Calculation Cover Sheet Cale no (CA-PR-O14 [Project ttle Process Web Page Proj no (086700589 (Client Worley Oil & Gas Phase/CTR [Calculation title __Verification of Surge Pressure in Pipes (CA-PR-Ol4.xls) Page __! of 4 (Calculation objective |To verify the ST units calculation sheet in the standard spreadsheet Prea014.xls, which calculates pressure surge in a pipeline as a result of ‘instantaneous’ flow shutoff. (Calculation method Manual calculations are attached for SI units. These calculations are in accordance with Joukowsky's Law and lpased on the "Elastic Pipe! theory (see pages 3 and 4). An original calculation was written in Mathcad. This was |checked and converted into an excel spreadsheet. The spreadsheet was updated to account for the effect of cifferent pipe supports and different pipe diameter(internal)/wall thickness ratios. Some examples from the lrefences and the Mathcad model were used to check the accuracy of the equations [Assumptions |The assumptions can be viewed in Section 12 (Ref 1) and Sections 1, 2 (Ref. 2) References T. Massey B.S., "Mechanics of Fluids", 7th ed, Stanley Thornes (Publishers) Lid., 1998 |2. Wylie B. B. and Streeter V. L.., Fluid Transients’, McGraw-Hill Inc., 1978, 3. HTS Handbook, FM12:Pressure surges in a pipeline with liquid flow’, 1990. |4. Van Vuuren S. J., "Theoretical Overview of Surge Analyses’, University of Pretoria (Attachment D) [Conclusions |The spreadsheet calculates the maximum pressure upstream of a source of flow shutoff for instantaneous shutoff (i.e. valve closure, pump trip, etc), Instantaneous refers to the time of closure relative to the pipe |period (wave propagation and reflection). The spreadsheet calculation in SI units is arithmetically correct land is self-containing and do not link to any other sheets, Therefore, it may be exported to other calculations. |The MathCad calculation, although using the correct formula for Wave celerty, assumes the pipe is perfectly lanchored and thus there is no correction of the Wave celery formula for diferent pipe geometry. This |correction factor differs for Thin and Thick-walled pipes, differentiated by the Pipe Internal Diameter/Pipe Wall |Thickness. The spreadsheet has been updated for ths. O_| sF-Jan-08 Issued for Use Chit on Ste/ HT U3 A_| 20-May-02 Issued for Internal Review cr Rev | DATE DESCRIPTION BY CHECKED ‘ems/project_execution/pefm 0b 2s Veticaton Pread’4 RevA.xs Rev 17 1 duly 1908Calculation Checklist Caleno CA-PR-O14 Project title Process Web Page Proj no (086/00589 Client Worley Oil & Gas Phase/CTR [Calculation title Verification of Surge Pressure in Pipes (CA-PR-Ol4.xls) Page __2 of 4 [Please check boxes for all applicable items checked or delete if not appropriate: \Catculations: Calculation number assigned and registered (usual format is Proj No-CAL-Discipline code-Seq No eg XXXX-CAL-E-O01, but format may be varied by Project Manager). Project ttle shown, Calculation ttle shown. Revision history box complete and signed. Index. Appropriate stamp for preliminary issues Calculation objectives (aims) stated. Calculation method defined or described (including formulae if relevant). Reference made to text, standard or code. Check versionJ/edition with that required for project. Source of input data stated (with revision number and date if relevant) Assumptions stated, Summary of results or conclusions if appropriate. For software based calculations, reference to software verification if available. Method clear and easy to follow. Input data correct. Calculation arithmetically correct OR software previously verified and reference to verification checked. Calculation result within expected limits. Calculation tolerances stated if significant. Units used as required by client. Abbreviations correct. Appropriate cross-references. Sketches included and clearly labelled, where required. Attachments included and referenced, as required. |Checking records: OD Checked and annotated copy of calculation filed (use "Check Print” stamp). OD Corrections made as required and calculation dated and signed on cover sheet by checker. Revisions: O Changes clouded. D Revision history block updated. O Cateulation re-checked if required. o o Oo Oo oa Q Oo Qa oO 31-Jan-03 Issued for Use CMs) én STL FI Z07. ‘A [20-May-02 Tssued for Internal Review cr REV DATE DESCRIPTION BY CHECKED p> ‘emafprojact_exscution/petmt0bais Verification Prea01 RevA.xis Rev 17 1 July 1998Calculation Cover Sheet Cale no CA-PR-O14 [Project title Process Web Page Proj no (086700589 (Client Worley Oil & Gas Phase/CTR [Calculation title Verification of Surge Pressure in Pipes(CA-PR-Ol4.xls) Page _3- of 4 discussed in refences 1 - 4. Basically liquids are not completely incompressible and in the [case of sudden change