The Impact of Friction Factor on the Pressure Loss Prediction in Gas Pipelines

7/28/2019 The Impact of Friction Factor on the Pressure Loss Prediction in Gas Pipelines

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SPE 30996The Impactof FrictionFactoron the Pressure LossPredic%oninGas PipelinesH. Ilkin Bilgeau and George J. Kopema Jr., Weat Virginia Mvemiiy

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Abstract&p_ti@k~tiy ti-tibytie~tofa~dmp ~tkipsted during diiferent phases of natud gas trsnspmts-tion. The outlet pmsaum can recomputed byacommongsspipelineequationsuch asWeymouth or Panhandle formulas at thedesiredflow rate and pipe size. In addition to selecting the proper* Qf~P@~*. ~ -- capacity and the related cost amdetermined based on the discharge pressure. The flow rate, inthese eqtmtions, is defined in terms of a turbulent fiction f-.~ =f&Q&i@ & dw roug!meisb the pipe An dkieacy factoris employed in the equations for adjusting deviations in thepreamm*csl~ Exiskmeofa sublayer, duetothepipesurfhce condition and accumulations ofm&msste, can gawratecases that cannot be defined properly by the use a single tictionfactor.ThepmpersizingufapipelinecanbeimpmvedbycMiningthe ranges of errors introduced with the use of diflereat fictionfactom.Di%&mtccmlstions existfm the calculation of the fiction factor,f as a fimctionof Reynolds number and the relative roughness ofthepipe. Thef~fdrfeither require sniterativepmcedumormay be solved explicitly. Also, each fiction factor coKslstionexists with its own valid limits mgsnling Reynolds number andrelativeroug&s. Thus, someequstions sresimpletousebutnotaccumtesndsamesm accurate butnoteasytoinqmate into thefinal equation.btis*, ti#atoftiefitim f-mti~*calculations for gas flow is presented. Various correlations fixiiktionfsctorssr eutilizdt odemonstmtet heir impscton thedesigoofnstmal gsspipelines. Also, a summary and a comparisonofmulta am presented for dii&ent flow rates, pipe sizes, and fmfield data.

IntroductionPmsaureistkdiving&rce fortheflow ofnsturslgasin gstherhgsystems and tranmusonpipelines. The pressure drop betweentwopointsallowsthec@neer tooptimizethepipeline diametersswell as the coqmsor using basic flOW e qu at io ns such asWeymouth or Panhandle equations.The basic flow equations consist of three mmponents calledelevation, velocity, and fiction. The elevation cmponent isdtptif?=grsti ty~whm-tiov~tikmgtbofahmhntal or inclined pipeline or gathering system,willbecome negligible due to its d eifect upon the result.Inpipeflow, the velocity of gas is much higher thau that of the oiland it playa a signifmut role within both the velocity componentaodtkii%tion componmt. Whenthe size of a pipeline is selected* velocitymmponent is fixed at the desired field gas productionrate.On the other hand the calculation of tiictional presaum dropcomponent requires the knowledge of pipe cxmditionin terms ofroughness. The pipe roughness plays a major role in the. .de@mu@mofpmsure bsaincethesmdme5s of the intern&surface is changing over time. The general approach m thedetermination of tictionsl pmsaum losses is to use au empiricalfiCt iOll k t o r . ~k rd fiCt iOII faCtOrSm? -ted by VSliOUSinve s t i ga to r s . a

Th e most commonly used iiiction factors were presented byColebmok-White? The Colebrook-White equation has beenapplicable over a very wide range of Reynolds numbers andrelative ro@mess values within an acceptable stmdard of_ III$WbrOOk-Whites formulation, the fiction factor is&tummedusmg sriiterative technique. That is the fiction fmtorappears on both sides of the equation and must be solvedwith atrial and amr approach.Overtime, manyauthommated approximations to the Colebmok-Whiteequatims.lQThese sppnmimations could be grouped intotwo types of equations - iterative and direct. The iterativeequations aUowedfora trial anden-orappmach tode&minethefiction f~tor and weE often not as precise as the Colebrook-White fmulstion.

