Gas Research Institute, vol.18, No.4, pp]. 3. Kumar, S.,1987,"Gas Production Engineering," Gulf Publishing Company, Houston, pp.348-349. 4. Tian, S. and Adewumi, M.A..May.1994,"Development of Analytical Design Equation for Gas Pipelines," SPE Production & Facilities, pp.i00-106. 5. Turner, N.C.,1991,"Hardware and Software Techniques for Pipeline Integrity and Leak Detection Monitoring," SPE Journal. pp.139-i4.
Table 1. Comparison of Measured and Predicted Outlet Pressures Test T CF) PI (ps i a) pz, measured (ps i a) p2, predicted (ps i a) di (%) 1 64.0 814.8 749.8 721.0-3.84 2 58.8 791.1 141.0 718.3-3.07 3 59.7 769.3 730.5 714.5-2. 19 4 58.9 154.5 720.4 706.8-1.89 5 58.3 729.8 711.2 704.4-0.96 6 58.3 716.6 701.7 696.6-0.73 7 63.3 602.7 587.6 579.7-1.35 8 63.0 612.1 576.3 556.9-3.38 9 62.5 611.1 559.0 527.7-5.61 10 62.8 515.5 495.7 486.9-1.18 11 62.3 518.7 481.0 461.8-3.99 12 68.0 812.7 795.0 784.0-1.38 13 70.0 811.3 774.8 754.2-2.65 14 71.8 809.0 756.5 7247-4.20 15 72.0 812.6 725.9 678.6-6.51 16 72.7 814.0 712.4 655.6-7.97 Test Conditions Approximate Gas Composition Ten C. 72.7, pi(psia) a 814.0 CHAa76.99, C2H6=5.21, CA-4=2.85, n-c4=0.67, i-cs=0.08 d(inch) = 19.4375, L(mile) = 63.07 n-csc1.08, C6=0.02, C7=0.12, N2=13.28, CO2=0.3, 02=0.1 Table 2. Comparison of Outlet Pressure and Ratio of Outlet to Inlet Pressure between No Leakage and Leakage Conditions for Horizontal Flow the (1.44SCFD) Horizontal Flow P2 (ps i a) Ratio (P2/1:4) No Leakage Leakage No Leakage Leakage 1% 2% 3% 1% 2% 3% 20 810.64 810.68 810.73 810.77 0.99587 0.99592 0.99598 0.99603 40 800.46 800.64 800.82 801. 01 0.98337 0.98359 0.98381 0.98404 60 783.2; 783.60 784.03 784.44 0.96217 0.96266 0.96318 0.96369 80 758.39 759.08 759.85 760.62 0.93169 0.93253 0.93348 0.93442 100 725.25 726.26 727.53 728.79 0.89097 0.89222 0.89378 0.89532 OK (144SCFD) Table 3. Comparison of Outlet Pressure and Ratio of Outlet to Inlet Pressures between No Leakage and Leakage Conditions for Upward Flow (h = 518 ft) Upward F low Pt (Psie) Ratio (p2/p1) No Leakage Leakage No Leakage Leakage 1% 2% 1% 2% 3% 20 799.22 787.96 788.00 788.05 0.98184 0 96801 0.96806 0.96812 40 789. 19 778.00 778. 18 778.36 0.96952 0.95577 0.95600 0.95622 60 772.18 761.09 761.52. 761.94 D. 94862 0.93500 0.93552 0.93604 80 747.71 736.74 737.52 738.29 0.91857 0.90509 0.90504 0.90699 100 715.03 704.13 705.40 706.66 0.87842 0.86502 0.86659 0.86814 5