in velocity (specifically a reduction in velocity), the transmission of a pressure wave (from the source of the change) through the liquid occurs. There are three types of velocity reduction: +1) Velocity changes are small enough for any inertial pressure to be ignored, 2) Velocity changes are fast enough for forces that produce temporal acceleration to be important and 3) Velocity changes are so quick (I.. instantaneous) that these forces become significant. It fs this latter group that is the focus of the theory and the spreadsheet calculation. Once the flow is reduced Ihe pressure wave velocity or celerity can be calculated from the following equation for non-rigid pipes: c= Jil pd/x+d BtB) lwhere: fensity (kgim®) «= Fluid Bulk Modulus (N/m?) ld = Pipe intemal diameter (rn) It = Pipe wall thickness (m) IE = Elastic modulus of pipe material (Nim?) actor based on pipe anchoring as follows: For Thin Walled pipe (ait > 25): la) Pipe anchored at its upstream end only B= 1 - w/2 b) Pipe anchored throughout against axial movernent: B |c) Pipe anchored throughout with expansion joints: B = 1 lwhere wis the Poisson ratio of the material. For Thick Walled pipe (dt < 25): la) Pipe anchored at its upstream end only B= [(2*t/d)*(1+y)}+{(d/(d+t)*(1-w2)] lb) Pipe anchored throughout against axial movement: B=[(2*t/d)*(1+u)]+((d/(d+t)*(1-4)] |c) Pipe anchored throughout with expansion joints: B = [(2"t/d)*(1+u)]+[(d/(d4+t)] O_| Sivan-03 Tssued for Use Cit 97 STL. A_| 20-May-02 Issued for Internal Review cr! Rev [DATE DESCRIPTION BY, CHECKED omsiprejact exccuion/petmtob.s Veritcation Proa014 RevA xls ev 17 1 duly 1998Calculation Cover Sheet Cale no CA-PR-O14 [Project title Process Web Page Proj no (086700589 \Client Worley Oil & Gas Phase/CTR [Calculation title Verification of Surge Pressure in Pipes (CA-PR-Ol4.xls) Page _4 of 4 |Theory (cont. [The time taken for propagation and return of the pressure wave upstream of the source of initiation (Ie. @ valve) will take: te2*Lie lwnere: It" = Pipe Period (s) |L = distance from initiation to source of reflection (m) wave celerity (m/s) If the valve closure time (to) is less than the Pipe Period (t*) then the closure is regarded as instantaneous land the resultant pressure Increase (valve closure) upstream of the valve will be equal to: AP =- p* Au * c (upstream side) AP = p* Au * c (downstream side) were: = density (kgim’) lau = Final uid velocity - nial fluid veocty in pipe (ms) Jc = Wave celery (rvs) [This is the pressure change from the normal operating pressure before the valve changed postion and reveals two things; firstly that Au = - u (inti) when complete pipe closure occurs and, secondly, this results in an increase in pressure upstream of the source of closure and negative for downstream, O_| 3h-Jan-03 Tssued for Use Cre Sh STL A_| 20-May-02 issued for Internal Review CT Rev [DATE DESORIPTION BY CHECKED emelprojectsxacutonpetmt0b.xls Verification Pros014 RevA.xle Rov 17 1 duly 1998Attachment A Cale no (CA-PROTE Project ttle Process Web Page Proj no 086700589 Client Worley Oil & Gas Phase/CTR [Calculation title Verification of Surge Pressure in Pipes (CA-PR-Ol4.xls) Page of Attachment A O_| Sitan-03 Tssued for Use Cig on STL ‘A_| 20-May-02 Tssued for Internal Review cr REV | DATE DESCRIPTION BY, CHECKED Verification PreaO4 RevA.xs cemalproject_executon(petm10b.als Rov 17 1 uly 1998Attachment A Calene CAPROI, Project title Process Web Page Proj no (086/00589 (Client Worley Oil & Gas Phase/CTR [Calculation title Verification of Surge Pressure in Pipes (CA-PR-Ol4.xls) Page of (Calculation based on 8" Rubber Hose Material (MathCad Model) Data, sommes? —_p =767.9kgni? Ret 3, used iow est densty along pipetne used © ive most conservative case k:=0.714@\ini? _BulkModut ofthe o. ts the recprocal ofthe costiciont ot compressbilly. Atlachment 1 provied the values of coeficient of compressbily for nonane, decane and dodecane at @5¢C. The values, ranged from 12.51 x10" Pao 16.338 10° Pa, Theaveragevaie of 14x10 Pa! was used. 09.010 gen Basilety (trom Yokohama thatnghoses) Beg Ex0.889GNqi? Baste modus of the pipe 4=247-7mm (Rot 6) 455- 247.75 (Pet 6] 2 Flow: 60000573 dy” Density sp =802.92g 0 Densty ofthe ol at 150 (Rot 2} sastow = (How) (Density gp) mastlow = 3.19210 “kg hr! ye man ners ] Velocty ofthe thd through te pat, Oe y=2396m—7 how. ver: oukow sy’s Law [Fat 4) O_| 3h-Jan-03 Issued for Use Cid ST ‘A_| 20-May-02 Tssued for Intemal Review cr’ Rev | DATE DESCRIPTION BY CHECKED ‘oms/project_exscution/petm 10b.xs Verifeation Proa014 RevA.xds Rev 17 1 July 1908Attachment A (cont.) Cale no. CA-PR-O14 [Project title Process Web Page Proj no (086700589 \Client Worley Oil & Gas Phase/CTR [Calculation title __Verification of Surge Pressure in Pipes (CA-PR-Ol4.xls) Page 4 of 4 where Hohange npressurein head Poot o-enty e-wave\elcity change in velocity of fuld From (Pt 6), = 563.0t6ms ‘Therefore, assuring fat all fhe velocty Is arrestod, jo avev, the surge pressure is glen by ‘sohing for Joukowsky/s Law. The formula obtained by substituting the aquations for P and pe. ‘Where Pi the surge pressure assuring tho ae worst cage of al flow beng arrested Maxirumsurge pressure experioncad in the pbaine (Fstantaneous valve closure). te= 102138 pe pord (time for shock wave to travel he lenght ofthe pipe and return) aT8 ave closure tre P=7.3S6bar —-Maxinumsurge prossure al valve closure tine (non-instantanecus vai closure) O_[ 30-Jan-03 Issued for Use are _ STL. A_| 20-May-02 Tssued for Internal Review rev [DATE DESCRIPTION (CHECKED, femsiprojact_execution/potmt0b.xis Veriication Proagt Rev xe Rev 17 1 July 1998‘Standard Calculation 086/00589-CA-PR-014 Rev. A, “Issued for Use", 31-Jan-03 Validated: Verification 086/00589-CA-PR-014 Rev. A , "Issued for Use, S1-Jan-03 OIL PIPELINE SURGING PRESSURE louenr PROJ No [PROJECT ‘CALC No [suaecr SHEET OF 0 [see] cys se [OiL PIPELINE SURGING PRESSURE. manufacture, Pipeline Numeer: Rubber Hose Example eur para: Five Pipe Geometry tcuis Density at, Po) = 7678] a'n® —_Intmal Diameter of pipetne (4) » 2a7 | mm st. Liuid Density (pes @ 18°C) 0282 | Kain? Thickness of patie () = 103.7 | mm Buk Modulus of Fue (c= Table 1 274 | GN.m* —Pipalie Leng (L) = 2875 | m Fic Fiowste (2) = 397 | min Vane dosure timo () « 7 008 let 20:*, the calculations described in Section 53 will give a reliable answer if some allowance is made for the maximum acceleration exceeding the mean. In all cases except the complete closure of @ valve, the uncertainties in the estimation of v, must not be forgotten. 6 EXAMPLES Two examples are given, the first dealing with the estimation of the sonic velocity and surges due to valve closure, and the second with reflections and surges due to the tipping of a centrifugal pump. FMI2 - : Sravoaeo Lace CA-P e-o1 & ee , FMI2 6.1 Example - Valve Closure Water is flowing by gravity through a steel pipeline from a reservoir to a receiver. There is a control valve 6 m before the end of the line, the final lehgth being horizontal. The level of water in the reservoir is 5.1 m above the valve. The intemal diameter of the pipe is 429 mm and the thickness is 14 mm. ‘The pipeline is anchored throughout The total length of the pipeline is_690_m, and it contains three bends, each with a pressure Joss coefficient (K,) of 0.25. The maximum safe PFESSUre @pyq,) is 20 bar (g) and the vapour pressure () is O2ber (abs). The initial flowrate (VQ) is O58m's. Previous calculations ave shown ° that initially the static pressure is 4140 Pa (g) before the valve and 364 Pa (g) after the valve, What. pressure surges would be induced if the valve were closed in 1 s, and would these.be tolerable? ‘The preliminary estimates can he made as described in Section 5. (1) The sonic velocity is determined as in Section 3, For water, Table 1 gives x =(2913 x 10° Nim”) p= 998 kg/m’ and cy = 1482 m/s. For steel, Table 2 gives E = 207 x 10” N/m’ and p = 0.30. As the pipe is anchored throughout against axial movement, B = 1 - 030° = 0.91. Equation (2) gives sonic velocity, allowing for the elasticity of the pi as: Correck Vole Table ( Of 3 © ster (1 fais xis 0.ez9 207 x 10° x 0.014 % x0s1 ) = 1302 m/s @ Wis given that the downstream length, Iy = 6 m, and the total length is 690 m, Hence the upstream length, L, = 690-6 = 684 m, There are no branches, |FMI2 Equation (7) gives the values of t* for the upstream and downstream lengths: th = 2x684/1302 Abe 0518 WG] =2x6/1302 Box 009 s — ‘The time of closure is given as t = 1 s, so Section 5.2 can be used for estimating the pressure surge on the ‘upstream side and Section 5.3 for the surge on the downstream side of the valve. @) Equation (3) gives the initial mean velocity: 4x 0.28 mx 0.429" = 194 m/s Since v, = 0 whem the valve is fully closed, from equation (8) the increment in velocity i: Av =0-1.94 -194 (@) The upstream pressure surge is given by equation OO: ” -998 x 1302 x (-1,94) Py a 2.521 x 10° Pa ‘Thus after closing the valve in a time less than t*, the static pressure on the upstream side of the valve is increased from its initial value of 4140 0 4140 + 2.521 x 10° = 2525 x 10° Pa (g). This exceeds the maximum safe pressure given as 2 x 10° Pa (g), and is therefore not acceptable, ero0neTES, a Gravwnneo Care CA~PR- Oe feracurent 0 Gent.) It is now necessary to consider the effects of surges generated by reflections at the open end of the pipeline fat the reservoir, and at the closed valve. During the time interval from ¢* to 2t* the surge of -2.521 x 10° Pa from the reflection at the