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~ H ILKIN BILGESU AND GEORGE J . KOPERNAJr... ----- -.---- . ... SPE 3099However, many direct fbrnmlations have made great strides ium~~~ ofm when COmpSfCdo the Colebrook-white equatk scveraI equatioIM-h ss Chen ~ *&@J=7.deviatehrnthe C&brook-White equation in such a small mannerthattkymaybeuaed inplaceafthe iterative-. Byuaingthese direct cslculatim quick and easy computation of the ii-ictionfactor may be accomplished with a calculator or a apn4ah@nmm mm An n t h e r t vn e of&m&t sohtb hVOktS fiction fUkX. ... . . -. .. -Jr- -- --- ________charts genemted by ~~ -= b- ~ * ReYn~~number and pipe rou@n6a values.Gaaflowcahdaticmsarebaedonequationsgiw=byfWymouhPanhandlqcatheAmuican GasAssociation (AGA). Within theseequations, tie Iiiction factor term fium the geaeral equation hasbeUlappdn@d byllktionfactorsdehed~ac ombinationof-. - - .# 41.. ..n..nnnt- lx?. Ann U7- flmu mta ndafiveUUGu -G ULw pl -. Susupyu .-, u ., .. .. . .roughness, or apec~c gravity. In these ~ where thefiction f=tor term has been appm~ anmeoua valuea ofeither pmaaure orgasf.lowrate will becahxdated. Inthesecasea,the applicable range ofReynolda number or relative mughnem todiameter ratios has been not either met or exceeded fm theemployed approximation.

BackgroundThe nations gas pipeline network is a vital sector of the energyinduaby anditcamies gas in either direction depedngontheneed. This continuous flow system cau be represented withindividualpipes where thegasflowhasto beddermbd Deriva-tion of the gas flow rate equation is given in dil%rentpublications2An energy balance between two enda of pipe yieldsthegasflow equation withterms forwork doneby thepump,elevation and kinetic energy changes, and fictional bases.Except laminar flow, theactual syatemenergy loaaescannotbeprdcledthmretically, and must be dctmmined experbmtally. AlUliVLTS i4 @ u se d c or re ct io n based on ~tation is thefiction factor. The fiction f-is a comelating function of boththe Reynolds number and the relative roughness. Reynoldsnumbers am ddned as the ratio of gas density, gas velocity, andpipe diamderto gas viscosity.The relative roughness is qressedas the absolute mughnem of the pipe to its diameter.

ApproschAompriam studywas conducted to determine the discrepanciesmaukinghn lhe use of diffenmt fiction factor comelationa.Onlytmbukmtflow regimes were considered and a minimum Reynoldsnumber of4xl@ was used. Six explicit non-iterative rehtionshipswere examhed with Reynolds numbers and relative m@nemesranging from 4xl@ to 8X10-7and b 1.0x10-7 to 5.0x102 ,mapectively. The empirical correlations presented by Churchill,Ajitaaria,w, Cheaf,Serghidea7,and the modified Mkumdae6wcmuaedintheibrm Medin Table l. Aniterative procedure wasused to cakxdate the friction factor VShES d d n e d in Colebrook-White correlation. The fiction factor values Wem also computed

wi th s ix n o n-it e ra t iv e COITClationsnd the percent deviations ifiktiontkctomhm Colebrook-white correlation were computedFanning fiction factor, which is one fourth of Darcys frictionfactor, was used in all cases throughout this study.Published data and measurements * a gas gathming pipelinwere used to calculate the flow rate with the basic gas flowequation. The basic equation was teamed with the friction f-comelationa utilizd earlier in this study. The data were alsouseto calculate gas flow rates using four difkrent versions of th--tm=byw-,=-ti-tiwPanhandle ~ and Panhandle B. Table 2 shows the fotm of flow-Wmrntbisq.mticflow-mwuatocakdateflowrates andpn=aumdrops withdiffemntempridfiction factor cormlationa.