Table 4. Comparison of Outlet Pressure and Ratio of Outlet to Inlet Pressure between No Leakage and Leakage Conditions for Downward Flow (h = -518 ft) q,c Downward Flow (144SCF0) p2 (ps i a) Ratio (13z/O)) No Leakage Leakage No Leakage Leakage IX 2% 3% IX 2% 3% 20 822.22 834.10 834.15 834.19 1.01010 1.02469 1.02475 1.02480 40 811.90 823.97 824.16 824.34 D. 99742 1.01225 1.01248 1.01270 60 794.40 806.80 807.22 807.64 0.97592 0.99115 0.99167 0.99218 BO 769.23 782.09 782.86 783.63 0.94500 0.96080 0.96175 0.96269 100 735.61 749.07 750.33 751.58 0.90369 0.92023 0.92178 0.92331 Table 5. Comparison of Outlet Pressure and Ratio of Outlet to inlet Pressure Leakage Location from Pipe Inlet (mi l e) for Leakage Variation for Horizontal Flow Horizontal F low 172 (ps i a) Rat io (p2/13 1 ) 1% 2% 3% IX 2% 3% 10 726.66 728.22 729.76 0.89271 0.89462 0.89652 20 726.26 727.53 728.79 0.89222 0.89378 0.89532 30 725.93 726.90 727.87 0.89180 0.89300 0.89419 40 725.65 726.33 727.01 0.89146 0.89230 0.89313 50 725.43 725.82 726.20 0.89119 0.89167 0.89214 Table 6. Comparison of Outlet Pressure and Ratio of Outlet to Inlet Pressure Leakage Location from Pipe Inlet (mile) for Leakage Variations for Upward Flow Upward F low P2 (ps i a) Rat io (p21p 1 ) IX 2% 3% IX 2% 3% 10 704.06 705.63 707.18 0.86494 0.86687 0.86877 20 704.13 705.40 706.66 0.86502 0.86659 0.86814 30 704.25 705.23 706.20 0.86518 0.86638 0.86757 40 704.44 705.12 705.80 O. 86540 0.86625 0.86708 50 704.69 705.08 705.46 0.86571 0.86619 0.86666 Table 7. Comparison of Outlet Pressure and Ratio of Outlet to Inlet Pressure Leakage Location from Pipe Inlet (mile) for Leakage Variation for Downward Flow Downward Flow P2 (13510) Ratio (pdpi) IX 2% 3% IX 2% 3% 10 749.94 751.49 753.02 0.92130 0.92321 0.92509 20 749.07 750.33 751.58 0.92023 0.92178 0.92331 30 748.25 749.22 750.19 0.91922 0.92042 0.92160 40 747.49 748.17 748.85 0.91830 0.91913 0.91996 50 746.80 747.19 747.57 0.91744 0.91792 0.91839 6
qi 111e cis 01 Figure I. A Schematic Diagram of Flowline Figure 2. A Flowline for Leakage Occurrence 815 805 1 795 At 765 755 745 930. 6C0 700 930 Preditaxl Piman (pia) Figural Measured Flessure vs Predicted he 785 775 735 723 0 20 40 60 80 100 Flow Rate (MMSCF13) Flame 4 Compuisoo of No Leakage and Leakage Conditions for Horizontal Flow 800 790 Da 780 tot 770 760 p750. LI.. 740 it 730 O 720 710 7W 0-4- No I -Amy -0- lase Mg 1216718e (2%) -1* leamge 20 40 60 SO MO Flow Rate (ItRifSCFD) Figures. Comparison of No Leakage and Leakage Conditions for Upwind Flow MO 830 B20 810 p 790 u 8 780 - -14 Inksge 770-4/-12111018e OH) 760-41-1takaP(2%) 750 Inane (3%) 740 730 0 20 40 60 80 100 Flow Rue (MMSCFD) Figure 6. Comparison of No Leakage and Leakage Conditions for Downward Flow 7
130 r IN 729 It E 72S n c!. 727 2% -, 51 707 5 Tr. 7 6 705 -A- 3 A 725 10 20 30 40 50 Leakage Location (liftle) Figure 7. Comparison of Outlet Pressures for Leakage Variations for Horizontal Flow 704 10 20 30 40 Leakage Location (Nth) 50 Figure S. Comparison of Outlet Pressures for Leakage Variations for Upward Flow 754 ç Leakage Location (Mk) Figure 9. Comparison of Outlet Pressures for Leakage Variations for Downward Flow 8