open,end reduces the pressure at the valve back to its original value of 4140 Pa (g). During this pekiod the direction of flow is reversed, Afier time 2t* there is a tendency for a further surge of -2.251 x 10° Pa to be set up by reflection at the closed valve, This exceeds the absolute pressure at the valve, ‘which under standard atmospheric conditions would be 4140 + 101325 = 105465 Pa. Consequently cavitation would ecur and the absolute pressure fall to below its minimum value of the vapour pressure, given as 20000 Pa. Tn conclusion, the arrangement described in the example is not satisfactory, and it would be necessary either to install a surge vessel (see HIFS Handbook Sheet FP4) or increase the time of closure of the valve (see example in HITFS Handbook Sheet FM13). (S) The downstream surge is given by equation (12): 4988 x (-1.94) x 6.0/1.0 +0 - 364 -11981 Pa 404 Thus the downstream static pressure after the valve closure is 364 - 11981 = -11617 Pa (g). Under standard atmospheric conditions the absolute pressure would be 101325 - 11617 = 89708 Pa. This is greater than the vapour pressure, given as 20000 Pa, so there would be no cavitation on the downstream side of the valve, 62 Example - Pump Trip ‘An organic liquid is pumped from a reservoir (A) through € centrifugal pump (P) and a T-junction (1) to two header tanks (B) and (C), as shown in Figure 3. The pressure above the liquid in (A), (B) and (C) is atmospheric and the level of liguid in (B) and (C) is 72 m above that in (A), The piping is 3" Schedule 40 and the thickness of the wall is 5.5 mm and the intemal diameter is 77.9 mm. The length of pipe from A to P is negligible, ftom P to T it is 8 m, with a pressure loss coefficient of 3.2, from T to B and T to C the total lengths are each 500 m, with @ pressure loss coefficient of 186, including all valves and bends. aNOIL PIPELINE SURGING PRESSURE Validate Vertteaton OS8/COSEO-CA-PF-OTA ow. A, lsued or Use, Steam louenr PROM No paovecr CALCN lsusieor SHEET oF 0 [rome] org ste lox RPELRE SoRaWG PRESSURE line Number: Ret 9 Example 64 Input Dara ld Pipe Geometry igs Dens 7, P r= SE] 9h? intra itor psn (a fe |Std. Liquid Density (pay @ 15°C) = kgim? ‘Thickness of pipeline (t) = mm leuk osiu ortudte-Table)= [ate —] GN m* Fein Longin) A rcs ona) = ‘0 | win Yavocosue tine (3 aa tsteazsr Jrowat acl (ora tana) conitns (7) tera Pipe Configuration east of eino) = [J toon? 1 Ppe encore at upsveam ond on 5 2. Pe anchored hep gas axl moves uns mass (E-Tabie 2) ZH] GN? 5. Pee anced win perio ins lisse ato i= Table a3 Ener Opin (1,203) z Contan @) aa learcunareo par Fasc meds of poe (2) = BI] cnn ss Fowao) 7.005869] to ict ort) 134] ms lieve Cee te 1302] mis as port) Pee paras 105] ees tx erp presi) = 2510] ba (rerese in Pressure) lwacna None Talo 1 reports igus Neo 1 “abl 2 Propats ot Matis Nt 1) Tad] Bak oss | —Densy | Sone Valo Tatra [Youn moaute] Poisons ao F n 2 r n Tin |e om wir a tie [79 9 Caster [eo 160 0-05 fica [ 1000 | ret ies Si | 200-210 [ 08-08 Etanot i980 [ 789 iT Const [20-50 cas mo, a 7330 pic [25-35 Os icra | oo 500 | Bes -e86 [T0185 Genesys aa ater zs [ 68 7 ‘Abii [6 ass Ttanimn —[ res a4 Fore cone | ca Noes: 1) HTS lst Tanserané Fi Flow Sonic) Handbook, osion F2"Pressre Suge inate wih Lig Fw Table 1.1860, 2 Giass frost (GRP) properties wi vay aca proportion toe, bong marl ae maha maneAttachment C Caleno (CA-PROI4 Project title Process Web Page Proj no (086700589 Client Worley Oil & Gas Phase/CTR [Calculation title Verification of Surge Pressure in Pipes (CA-PR-O14.xis)___ Page of Attachment ¢ O_[ Sitan-03 Tssued for Use or STL ‘A_| 20-May-02 Tssued for Internal Review Cr REV [DATE DESCRIPTION BY (CHECKED emslpreject_oxecuton/palmtdb.ds Verification Proa014 Rev ats Rov 17 1 duly 1998CA~ PRO Shanda Cale NV ie y 3 y sox nsro ey : veer ” SLO ee Upoxe Ea sax poago Loe Sep a 569-0) spt po #0 E91 pple t cd Yossvant = caselot x cxf = dy/*=9 Rt ZB66= 4 ple eaD Ce YT GIN 30, sald owmpaarose ¥ Ex NdaET ‘or Avs Somer ofa 20 qqS0u 0009 say ELST pe sane vi tm en a nd 0 in ‘TOIsua} puT TweYs OY, ‘Surpuag puv UoIsuay se ITs yeULIO}ap Teas Fun put Sampo eNotes io poe AL ww ‘SC Mor aNmiwvan wor sounds “INAS SIEVE 55-5] (2)2+ t= [Qe LO ey van 20108) SEABOWIED, WEA HIV ME aaeast VV we WV a ‘osuay 01 np 2t0az001 ese Bupoofan “cq yytap paw wap yo Conse svow see8use! Mh 29 paraeffou aq rs oy yxy ony ean oY Eps | Jo SPIER oF NPS UIA PLAS CHL 3a caps au} fo CEBU uote} ao} snp spss HH a Ho ol St 2 av wed) TW a vv > ymporan jo ssauonn peg spi fo npn axenbs 320 ase sejnBoe2o2 PUP oa pareroteo st Aru arenes og wes AVY HY ea Meares 99 katt spesdsovea eps0=4) ‘HI i suns ss seu 40 HE se BUEPSAL qossiog pa mpous ying seudordde ot spaodsanem arg soy aaojonsmes ore saded reeds 205 padoyerop #8 Sua) OG SAE