SPE SPE 15657 Two-Phase Flow Through Chokes by R. Sachdeva, Z. Schmidt, J.P. Brill, and R.M. Blais, U. of Tu/sa SPE Members Copyright 19S6, Sociify of Petroleum Engineers This paper was prepared tor presentational the 61st Annual Technicsl Conference and Exhibitionof the society of Patroleum Engineers bald in New Orleane, LA C4Xober5-S, 1SS6. Thie paper wasselected for praeentafii by an SPE Program Committee followingreview of informationcontained in an abelract submittedby the author(a). Ccmtenteof Ihe pzper, ae preeented, have not been reviewad by the S03aty of Pefroieum Engineers and are eubject to correctionby the -e). TfW me~~i aa PI-tad, doee not fwwiaafify reffactany Poa{th of WreSoWY of Patrofaum Engineers, its officers, or members. Pzpara ~t~ at *E win9S am SUfs@CI to pubfkef~ reviewby Edtiorial Commifteee oftheSociiofpetroleum Engineers. Permieaionto copy is reaW%ed to ●l abstract of not more then300 words.Ilfue!ralione maynotbe copfad.Theebetrectshouldoonlainconspicuousacknowledgment of whereandbywhomthepaperiapreeamed.WritePubfioafbnaManager,SPE,P.O.SoxSS3S3S,Riiherdaon, TX7MSS4SS6. Telex,730SSSSPEDAL, — ASSTRACT THSORY Two-phase flow throughwellheadchokes,includingboth For the purposeof modeling,a wellheadchoke can be criticaland subcriticalflow and the boundarybetween treatedaa a restrictionin a pips. IWO types of two- them, was studied. Data were gatheredfor air-water phase flow can exist in a choke: cr%ticaland subcri- and air-keroseneflows throughfive choke diameters tical flow. During criticalflow, the flow rate from 1/4 in. (6.35 m) to 1/2 in. (12.7rem),and throughthe choke reacheaa maximum value with respect resultsware comparedto publishedcorrelation. A to the prevailingupatreemcondition. The velocity new theoreticalmodel for predictingflow rateaand of the fluids flowingthroughthe restrictionreachee the critical-subcriticalflowboundarywea tested the sonic or preaaurewave propagationvelocityfor against theee data, as well as data from two published the two-phaeefluid. This Impllea that the flow ie studiee. The new model substantiallyimprovesthe “choked”becausedownstreamdisturbancescannot propa- existingmethods for predictingchoke behaviorin two- gate upstream. Therefore,dacreaaingthe downstream phase flow. preaauredoes not increaaethe flow rate. If the downstreampressureia graduallyincreased,therewill INTRODUCZ’1ON be no change In either the flow rate or the upstream preseureuntil the critical-subcriticalflowboundary Chokes are widely used in the petroleumindustryto is reached. If the downstreampressureia increased protect surfaceprocessingequipmentfrom elugglng,to slightlybeyond the boundaryconditions,both flow control flow rates from wells, to provide the rate and upstreampreseureare affected. The veloci- necessarybackpressureto a reservoirto avoid for- ties of fluidspassingthroughthe choke drop below mation damage from excessivedrawdown,to maintain the sonicvelocityof the upstreamfluids. Hera, the stable pressuredownstreamfrom the choke and dampen flow rate dependson the pressuredifferentialand large pressurefluctuations. changesin the downstreampreseureaffect the upstream pressure. This behaviorcharacterizessubcritical Either criticalor subcriticalflow may exist. Since flow* differentmethodsapply for predictingchoke behavior in theee regimes,the predictionof the critical- Althoughit is often desirableto operatewalls under subcriticalflow boundaryis also important. The criticalflow conditionswith niform flow rate and Y majorityof correlationsavailableapply to critical downstreampressure,Fortunati reportathat a flow only. Pressuredrops throughchokes can be majorityof walls in the field operateunder subcriti- substantial. For example,in criticalflow the cal conditions. However,moat of the correlations pressuredownstreamfrom the choke may be as low aa availableto petroleumindustryare for criticalflow. 50% or even 5% of the upstreampressure. Modern tech- niques, like Nodal*Analysis,of analyzingthe entire ExistingMethods A completemodel for two-phaseflow productionsyetem requiretwo-phaaemodels of corn- throughchokesshoulddefine the boundarybetweenthe parableaccuracyfor each systemcomponent. Thue, to criticaland subcriticalflow regimesand predictthe optimize the performanceof the entire production functionalrelationshipsof flow rate throughthe system,an improvedtwo-phasechokemodel is required. choke and the pressuredifferentialacrossthe choke for a given set of fluid propertiesand flow con- *Nodal Analysia iS a trademarkof Flopetrol-Johnston- dltions. Most existingmethodsmodel criticalflow Schlumberger only and a few even attempt to define the critical- subcriticalflow boundary. These models are surveyed. Referencesand illustrationsat end of paper.