ResuttsThesixcorrelationa uaedinthis atudywerepmgnunmed fm=with a apre@ket. Due to its widely accepted use, the iterativCoWrook-White correlation was taken as the base case. AIiicdonfactorViIh ES W~ COll@Cd and the deviations iiwmbascase Wue &mmned. Table 3 lists the percent deviations iikiction fib calculations with Six difkrent correlations iiomCoMmok-White correlations. Various flow rates and pipe aimwere canaiti however, only six Reynolds numbers at sevedifferent relative ro@mesa valum are listed m Table 3. It ihta@ingthStthediff~ in the tliction factor valueabecommore significant in the lower and higher Reynolds numbers.TbAtshn apipdine m the Vensngo County, Pennsylvaniawausedtocompute gaaflow rates with five equationa asliatedinTable2. Meammdvalueswem the gascunpoaitim pipe diameteinlet and outlet pmmurea, and the gas flow rate. Data for pip~ was not availableanda value of 0.0006 was used asbeat edimate since the pipeline is relatively new. An edmate fmthe pipelines efhciency was also needed. A value of 0.88 wachosen florn the generally accepted rmge of 0.88 and O.%. Thselection is believed to reflect the closest approximation to thdkiency of the pipeline with several valves and drips. Once thvariatdesW~ de t en n in ~ each equation WSS SOh k !d for the flora@w Atthispoinh eachtlowequation waa~edandtioutletpmamre, pz,was computed. This process allowed a doubcheck of the dataThe results ufthis portion of the study reveal that the computeoutlet pmaauma vary slightlywhen compamd with the calculateflowrateaaa ahownin Table 4. Theaveragepercent deviationsrthecaMatedpresaLmvvcmobaeWedtobelessthan9percentfbrallcaxs However,theaveragepercuKdeviationainthecrdcuhitedgas flow rates were highest fm the Panhandle-B equation anlowest tbr the basic flow equation as ahown in Table 4. Sinflmbwpwwfwdmpbttiflowmewmtmnahed intocumulativepmductk. The cumulative productiofor tltleen days of field data and the cumulative gas values comp@edwithilvedi&rentflowequationsareshowninFigurel.AU

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SPE3099S THE IMPACTOF FRICTtONFACTOR ON THE PRESSURE LOSSPREDICTION IN GAS PIPEUNES 3

fmulasyieldhigbugasvolummtian~intiefieldkfti days, tie deviations in the gas volume predictions wemgreater than 100 percent with Psnhandle B equation yielding thehighest deviation.AIIMWM gaslowequationsonsidtmd thebasic flow equation~ C.JA da+. A &,Au ,wmeyieidedmhveatdev%tkinlwl-u A , . Cond!uddto fi~~ & @ect of fjidk)llfactor correlati& used in the bsaicequation Sixnon-iterative tiiction factor correlations were used inthe basic equation and separate calculations were camied out todetermine flow rate and pmsaure values. The calculated valueswemcompamd withtbefi@ data andthe average percentdeviations listed in Table 5 were observed Table 5 mggesta thatalltion thctor carelations employed in the flowequation yieldsan.waverage percent deviation of 5.5 pement m pmasure values.IkeWerss%permkdevii h?!owraa ~ ** m= -!!correlations, but much higher in magnitude than tbe averagepercentage values observed iu pmsaure cahlations. NaL fourcomlatiom%ernplciyedm therate equationa, were used to calculatethe friction factors between Reynolds numbers of 34,500 and48,000. Figure 2 shows the calculated fiction fkctor values andtbevslues determbed by the Colebrook-White comelation.Figure2 suggests that the friction fsctor values employed in flow equa-tionsyield lowvalues compamdto COlebrook-White.The undem-timation of fiction factor values caused the calculated gas flowratestobebighcrthsttbe ac4usltie4dcnditionaa sshownrnFigurel.wbmtheconditionspemlit meammmatofapmasur edmpin--- L- . A +. AA -,X. :. *batlexisbgpipeb SyKtt - w b w piu%lw &w m -selection of the appropriate fiction factor equation.