OHM sossoy anaxrsky pun “spsmpoost Teuouoty pe ‘SEE ad aug Jo aT wautque ath ‘wonaas ej wopaduon vpn amy 30 saNPeD Ag MecNtOr ap apne palapeswoo wang YoU Ove TAHA wq cOuLHOSN OACS NS watt "Fy wat {to mmajgyo0o au Joy poyussand 99 19 aun si0g ut paee(800 a2 HAP Srey amy tm Jeo. pinOm yoqUs TER wey azOw ob poadsovee 9) at Snore iaqwor youu aqh sive oeo> oy uy eae Y SEH NIA! Pew T teed) saneTgnvL GIN FE a TLStandard Calculation 086/00589-CA-PR-014 Rev. A, "Issued for Use", 31-Jan-03 Validated: Verification 086/00589-CA-PR-014 Rev. A, "issued for Use’, 8t-Jar-03 OIL PIPELINE SURGING PRESSURE louenr PROJ No lprovecr. ‘CALC No [susecr SHEET OF 0 [ama] org] sna loi PIPELINE SURGING PRESSURE lpipatine Number: Reh 2 Example 2-1 (PUT DATA: lriuia Pipe Geometry liquit Donsty at 7, P (p)= 2082 Intomal Diameter of ppstine (2). 7500] mm sts. Liguia Density (94, @ 15°C) “Thickness of pipaline () = 64 mim [auc mocksus of Fas («Table 1). 22 Pipoline Length () = 1 m lui Flowrata (a) = 1 Vale closure time () 1 808 Ist [Tables “Table 1 - Properties of Lguids (Note 1) Tigud —] Buk Modulus [Density | Sonic Veloaty Young's modulus] Poisson's alo © 2 e E v (ui) eon) (evs) (GN ne 7122) 720) 1192) Castiron 20-160] 025-03 IMetnanct 1000) 721 1123) ‘Stoo! 200-210 | 028-03 femano! 080) 729) 1170) Concrote 20-30 0.15 FFoivene 1592 866) "1330 Pvc 23-33 05, iMiooral Gis _| 1600-1800 | 659-605 | 1000-1480 (GRP (Not 2) 2 0.35 ator 2183 oa 1482 ‘Annum cy (033 “anu 103, 034 Fibre Comer 24 o7 Notes: 1 HITFS (Heat Transter and Fluid Fow Service) Handbook, Section FM12 Pressure Surges in& pipeline with Liquld Flow, Table 1, 1900. 2 Glass reinforced plastic (GAP) proparies wll vary according to proportion of flo, bonding material and method of manufacture‘Standard Caloulation 086/00589-CA-PR-014 Rev. A, "Issued for Use", St-Jan-03 Validated: Verification 086/00589-CA-PR-014 Rev. A., “Issued for Use", St-Jan-03 OIL PIPELINE SURGING PRESSURE lcuewr PAO No pROWECT CALC He lsusicot SHEET e 0 [awe] ergot Oi: PERE SURGING PRESSURE epee Numer: Ret. 2 Example 21 INPUT DATA ia Pipe Geometry [Liquid Density at T, P (p) = gin? Internal Diameter of pipatine (d) = 750.0 mm Std. Liquid Density (pqs @ 15°C) kim? “Thickness of pipeline (t) = 50.0 mm [Bulk Modulus of Fluid (x - Table 1) GN. m? Pipeline Length (L) 1 m Fluid Flowrate (Q} = me Valve closure time (1): 1 secs levearsr 7 owt aati) ort stata) condtons otra Pipe Configuration sesty of pest [=] taom® 1 Pow arched at upstoam ond on be 2 Pe anche neugau apa i movenent froungs modus ( Tal 2 BE] cm a Pe ancheree win oansin ins isc ato (y= able 2)= as Entor Option (1.2013) z Corstan(@) 08 cavcutare para: este ms of ipo (2)= Bare] oNm* tas Fate cea] tot Netty tn cco] ms ave cee T.a76—] ls pe et 2) Fe pra) cco] Secs ta. sige presse () = bar inteasen Pressure) ln Spreadsheet il overestinate Surg Pressure for Ve closure tie (> Pipe Pere (te) Table 1 roporiog ois Noo 1 “alo 2- Proprio of Matos Nt 1) Buk woos | Densay [Sone Voor Tato vous noc] Possons alo fF 2 ¢ = z (MINima) ikon) ‘(mn/s) TN) iz [700 02 Conee | 00-160 [ozo to [7st ties Suet [00-10 | 038-03 1080 1170 Conca | — 20-90 ca "92 1390 eye [23-33 os fener i | ooo 606 [as -286 [bo 180 Seals oss 708 8 ma ‘Ain [69 058 Taam I oe ibe coon |__ 24 ca Noes: 1 HTFS (Hat Tans and Fd Flow Sonic) Handbook, SestonF2 Pressure Supe ina iplne wh Lui Fw, Tablo 11960 2 Glass rolforced plastic (GAP) propartos vil vary according to proportion of fore, boncing material and method of man tacoAttachment D Cale no (CA-PROI [Project title Process Web Page Proj no (086/00589 (Client Worley Oil & Gas Phase/CTR [Calculation title Verification of Surge Pressure in Pipes (CA-PR-Ol4.xls) Page __4 of 4 Attachment D O_| Si-tan-03 Issued for Use cr STL ‘A_| 20-May-02 Issued for Intemal Review cr Rev | DATE DESCRIPTION BY CHECKED \Vertication Proaot RevA.xle ‘ems/project_exocutonipetmtob aks ev 17 1 July 1998Srawoneo Care CAWPR- OIG Derreumeny O ‘University of Prétorid THEORETICAL OVERVIEW OF SURGE ANALYSES by SJ VAN VUUREN Tel : (012) 420 2438 Fax : (012) 362 5218 E Mail - fvuuren@eng.up.ac.zaStampneo Care CA-PR-O1% Arracumenr D THEORETICAL OVERVIEW OF SURGE ANALYSES ‘THEORETICAL OVERVIEW OF SURGE ANALYSES INTRODUCTION “The terms "water hammer" and "transient flows" are used synonymously to describe an unsteady flow of fluids in pipelines, although the former term usually refers to water only." Different types of flow variation can contribute to transients, varying from a single identifiable alteration to an oscillating, periodic, or pulsating disturbance. In pumping stations (where rotary pumps with electric drives are used) and water supoly systems, transients are normally governed by @ change in the operational status of the pumps or valves, by varying demand