Transcript
SPESPE 15657
Two-Phase Flow Through Chokesby R. Sachdeva, Z. Schmidt, J.P. Brill, and R.M. Blais, U. of Tu/sa
SPE Members
Copyright 19S6, Sociify of Petroleum Engineers
This paper was prepared tor presentational the 61st Annual Technicsl Conference and Exhibitionof the society of Patroleum Engineers bald in NewOrleane, LA C4Xober5-S, 1SS6.
Thie paper wasselectedforpraeentafii by an SPE Program Committee followingreview of informationcontained in an abelract submittedby theauthor(a). Ccmtenteof Ihe pzper, ae preeented, have not been reviewad by the S03aty of Pefroieum Engineers and are eubject to correctionby the-e). TfW me~~i aa PI-tad, doee not fwwiaafify reffactany Poa{th of WreSoWY ofPatrofaumEngineers, its officers,ormembers.Pzpara~t~ at *E win9S am SUfs@CIto pubfkef~ reviewbyEdtiorialCommifteeeoftheSociiofpetroleumEngineers. Permieaionto copy isreaW%ed to ●l abstract of not more then300 words.Ilfue!ralionemaynotbe copfad.The ebetrectshouldoonlainconspicuousacknowledgmentofwhereandbywhomthepaperiapreeamed.WritePubfioafbnaManager,SPE,P.O. SoxSS3S3S,Riiherdaon,TX7MSS4SS6. Telex,730SSSSPEDAL,
—
ASSTRACT THSORY
Two-phase flow throughwellheadchokes, includingboth For the purposeof modeling,a wellhead choke can becriticaland subcriticalflow and the boundarybetween treatedaa a restrictionin a pips. IWO types of two-them, was studied. Data were gathered for air-water phase flow can exist in a choke: cr%ticaland subcri-and air-keroseneflows throughfive choke diameters tical flow. During criticalflow, the flow ratefrom 1/4 in. (6.35 m) to 1/2 in. (12.7 rem),and throughthe choke reacheaa maximum value with respectresultsware comparedto publishedcorrelation. A to the prevailingupatreemcondition. The velocitynew theoreticalmodel for predictingflow ratea and of the fluids flowingthroughthe restrictionreacheethe critical-subcriticalflow boundarywea tested the sonic or preaaurewave propagationvelocityforagainst theee data, as well as data from two published the two-phaeefluid. This Impllea that the flow iestudiee. The new model substantiallyimprovesthe “choked”becausedownstreamdisturbancescannot propa-existingmethods for predictingchoke behaviorin two- gate upstream. Therefore,dacreaaingthe downstreamphase flow. preaauredoes not increaaethe flow rate. If the
downstreampressureia graduallyincreased,there willINTRODUCZ’1ON be no change In either the flow rate or the upstream
preseureuntil the critical-subcriticalflow boundaryChokes are widely used in the petroleumindustryto is reached. If the downstreampressureia increasedprotect surfaceprocessingequipmentfrom elugglng,to slightlybeyond the boundaryconditions,both flowcontrol flow rates from wells, to provide the rate and upstreampreseureare affected. The veloci-necessarybackpressureto a reservoirto avoid for- ties of fluids passingthroughthe choke drop belowmation damage from excessivedrawdown,to maintain the sonic velocityof the upstreamfluids. Hera, thestable pressuredownstreamfrom the choke and dampen flow rate dependson the pressuredifferentialandlarge pressurefluctuations. changes in the downstreampreseureaffect the upstream
pressure. This behaviorcharacterizessubcriticalEither criticalor subcriticalflow may exist. Since flow*differentmethods apply for predictingchoke behaviorin theee regimes,the predictionof the critical- Althoughit is often desirableto operate walls undersubcriticalflow boundaryis also important. The criticalflow conditionswith niform flow rate and
Ymajority of correlationsavailableapply to critical downstreampressure,Fortunati reporta that aflow only. Pressuredrops throughchokes can be majorityof walls in the field operateunder subcriti-substantial. For example,in criticalflow the cal conditions. However,moat of the correlationspressuredownstreamfrom the choke may be as low aa availableto petroleumindustryare for critical flow.50% or even 5% of the upstreampressure. Modern tech-niques, like Nodal* Analysis,of analyzingthe entire ExistingMethods A completemodel for two-phaseflowproductionsyetem require two-phaaemodels of corn- throughchokes shoulddefine the boundarybetween theparable accuracyfor each system component. Thue, to criticaland subcriticalflow regimesand predict theoptimize the performanceof the entire production functionalrelationshipsof flow rate throughthesystem,an improvedtwo-phasechoke model is required. choke and the pressuredifferentialacross the choke
for a given set of fluid propertiesand flow con-*Nodal Analysia iS a trademarkof Flopetrol-Johnston- dltions. Most existingmethodsmodel criticalflowSchlumberger only and a few even attempt to define the critical-
subcriticalflow boundary. These models are surveyed.Referencesand illustrationsat end of paper.