ConclusionsFrom this study, the followings were concluded.1. Among the fiction factor congelations ~ the MoodyscUmMionyiddathelargeatdevidmswitbmorethsnI2%athighReynolds numbers. Cben and Serghides correlstiom yield theknvest percent deviations in all ranges considered in this Shldy.2. WheJleachoftheaixfiictimfactorcolTelationswemusedintbebasic equatiorLthey COmp~ t kvorably wit h t he r esu lt s @VUl bytbe basic equation using the C&brook-white fiction factor.~, the ~Cllbd VSkS W- bigberby 5.5 percent fdr thePRSSUI@~by anaverage of43 percent for the gssflow rates.3. Tbe gas flow rates calculated with Weymout4 Panhsndle &PsnbandleB, AG~ and basic flow fmnulas yieided bigber valueswhencompamdwithllelddsta Fortbefielddataused inthisstudy,the-basicfiowequmionyieidedtheiowestdeviationin&lefiowi-ate~~m .~c~ * q!.y~. ~.eum~ t h k AA9ti~ ~~ S=OIIISuwwvw,. ----gaarateswere Overeahmstedbecauae tbefliction fhctorvalueswereyielded lower than actual field conditions.

Nomenclaturey = Specificgravity,dimensions~D = diameter,L, in.E = pipeline e%iciency,dimensionlessf= mt ionfsctor ,dimensionless~= An t=nmlmesT. i ny .y . . . ..& - .- . - -,.L = hgt b of t hepipeline, L, miles.P,= idet pfeasumrn/L2,psipl = outletpressure,niL2, psip== Standadpressure,m/L2,psiq== Flow rateat atandd conditions,L3L SCF/DRe= Reyno ldsn umb er , d im e n s io n le s sL=~,RT==atandad ~$ R~=. ~a- ~.~~ f@u dimeneinnl-~-., .-..-..

SubaeriptsSc= atandd conditions?n=meauormixtm

References1.Jain,A& AccurateFrictionEquation forFrictionFsctcm (May1986) 674.2. Chumhill, S.W.: ~riction-factor Equation -S d th l id-fkw

Mgime$ chemicalEnginaring(November, 1977) 91.3. Chcn,NK AnExplicitEqus60n fw FrictionFaotorinPipc3M.Eng. Chcm.Fundam (1979) 18,N0. 3, 2%.4. Round, G1.: An ExplicitApproximationfor the Fric60nFactor- Numb Relation fbrRough and Smooth Pipmfl TheCanadii Journalof Chcmieal Engineain& Vol. 58 (Febnuu1980) 122.5. _NIL %@OIIS, Prqrarn Aid GSS-~W t idat ions, @& Gas J., (Aug. 9, 1982) 138.6.Nkuradse, J.: Stmnwngsgcsetzi in Rohmn,Ver.Duetch. IngFomohungshek(1933)361.7. ~ TX.: %atimak FrictionFactorAccumtciy ChcmiadEnginecr(Mareh5, 1984) 63.8.Moody,K.L.:An Apprdmatc Fonmda fix pipe FrictionFactorTmns.ASME, (1947) 69,1005.9. ~ C.F.:TurbulentFtowinPips with particularrcfkmncb theTransitionRegion belween SmoothandRoughPipeLaws;J.ofthchwt. ofChil En@necm,(1938-1939) 11,133.10.Haalan&SE.: Siiplc and-Formubs fw theFrictionFactoin Turbulent~ ~W: J o u m d of ~UidS Eq@mcr@, (Marc1983) 105,89.