experienced by the system, cor by unpredictable circumstances such as pipeline or power failures. This lecture provides an overview of the theories describing surge phenomena in close conduit systems, Attention is also given to calculation methods used to determine surge pressures. The value of a holistic procedure (Transient Risk Assessment Procedure, TRAP) to determine the possible causes of surge pressures is emphasised and various measures that can be taken to prevent excessive pressures are discussed. No reference is made to the utlization of computer analyses to calculate surge pressures, although various programmes are available and in use, since the SURGES programme will be discussed in detail later. An example is evaluated to demonstrate the use of TRAP for estimating maximum transient pressures and to establish what analyses should be undertaken to determine surge pressures for optimum design, It is the aim of this lecture to create greater understanding of how pressure transients are caused and of the need to consider pressure surge effects prior to finalizing of pipe sizes, pipe classes, pipe material, and mechanical and electrical plants. ‘THE BASIC THEORY OF TRANSIENT FLOWS. ‘Transient flow theories for instantaneous disturbance in pipelines ‘A change in the steady-state operating condition of a fluid system, unintentionally by means of the closure of a valve or unplanned pump operation, or due to system failure, is communicated to the system by pressure waves travelling at approximately sonic velocity and propagating fram the point in the system at which the change in the steady flow condition was imposed, The system attains a now state of equllbrium, after some time, if the change has not reached destructive proportions. The rate of change is of prime importance and governs the method to be employed in calculating the effects of pressure wave propagation. If the rate of change is slow, one can assume that the fluid is non-compressible, i.e. the change in flow condition is instantaneousiy transmitted through the system. The analysis based on this assumption Is referred to as the rigid column theory®. Systems with high pressures and high flow rates offen require control systems to implement operational variations, ‘The compressibility of the fluid as well the as elasticity of such systems need to be considered to provide satisfactory results (compared to the measured values). This theory Is referred to as the elastic theory.Srawvarn Cae. CAM PR-oiH Arracinews 0 THEORETICAL OVERVIEW OF SURGE ANALYSES The raid column theory if Newton's second law governing the flow in a pipeline with a cross-sectional area of A(m?) and a length L(m) is applied, the following relationships from which pressure fluctuation, AH (m), can be delomined fora valve closure atte end of the ie results: -k dy m4 am. AME oe B “ where represents the change of flow velocity, dv, over a period of time, dt. dt It has been established® that the rigid column theory provides acceptable results for the pressure fuctuations resulting ftom @ vale closure if, dt > 2, where at equals the time-lapse in seconds botweon the two aquirium stages and (ni tp length ofthe ppsine es bibre + after ‘The sastc theory f TThe Elastic theory is based on the essumotion that, wherever a disturbance occurs, the press wave that is created wil propagate along the pipeline at a rapid, but nevertheless finite, rate. This results in the wave moving through the system, reaching specific points after a period of time (dependent on the wave celesty of the system and the location relative to the position where the disturbance Was introduced), provided original stsady flow conditions are experienced. It can be Understood, therefore, that propagation of the pressure wave (positive) results in compression of the fiuid and the deformation of the pipeline as the pressure wave moves through the system. in applying the elastic theory to determine the magnitude of transient pressures, the elasticity of the pipeline can be neglected (rigid pipe theory) or taken into account (elastic pipe theory), This ieads to the following two variations of the pressure-flow-relationships. The elastic (cae) pve theory Using Newton's second law it can be determined that « Ap=¢ ane gtk, P=EcM%, bg oe 2 2 Gite pressure fluctuation (Mim?) wave capacity for a rigid pipe (mis) unit mass of water (kg/m?) flow velocity (m/s) ‘The wave celerity, ¢, can be deter te Bulk modules for the fluid (Nimm?) 12d by: ° where K This relationship was derived by Joukowsky and is referred to as Joukowsky’s Law.Srouonen Care CA-PR-ote Arracuenr 0 THEORETICAL OVERVIEW OF SURGE ANALYSES Tho Elastic pipeline theory Elasticity of the pipe reduces the wave celerity and, applying the principle