t TWO-PHASEFLOW THROUGHCHOXES !lPu. 1%!.——.-..-.—-
Tangerenlg did the first significantstudy on two-
--- .-”,conditionsrecommendsCD = 0.85 for liquid end ~ =
phase flow throughrestrictions. He asaumedpolytro- 0.90 for gas in absenceof prior knowledgeof ~.pic expansionof gas that is disperseduniformlyinthe mixture having liquid as the ontinuousphase. He
RoslgEXPERIMENTALPROGRAM
studiedonly criticalflow. extendedTangeren’swork by assumingliquid phase ia homogeneously Two-phasedata were gatheredfor critical,boundarydispersedas dropletsin a continouagas phase. He and subcriticalregionsfor five choke sizes: 16, 20,ahowed that accelerationalpressuredrop completely 24, 28 and 32 sixty-fourthsof an inch (6.35 usotodominateschoke behaviorand slippageeffectsare 12.7 ma). Keroseneand water were used to cover the
negligible. approximaterange of liquiddensitiesencounteredinthe field. The gas was air.
Fortunati7,drawing on Guzhov and Medviediev10, deve-loped correlationsfor both criticaland subcritical Fig. 1 is a schematicdiagram of theflow and the boundarybetween these regimes. His m. A two-stagecompresso$~uppliesair atmodel is valid if downstreampressureexceeds 1.5 a maximum rate of 0.6 MMscf/D (708 m /h) at ga~eatmospheres(152 kPa). His correlationrelates the pressureof 120 psi (827 kPa). Air iS metered by 2
upstreamand downstreampressureto a mixturavelocity in. (51 mm) or 4 in. (102 tmn)orificemeters.at 19.8 psia (136 kPa). Fluid propertiesare calcu- Kerose~e and water are stored in separate2000 gallonlated at downstreamconditions. (320 m ) tanks. Liquid la providedby s3centrifugal
pump with a capacityof 200 GPM (12.6 dm /s) at aAshford2developeda model for two-phas~6critical gauge pressureof 125 psi (862 kPa). A 4 in. (102 muchoke flow by extendingthe wrk of Ros . He assumed orificemeter measuresliquid rates. For low liquidconditionsand a critical-subcriticalboundarydefini- r..ea,a rotsmeteris used. To ensure fullydevelopedtion similar to Tangeren’s. A similar approachfor two-phaseflow, the gae-liquidmixing tee is placedsubsurfacesafety v$lves was also presentedby Aahford 200 tt (60 m) upstreamfrom the choke.and Pierce. Gould plotted the Aehford boundary,showing that differentvaluea of the polytropicexpo- Figure 2 is a sectionof the choke. The choke iS
nent yield differentboundaries. installedhorizontallyto eliminatethe perturbingeffects of elbows or choke housing. The two-phaae
In additionto these theoreticalapproached,numerous mixture flows throughthe choke and then into theempiricalmethods also exist to predictchoke beha- aeparatorkept at low tmrkinggauge pressure(8 psivior. A popular form of correlationsfor critical (55 kPa)) to ensure that the separatedliquid automa-flow is of the form: ticallydrains into the storagetank.