11.Zigrand,D.J. and $kStCl, N.D.: %xpIicitApproximationsto th8ohdionofCoMmoks FrictionFactorEquation,AIChEJourm(May 1982) 28,N0. 3,514.12.KazD.L and@R L; Mtund GasEngineaing - ProductionsndStorage? -W-m Publishing(h@illy, New York, N.Y.,:990.

S1MetricConversionFactors~ ~~-~g* lzn l .~-.in . x 2.54* E+OO=cmpsi x6.894 757 E+OO= kpa

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4 H. ILKINBILGESUAND GEORGE J. KOPERNAJr. SPE 30WB

TABLE 1- FRICTION FACTOR CORRELATIONShmatigator FrictionFactor Corralatbn coaatantlln-1 .L-__l. wn:.- / ~Jj ~ ~613\oIeoruuK- w IJllc

1.3.7065 Re@+ = 41 . J

Churchill f={:)+ (c,:c,p] C1 (24574(+)+(%)))

G = (~)

Ajitaaria f=O3{(#73m#n+nllMoody I i-,.-E0. k \ lB ~ ~f = .w l I ( F -5) ~Chm ~ ( y~ ~.~~~ } ~ = l)y~v.lw / 7.~A9)*l. I=411 - --#ogc3# ,3.7065 I I 3 2.8257 I xl ,Serghi des

[ 1C4.781~ 2f = 4.781- C~ - C, + 4.781 C4= -{%+%)i ~~1

2.5!C4)c5=-210 3.7 + Re J

Nihradse =24571(3;+%4

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SPE30996 THE IMPACTOF FRICTION FACTORON THE PRESSURE LOSSPREDICTION IN GAS PIPELINES 5

TABLE 2- GAS PIPELINE ~W EQUATIONSEquations FluwRate Friction Factor CorrelationBasic NOW T I JJ (P; - pz~s o-sq= = 38.774(:) [

$YLTwFn ]Es

Weymouth 0.00810 (p: - p2~s333105Eq= = 433.49(5) [ f=WA dossSC

Panhandle A 0.0192l.~[ (p: _ p:#S&l 0.5394q= = 435.87(f) ]E f=SC y08%LT~m (f;*

Panhandle B T l.~ (P: _ p2~4.%1 o.51 I f= 0.00359_- = 737(f) [- ]ESC Ymi~~=m I @J-AGA T l .O(p; - p2~s s% = 38.774(;) [ 1% f= 1SC JWmZrn [410g()f

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6 H. ILKINBILGESUAND GEORGE J. KOPERNAJr. SPE3099

T-U 3- PERCENT DEVIATIONS FROM COLEBROOK-WHLTE COIUUU.ATIONkm Re f - CokbmoH?Wte Mody -- N~

i 4 7 4 f# 13 0.QiW 1.56 Q.82 Q.45 Q.47 0.16 1.58k1-04 0.0077 0.25 0.70 Q.34 0.20 0.20 0.251C+Q5 0.0045 0.75 3.31 3.66 0.02 0.35 0.75MQ6 0.0029 0.38 5.28 S.62 Q.Q5 0.46 0.38lcto7 0.QQ20 0.46 0.28 0.62 0.08 0.48 0.461cI08 0.0015 1.37 12.82 12.57 0.09 0.38 1.37

146 4#03 O.OIQQ 1.56 0.82 0.45 0.47 Q.16 1.581AM 0.0077 0.25 0.70 Q.34 0.20 0.20 0.25MQ5 0.0045 0.75 3.31 3.65 0.02 0.36 0.751C+Q6 0.0029 0.34 5.19 5.49 0.03 0.43 0.34le+Q7 0.0021 0.50 0.03 0.09 0.03 0.37 Q.50M-OS 0.0016 1.10 11.60 12.02 0.10 0.09 1.10