of preservation of energy, it can be shown that: (3) wave celerity for an elastic pipe (m/s) bulk modulus of water (Nim) elasticity of pipe material (Nim?) diameter of pipe (m) wall thickness of pipe (m) * Values of K and E (for different fluids and pipe materials) are shown in Annexure 1. The influence of the pipeline support on the wave celerity The support conditions for thin-walled pipelines (elastic) influence the wave celerity due to the restriction imposed on longitudinal deformation by the supports. One generally distinguishes between the following two situations that increase celerity: * Case 1: Pipeline anchored at its upstream end only * Case 2: Pipeline anchored throughout against longitudinal movement. Celerity for these cases can be calculated as follows: «) where: c¢ = celerity for the pipeline (supported) and the value of «, can be determined by caset: qzi-# 2 Case 2: andy Poissons ratio (Annexure 1 provides values of » for different pipe materials). These theories referred to above, however, do have one a serious shortcoming in that they assume that the disturbance (valve setting, pump status etc.) is instantaneous. It is essential to ‘extend the theory to incorporate a time dependent relationship between the pressure and the flow rate to be able to simulate complex systems accurately. Before those relationships are derived (Theory for Complex Systems) it is necessary to discuss wave propagation brietly, since it provides @ visualisation of how the influence of any disturbance is transported through the system. ‘The propagation of transient waves in closed conduit systems ‘Wave movement in a pipeline can best be ilustrated by assuming 2 valve closure in a pipeline that links two reservoirs A and 8 (Figure 1). At the calculated celerity, the wave travels throughStampnen Cac CA-PR-O% Aecncument 0 THEORETICAL OVERVIEW OF SURGE ANALYSES the pipeline to a boundary condition (reservoir or dead-end) and back to the point of origin within ‘Assuming valve closure Is instantaneous, the fluid adjacent to the valve in each pipe is brought to rest and pressure waves conveying this information are propagated in each pipe at the ‘appropriate sonic velocity ¢, Ata later time f, the situation is that shown in Figure ‘(a), where the wave fronts have moved a distancel ’ = et along the pipeline. Deformation of the pipe cross- section is also incorporated a distance’ as shown. ‘The pressure waves reach the reservoirs, terminating the passage through the pipes, at @ given time t =Lic following valve closure (Figure 1(b)). At this instant, an unbalanced situation arises at the pipe-reservoir junction, as it is clearly impossible for the fluid adjacent to the reservoir inlet to maintain a pressure different to that prevailing in the reservoir. Hence, 2 restorative pressure wave with a magnitude sufficient to bring the pipeline pressure back to its value prior to valve closure is transmitted from each reservoir at time U/c. For the upstream pipe, this means that a pressure wave is propagated towards the closed valve, reducing the pipe pressure to the pressure in the reservoir and restoring the pipe cross-section, The propagation of this wave also produces a fluid flow from the pipe into the reservoir as the pipe ahead of the moving wave is at a higher pressure than that of the reservoir. As the system is assumed to be frictionless, the magnitude of this reversed flow velocity is the exact opposite of the original fiow velocity, as shown in Figure 4(e), [At the downstream reservoir, the converse occurs, resulting in the propagation of a pressure rise wave towards the valve and the establishment of a flow from the downstream reservoir towards the valve (Figure 1(c)). For the simple pipeline considered here, the restorative pressure waves in both pipes reach the valve at time 2i/c. The entire upstream pipe has, thus, been returned to its original pressure and a flow has been established out of the pipe. At time 2l/c, when the wave reaches the valve, there remains no fluid ahead of the wave to support the reverse flow. A low pressure region, therefore, forms at the valve, destroying the flow and giving rise to @ pressure reducing wave, which is transmitted upstream of the valve, once again bringing the flow to the rest along the length of the pipe and reducing the pressure within the pipe (as shown in Figure 1(d)). It is assumed that the pressure drop at the valve Is Insufficient to reduce the pressure to fluid vapour pressure. As the system has been assumed to be frictionless, all the waves have the same absolute magnitude and are equal to the pressure increment, above steady state residual pressure, generated by the closure of the valve, If this pressure increment is A, then all the waves propagated are 2h, as shown in Figure 1. Hence the wave propagated upstream of the valve at time l/c has a valve -h, and reduces al points along the pipe toh below the inal pressure by the ime It reaches the upstream reservoir at timeSrawpaeo Cre CA-PR-O% Pemenment D eee 8 i |’ fd o iL = (e} Tine oe (oy ewe Figure 1: Precsuro and velocity nrofiles at a number of instances (time ster.) following an instantaneous valve closurc. Frictional losses have boon ignored. 