Temperaturesare measureddirectlyby thermometers.A q; RB Barton recorde:amonitorgas and liquid rates through
Pl = .,.*....*.*..........(1) orifice meters and the rotameterIs read directly.dc64
Calibratedpressuregauges help maintain a rough checlon the pressurerecordingsystem shown in Fig. 3.Pressureupstreamfrom the choke is obtained from a
Baxende114,Achongl, ROS1“? 13
and Pilehvari have deve- single pressuretap. Seven pressuretaps downstreamloped varia ions of this equationoriginallyproposed
ifrom the choke ensure that fully recoveredpressures
by Gilbert. Table 1 shows the coefficientsA, B and are recorded. Pressuresfrom the test pipe areC suggestedby various investigators. Note that the tranamlttedto a transducermanifold by 1/4 in. (6.4critical flow rate is independentof the downstream mm) 200 pai (1.4 MPa) flexibletubing. At any time,pressurewhich, therefore,does not figure in the only one of the three transducers(maximumgaugeGilbert-typeequations. Also, fluid propertiesare pressurereadings32 psi (221 kPa), 75 psi (517 kPa)neglected. and 125 psi (862 kPa)) is used. Each transduceris
15connectedto a Validynedemodulatorfor shaping the
Poettmannand Beck used the work of Ros to construct output signal. These outputsare transmittedto acurves for 20°, 30° and 40° API crudes. This work iS strip-chartrecordervia a three-wayelectricalswitclalso limited to criticalflow and he presenceof to select readingsfrom the appropriatetransducer. J
lJwater invalidatesresults. Omana , on the basis of filter consistingof a capacitoland a variable47 two-phasetests on choke diametersfrom 4/64 in. resistorconnectedin parallelsmooths the signal Int<(1.59 IOM)to 14/64 in. (5.56 mm), arrivedat a corre- the recorderso that time-averagedpressurevalues arilation valid for sm 11 choke sizes and flow rates less recorded. Csre is taken so that all the recordingthan 800 BPD (127 m~~). He arbitrarilydeemed the flow system componentsare calibratedproperly.to be criticalwhen the ratio of downstreamtoupstream pressureis less than 0.546 and when super- Test ProcedureInitially,the system is stabilizedficial gas velocityexceeds superficialliquidvelo- with the valve downstreamfrom the choke fully opsncity* under two-phaseconditions. Flow is consideredstabl~
if both averagepressuresand flow rates are stable.Of the above methods,only those of Aehford and Flow is usuallycriticalat this stage sincePierce, Fortunatiand pilehvarican be used for increasingthe downstreampressureand allowlngthesubcriticaltwo-phaaechoke flow. Althoughthe system to stabilisedoes not affect either themethods of Aehford and Fortunatialone are derived upstreampressureor the flow rate. The valvefrom basic principles,they both recommendeddischarge downstreamfrom the choke is slowly closed and systemcoefficients(CD) exceedingunity. This violates the stabilizedeach time until the critical-subcriticalfirst law of thermodynamics. For comparison,
theflow boundaryia reached. The flow condition is
value of CD for liquid flow throughan orifice is deemed to be at the boundarywhen a very slightapproximately0.62. In addition,the API 14 RP method increasein downstreampressureproducesa slightfor subsurfaesafetyvalve performancein two-phase change in the averageupstreampressureand a alight
iecreasein flow rates. Furtherclosureof the valveyieldseubcriticelflow data. Each run typicellyfieldstwo critical,one boundary,and two subcriticaliata pointe. Fig. 4 shows the locationof the data onthe Mendhane’1flow patternmaP. The orificemetersand the preseurerecording:alibratedand operated.
9 flow is one dimensional● phase velocitiesare equal at the throat● the predominantpressure term is accelerational~ the qualityis constantfor high epeed processc the liquid phaae is incompressible
The final equationsare capableof both findingtheboundarybetween critical-subcriticaltwo-phaaeflowEnd calculatingthe flow rate throughthe choke forcriticaland subcriticalflow. Model developmentsppearsin the Appendix.
Soundar The critical-subcriticalboundaryis obtained-ting and convergingon y from the followingequation:
k(l-xl)vL(l-y) k
z+F1
‘1 ‘G1Y= {
k n n(l-xl)VL nl-xl)VL21
Gl+ z+- ‘:‘1VG2
(2)● .● ● .....● ..● ● ● ● o.,
Note that the convergedvalue of y from the aboveequationis the criticalpressureratio (yc). Ay>yc implies subcriticalflow whereas y~ yc indicatescritical flow.
Figure 5 shows the critical-subcriticalboundaryundervarioue conditionsfor a hypotheticalcase. ForIllustration,curve A is used as a reference. Curve #is plottedusing the followingvalues:
k = 1.4, Sp.Gr. (liq) = 0.9, Pi = 80 psi (552 kPa),Tl = 100”F (37.8”C),CP =0.24, ~= 0.8.