IC-05 4CI-03 0.0100 1.56 0.81 0.45 0.47 0.16 1.58M-04 0.0077 0.25 Q.69 0.33 0.20 0.20 0.25letQ5 0.0045 0.71 3.23 3.53 Q.01 0.35 0.71MQ6 0.QQ30 0.17 4.52 4.49 0.06 0.31 0.17lrrlQ7 0.0022 0.66 1.13 2.03 0.17 0.08 0.661c+08 0.002Q 0.43 5.71 7.12 0.09 0.02 0.43

le-w 4e+Q3 0.0100 1.58 Q.75 0.42 0.45 0.16 1.60M-04 0.0078 0.32 0.68 0.39 0.16 0.19 0,32M-05 0.0046 0.37 2.53 2.37 0.12 0.24 0.37le+06 0.0034 0.47 1.56 0.09 0.25 0.Q5 0.47kl-07 0.0030 0.38 Q.89 3.12 0.09 0.02 0.38le+08 0.0030 0.09 1.37 3.72 0.01 0.03 0.09

le-Q3 4e-Q3 0.0102 1.86 0.27 Q.20 0.31 Q.14 1.881C+04 0.QQ81 0.84 0.38 0.65 0.02 0.14 0.84ktQ5 0.QQ55 0.74 0.18 1.85 0.27 0.03 0.74leto6 0.QQ50 0.43 0.65 3.70 0.08 0.03 0.431C+07 0.0049 0.09 0.84 4.05 0.01 0.04 Q.09lct08 0.0049 Q.01 0.86 4.08 0.00 0.04 0.01

142 4d-Q3 0.0123 2.98 4.39 2.99 0.00 0.07 3.10le+04 0.0108 2.11 4.18 1.89 Q.15 0.01 2.111C+Q5 0.0096 0.65 4.22 Q.76 0.05 0.05 0.65M-M 0.0095 Q.13 4.23 0.59 O.Q1 0.06 0.13k+07 0.0095 0.02 4.23 0.57 0.00 Q.Q6 0.021c+Q8 0.0095 0.01 4.23 0.57 0.00 Q.Q6 0.01

5e-Q2 4rto3 0.0192 0.56 18.45 15.87 0.04 0.03 3.131C+Q4 0.0184 1.70 18.56 15.57 0.01 0.06 1.701C+05 0.0179 0.31 18.69 15.39 0.00 0.08 0.31le+06 0.0179 0.06 18.71 15.38 0.00 Q.08 0.06lctQ7 0.0179 0.02 18.71 1538 0.00 0.08 0.02letQ8 0.0179 U.oi iik i i 1 5 .3 !3 ()~ 0.0!? O.Q1

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SPE30996 THE IMPACTOF FRICTION FACTORONTHE PRESSURELOSSPREDICTION IN GAS PIPELINES 7

TABLE 4- AVERAGE PERCENT DEVIATIONS INTHE CALCULATED FLOW RATE AND PRESSUREVALUES

mEqm8tion Avg. % FlowRaie Avg.% PnssareIhrorBasicmow 41.9 8.5Woymnuth I 62.4 I 8.9Pdnodk-A I 106.6 I 7.5Padmdk_B .1 1226 I 7.8

AOA I 106.6 I 7.8

TABLE 5- AVERAGE PERCENT DEVIATIONS INTHE CALCULATED FLOW RATE AND PRESSUREVALUES us

Avg.%Flaw R8teI&or42 . 042.843.343.542.542.1

:QUATIONAVS.% PresRR

Error5.55.55.55.55.55.5

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~ H, !LKJNBILGESUAND GEORGE J. KOPERNAJr. SPE 2099

o02 4 6 8 10 72 74 76Time, days

0.006

0.002

....................... ................... .. . ....... ............ ................ ......... .... . ..................... ..........................

............................... ..& .... .. . .... .... .... .....&..h A&?A=&$s+S=-3-A=A.... .........

E+ -+9H3=0+3-&a--Q9-a

Fii. 2+* f$dm V8hSS COIItpUtd With tiVO different fOillNhS US8d ill ~ ti ~U#kMIS.

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The Impact of Friction Factor on the Pressure Loss Prediction in Gas Pipelines