5Srawonay Care CA-PR-Ole Arracament 0 ‘THEORI-TICAL OVERVIEW OF SURGE ANALYSES Similarly, the restorative wave from the downstream reservoir that reaches the valve at time 2f/c establishes a reserved flow along the downsiream pipe towards the closed valve. This is brought to rest at the valve, with @ consequent rise in pressure, which is transmitted downstream as a +h wave arriving at the downstream reservoir at 34/6, at which time the whole of the downstream pipe is at pressure +h above the intial pressure with the fluid at rest. ‘Thus, at time 3c an unbalanced situation similar to, the situation at_¢ = Le again arises at the reservoir ripe junctions, with the difference that itis the upstream pipe which is at a pressure below the reservoir prassure end the downstream pipe that is above resgyvoir pressure, However, the mechanism or restoring wave propagation fe Wenieal wit that of =, reuling In 2 #h wavs being transmitted from the upstream reservoir, which effectively restores conditions along the pipe to their inal stato (as shown in Figure 1(0)), and a -h wave being propagated upstream from the downsticain reservoir, which establishes a flow out of the downstream pipe. Thus, at time f = 4 /c, winen these waves reach the closed valve, conditions along both pipes are idertical to those at t = 0, Le. the instant of vaive closure. However, as the valve is still shut, the cstablished flow cannot be maintained and the cycle described above is repeated. The pipe system chosen to illustrate the transient propagation is a special case as, for convenience, the pipes upstream and downstream of the valve were identical. In practice, this would be unusual, However, the transient propagation described would still apply, except that the pressure variations in the two pipes would no longer show the same phase relationship. The movement of the wave as illustrated in Figure 1 shows how important it is to visualize the wave movement, since It can happen that the effect of the waves can be superimposed, potentially resulting in unexpected pressured circumstances that could cause failures.Sranwvee Care CA-(h- OF 0 Reracument Appendix 1: Properties of liquids and pipe materials 1 ity for water Temperature "c 2. Fibre cement 24 Cast Iron 90-160 Conerete 20-30 Ductile ron 172 Mild Steel 200-210 uPVC 23 3. Poisson's ratio of different materials Material # Fibre cement 017 Cash Iron 0,25 Concrete 0,15 Ductile Iron 03 Mild Steel 0,28 uPVC os APPENDIX 1-1Attachment E Cale no CA-PR-O14 Project ttle Process Web Page Proj no 086700589 Client Worley Oil & Gas Phase/CTR [Calculation title Verification of Surge Pressure in Pipes (CA-PR-O14.xls) __ Page of Attachment E O_[ Si-Fan-03 Tssued for Use oH ST ‘A_| 20-May-02 Tssued for Internal Review cr REV [DATE DESCRIPTION BY (CHECKED cemarojact_executonipetmtob.ds Verifeaton Proadt RevAxle Rev 17 1 duly 1996‘Standard Calovlation 086/00589-CA-PR-014 Flev. A , "issued for Use", 31-Jan-03 Validated: Verification 086/00589-CA-PR.014 Rev. A, WW] OIL PIPELINE SURGING PRESSURE Issued for Use", 81-Jan-08 lcuent PROM No [PROJECT ‘CALC No jSuBJECT ‘SHEET OF © _ [armas | orga STLFTh [OIL PIPELINE SURGING PRESSURE cine Mumoer: Tobe ached INPUT bara: ua Five Geometry [Liquid Density at T, P (p) = 998.2 kgm? Internal Diameter of pipeline (d) = mm |Std. Liquid Density (P44 @ 15°C) a kgm? Thickness of pipeline (t) mm [Bulk Modulus of Fluid (x - Table 1) 22 GN. m? Pipeline Length (L) m [Fluid Flowrate (Q) = 397 mine ‘Valve closure time (t.) secs: —— let Pipe Period (te) [rabies | “Table 1 = Propertis of Liquids (Note 1) “Table 2 Properties of Materials (Note 1 Tiguid [| Sule Modus | Densiy [Soni Velooly Material [Young modus] Poissons rato x ° © E v ang) [ain wy Tau ore 1122) 720 1192) Gastron | 00-160 | 025-08 [Meranot 10001 791 1123 Stee 200-210 | 028-03 Etanoi 1080) 729 1170 Concrete 20-90 0.15 [rouene 1552 288 1890 PVC 23-35 05 [Mineral Ois | 1600-1900 | 668-986 | 1900-1480 ‘GRP (Note 2) 50 0.35 ater 2195 298 1482 ‘Aluniium 68 0.38 Tierium 105 04 Fire Cement 24 a7 Notes: 1 HTFS (Host Transfer and Fluid Flow Service) Handbook, Seti FM2'Pressure Surges ina pipatine wth Liquid Fow, “Table 1, 1900 2 Glass reinforced plastic (GRP) proporie wil vary acoorcing to proportion of fibre, bonding material and method of manufactur,