The effect of increasingupstreampressure(Pi) ieshown by curves B and C. As ?~ increases,gaa becomesmore dense, and the sonic velocityof the mixtureincreases. Thus higher flow rates throughthe chokeare needed to attain criticalflow. Thie necessitateslarger pressuredifferentiable,which are reflectedbylower criticalpressureratios. Thus, all other pera-
) V. 8Kll& b K. No BLAAS
meters being equal, the criticalpreeeureretio forP - 800 pei (5.52MPa) is lower than that forT;+s=440 pal (2.76 MPa) or P1 = 80 pal (552 kPa).agrees with predictionsof the model aa evidencedbycurvee A, B and C. Similarly,if temperaturewere toincr?asewhile other parametersremainedconetant,gasdensity would decrease. This would thus cause highercriticalpressureratios to exist ae shown by com-paring curve D with curve A.
Changing the specificgravity of the liquid phasewhile holdingother parametersconstantyields a pre-dicted boundarygiven by curve E. Comparingcurve Ewith A showe that liquiddensity hardly effects thecritical-subcriticalboundary.
Note that at x = 1 (puregas case), the criticalpressure~atio equals that obtained by thefollowing wall known boundaryequation for an all ga6case
............00...(3]
Also note that after about x = 0.7, the boundarycur-ves dip downwardbecaueeof high values of qualities(xl) balng used In Eq (2). Such high qualitiesareseldom encounteredin practice.
Criticalend SubcriticalFlow Ratee Once the boundarjIiaabeen determined, low rates throughthe choke areobtained from the followingequation:
(l-xl )(I-y) xlk
[ — (vGl+ k-1- YVG2)]}O*5 ....(4.
‘Lwhere,
G2 = ‘G2A+‘2 .*****.**.O.**O.....(5.c
1--k-v
‘G2 G1 y...............0.....(6.
and,
1
L--
—-xlvG1y k+(l - XL)VL‘M2
.........(7.
If ycg Yac Ual (yc being obtained from Eq(2)), criti.1cal flow ex sts, and the appropriatevalue of y is
given by Y = Yc. If yactual> YC, subcriticalflowexiete and y = yac Ual should be ussd in Eq (4). OnctG2 iS knOWn, liqUi $ end gas rates can be easily calcwlated since X1, Pl, and the area of choke are known.
For the sake of simplicity,no effort waa ❑ade todistinguishbetweenfree and diseolvedgas and a mix-ture of liquids. In this di.ecueaion,the terms gaaand qualitypertain to free gas. Also, if more than
-—-. .—. - ..-.-—.—--- ...-— —--
D
,
D
TUO_PHASEFL(I
me liquid is presentin the two-phasemixture, thecommonmethod of using the averagewlghted propertiedspplies. Similarly,the value of liquiddensity used6houldaccount for effectsof dissolvedgas and thegas compressibilityfactor should be used to obtaincorrectin situ volume of the free gas.
EVALUATIONOF PRESENTMODEL
ka with any model, the best test of the hypothesesinvolvesthe applicationof the model to empiricaliata. l%ia was done using:
the data from the authora’experimentalProgram,which used air-keroseneend air-waterflows: atotal of 553 two-phasetest points.the two-phaseair-watermeasurementsre~ortedbyPilehvari: a total of 189 criticaland 441 subcri-tical data points.the 27 two-phasefield data points publishedbyAshford. -
Major existingmodels were also evaluatedagainst theiatagathered.
DischargecoefficientselectionFor fluid flow throughreatrlctlons, LS common to use dischargecoef-ficients(CD) as a finalmodifyingfactor in the flow-rate equation. It is usuallyhoped that ita use wouldnbsorbarrora due to assumptionsmade while developinge model. Thue, the values of ~ depend on the asaum~tionamade during model development. A “perfect”model will have CD = 1.0, i.e., the use of C will be
fredundantif all flow proceaaesare accurateyaccountedfor. LSWS of Themodynereicsimply thatvaluesof ~ less than unity should result. Often,CD Is also correlatedwith factorasuch as Reynoldsnumber,preasuradifferential,gaa expenaionfactoretc. Obviously,if a model adequatelyaccountsforsuch variables,such dependenceshould not exist, Thepresentmodel was developedfor one-dimensional,two-phase flow througha restriction. Choke installationinvolve elbowsupstreamfrom the choke. Effects ofpresenceof these fittingsthat perturb the flow imm-ediatelyupstreamfrom the choke were not accountedfoxduring model development. AS will be seen later, the❑anner in which a choke is installedbecomesthe onlyfactor on which the CD of the presentmodel depends.Two values of CD are suggesteddependingon the chokeinstallation. These values are constants,and, basedon the results from error analysis,no furthercorre-lation for ~ (in terms of other parameter) wasnecessary.
Evaluationof existingmodels and proposedmodel withdata gathered As mentionedearlier,it waa hoped thatthe use of a dischargacoefficient(Cn) would absorberrors resultingfrom variousasaumptlona,especiallythat flow is one-dimensional. A value of CD = 0.85yields optimal answerswhen applied to data gatheredwith the choke free of effect of the upstreamelbow.Table 4 shows the presentmodel, :.*enuse with a CD -0.85, gave better reaultathan other models (Tablee2& 3). This value is recommendedwhenever the chokeconfigurationused ia similarto the one in the testfacility,i.e., whenever the flow is undisturbedbyelbow upstreamfrom the choke.
Model Analysiswith Pilehvari’.edata Pilehvari’schoke was installedin a choke housingti.tkelbowupstream from the choke. The assumptionof unper-turbed,one-dimensionalflow is lees valid here.
nNtouGNCHOKSS SPE 15qSecause of added turbulencecausad by the albow, thavalue of ~ would be lower than 0.85, since the flowis less almilarto what the model assumes. C = 0.75
Ygave the beat reaulta. Note that more emphae a waaplaced on the absoluteaverageerror and standarddeviation than on the average error since the formertwo are better parametersfor error analyais. Theresultsof the enalyaisare shown in Table 5 for two-phaae data comprisinga total of 630 points. Thistable shows that with Cn = 0.75, the presentmodelyields substantiallybe~ter resultswith Pilehvari’sdata for both criticaland subcriticalflow than hisown correlationsgave.
Model Analysiswith Aehford’sdata Ashford collecteddata and his choke configurationis similarto
th~ one used by Pilehvari. Again, the presentmodel,with ~ = 0.75 gives substantiallybetter results(Table 6) than Aahford had obtainedusing hissuggestedvalue of CD = 1.
Note that both Pilehvariand Aahford had a differentchoke configurationfrom that used in the presentstudy. Their chokeswere mounted with an elbowupstream. The presentmodel yields good resultawithCD = 0.85 for a choke free of upstreamdisturbancesand with CD = 0.75 for a choke configurationinvolvingan elbow upstreamfrom the choke. Choke configurationthus eeems to play a definite role on the value of CD.The analyaiaabove leads to the followlngrecommen-dations on the use of the prasentmodel:
● use CD = 0.75 when the choke is installedin ahousing (aa is common in the field),
● use ~ = 0.85 for a choke where the flow isundisturbedby the effects of an elbow immediatelyupstream from it.
Model APPlicationto Sub-SurfaceSafety Valves Themodel was derived for two-phaae low througha pipe
restriction. The term restrictionimplies-that-fiowvelocitiesare substantiallyincreaaedin the restric-tion such that the accelerationalpressuredrop termdominates. Usually,the ratio of diameterof thesafety valve to the tubing is above 0.8 and thus theuse of the mdel will not be correct since the acce-lerationalpressuredrop term w?.lLnot be predominantHowever,should a ratio of 0.5 or less exist (lesserratios increasingthe model’s validity)this methodmay be used. A CD of 0.85 should be used since thevalve configurationwill be similar to the choke con-figurationin the experimentalprogram of this study.
CONCLUSIONS
(i) The proposedmodel performsbetter than theexistingmodels in predictingtwo-phaseflowthro@ chokes.
(ii) For chokes installedin a housing At thewellhead,where effectsof elbow (or chokehousing)are present,a dischargecoefficient(CD) of 0.75 should be used. Such con-figurationsare common in field practice. Forchokes where such effectsof choke housingarenot present,CD = 0.85 is recommended.
(iii) Since the model la derived from dynamic prin-ciples,and was tested successfullywith threedifferentsets of data, it la expected to workwell in the field.
PE15657 . SACHDSVA. Z. Sm’mYr &
4CKNOWLEDGEIIIENTS
rhe authorswould like to thank the Universityofrulssqnd the Tulsa UniversityFluid Flow Projects{TUFFP)’for support. Helpfd suggestionsfrom Dr. O.$hohamand Dr. B.M. Kelkar of The Universityof TulsaZre sincerelyappreciated.
!lOMENCLATURE
Symbol Description
4
B
..
.“D
‘L
cP
Cv
*
’64
E
F
m
Kc
G
k
Lc
M
n
P
q’
SD
v
v
x
Y
Area (ft2), coefficientIn Eq. (1)
Coefficientin Eq. (1)
Coefficientin Eq. (1)
Dischargecoefficient
Specificheat of liquid
Specificheat of gas at constantpressure
Specificheat of “-- “ ‘---’--”‘“-l----
Diameter,ft
Choke diameter,
PercentError
/64ths of in.
Average pecenterror
Absolute averagepercent
Gravitationalconstant
Masa flux, lbm/ft2/sec
Ratio of specificheata,
Length of choke, ft
MSSS flow rate, lbm/sec
error
~ /cpv
Polytropicexponentfor gas
Pressure,psia
*Volumetric flow rate at standardconditions,STB/D
Standarddeviationfrom average percenterror
Velocity,ft/sec
Specificvolume ft3/lbm
Free gas quality
Downstreamto upstream pressureratio
Greek Symbols
a Void fraction
P Density,lbm/ft3
T Wall shear stressw
Subscripts
1 Upatreemconditions
2 Downstreamconditions
c Choke, critical
G Gas
L Liquid
la Mixture
P Producing,pipe
a Superficial
REFERENCES—.—
1.
2.
3.
4.
50
6.
7.
8.
9.
10.
11.
12.
Achong, I.: ‘“RevisedBean PerformanceFormulafor Lake MaracaiboWells’”,InternalReport(October,1961).
16, Roa, N.C.J.:“’AnAnalysisof Critical I Also,SimultaneousGas-LiquidFlow Through aRestrictionand its-ApplicationTO-FIOW %2M%1 (1-X2) G2Metering:”Applied Sci. Research(1960),~, ——— -.
Section A, 374.‘L2 = (q) ~2
....*..(A.6)M ‘2 h ‘L2
17. Ros, N.C.J.: “TheoreticalApproachto the Studyof CriticalGaa-LlquldFlow Through Beana,”InternalReport, (Feb. 1959).
18. Sachdeva,R.: “Two-PhaseFlow Through Chokes,”M.S. Thesis,U. of Tulsa, 1984.
19. Tangeren,R.It.et al: “CompraasibilityEffectsof‘1’wo-PhaaeFlow,”J. App. Phya.,20, number 7,(1949).
ZOO Wallia, G.B.: One DimensionallWo-PhaseFlow,McGraw Hill, (1969).
APPENDIXA
MOOEL DEVELOPMENT
Critical-SubcriticalRoundary
Equationsdescribingconaervatianof mesa, momentumand energy were used to determinerelationshipsforcriticaland subcriticalflow and the boundarybetweenthem. For horizontaltwo-phaaeseparatedflow, thefollowingmomentumequationat the thzoatcan be writ-ten:
’144 Ac dP2 = d(MG2 VG2 +%2 ‘L2) ~c
+ d(Tw*ndcL=)
.................(A.1)
Ros has shown that in two-phaseflow throughchokes,the accelerationterm predominatesand that the wallshear forcescan be safely neglected. He also ahowedthat there la practicallyno slippageat the throatand hence we will assume equal phasicvelocitiesatthe throat: (vL2 = vG2 = v2). Hence Eq. (Al) redu-ces to:
- 144 ‘CA2 ‘P2 = ‘(V2 %2+ ‘2 ‘G2)
-d[
%2G2{ V2~
‘G2
2 +“2@ 1-d
[G2A2 { (1-X2)V2 + X2V2 }1
since, G2 = (%2 + ~L2)/A2,
and similarly,
- (~) ~‘G2 ( Q PG2
.........(A.7)
Eliminationof a2 between Eqs. (A.6) and (A.7) andass~ing vL2 = vG2 = v2 gives:
‘2“2”~ . . . ..*** .*... (8)8)
where,
–=L+(;J1Pm PG
...........(A.9)
ExpandingEq. (A.2) yields:
dv dG2-144 gc=G2-&+v2T .,....10)IO)
2 2
For a fixed set of upstreamconditions,during criti-cal flow, the masa flux reacheaa maximum with respectto the downstream(throat)pressure.
Since G2 = (%2 + ML2)/Ac,the boundarycan be definedaa:
VP. 1W,57 R. RACHDEVA. 2. RCHMIM’ - J. P. RRILL & R. N. BLAl~-- ----- .-. ----—- ... . -. --.----- . -. .- ----- —-.. ... --.--DiffferentiatingEq. (A.9) w have: Usually,V22 >> VIZ (since dc = d2 << d Ip ) for a
choke. Noting elmo that V2 = G2/P~, d.?A.21) redu-dVti dv
L2dvG2
ces to:_ . (1-X2) q + X2%dP2
.....(A.13)
144 gc[(l-xl)VL(P1 - P2) + xl&(P1vGi
The liquid phase can be assumedto be incompressible:
dVL 2
F=o .............(A.14) -P2 VG2)] G2
..o.......o...(A.22)2P:
Typical velocitiesof mixturesflowing throughchokesare high (approximately50-150ft/s). Thus, there isvirtuallyno time for maas transferat the throat.Thus, we have:
Eliminationof G22 betweenEqs. (A.19) and (A.22)yields:
‘1 = ‘2..o..............(A.15)
CombiningEqs. (A.13),(A.14) and (A.15) gives:(l-xl)VL (Pl -P2) +g (PIVG1
d’144 g G-;. x —
c 1 dP(VG2) ....O..(A.16) nP
2 - ‘2 ‘G2) = ~ (~) ............(A.23)2&
X1VG2
During gas expansisnat the throat,a temperaturegra-dient existe between the phaaea,resultingin fastheat tranaferbetween them. We also know that thisprocess is in-betweenthe extremesof isothermalandadiabaticprocesaea(for which the value of n wouldrespectivelybe unity and ~/~). l%us, the heat flowin the gaa-liquidmixture is approximatedby apolytropicprocesssuch as
n‘2 ‘G2 = c
(c-constant) .........(A.17)
where, the polytropicexponentgiven by Roa iaY=
‘1(c - Cv)
n=l+ c + (l-xl)CL ...*........(A.18)‘1 v
Denoting,
‘2Y-y . . . . . . . . . . . . . . . . ..(A. 24)
and rearrangingEq. (A.23) yields:
k (l-xl)vL(l-y)
E+ x. v-.
{k n n(l-xl)VL+ n r]l-X1)VL z ‘
=1 + z + xlvG2 T ‘1VG2
...............(A.25)
Equationa (A.16) and (A.17) give: I While developingEq. (A.25),we had aaaumed in EQ.
nP(All) that the flow conditionwaa such that the-maas
G; =flux did not changewith respect to the downstream
Q(144gc) ● ...● ..● .,,...,.,...,(A.19) pressure (P2), that La, flow was at the critical-‘1VG2 subcriticalboundary. Thus the downstream-uDatream
Now, proceedingwith the previousaasumptionaof hori-pressureratio at the critical-subcriticalb~undary(yc) can be obtainedfrom Eq. (A.25) by solving for y
zontal flow,negligiblefrictionand equal phaae velo- it,eratively.Once upstreamconditionsare known, Eq.cities, the energy equationreduces to: (A.25) can be solved using
2-144 gc # = d[~)
m...............(A.20)
or,
-144 gc[(-+ ~] ‘, ‘d (+, ..,.Oo.(A.21)
We will inte rate Eq. (A,21) between P1 and P2, notingithat liquid ensity and gas quality remainconstant,
and that the gas expansionis adiabatic,
1--
‘G2 ‘VGIY k ............(A.26)
Let the value of y from Eq. (A.25) be yc. This ia thecritical pressureratio that determines the boundary.If actual conditions are such that yactual > yc, then
the flow ia subcritical and if yactual~ yc, the flowis critical.
I m%ln.mtA Cu m nu Wmt’Mt#xu rwwM?E@ --- . . . ..“” . .J#8”” . -“ .,-””-, ““”M*
Tha first step ia to determineyc from Eq. (A.25). Ifyactual~ Yc, the flow la critical. Thus Y =y should be ueed in Sq. (A.27) to calculatethe cri-tfcal flow rate,
SubcriticalFlow: While deriving~. (A.27),noaaeumptlonwas made ae to the nature of the flow.Again, the firet step la to determineyc from ~.,----(&.L>). if accuai conditionsare such that yactual>yc, the flow la subcritical. For subcriticalflow,y= yactualahGuld be used in Eq. (A.27) to determinethe subcriticalflow rates.
DischargeCoefficient(CD)
As explainedin the paper, CD = 0.75 should be usedwhen a choke ia Installedin a housing i.e., has anelbow upstream from it (as is common in the field).If the choke is inetalledsuch that there are no flow-perturbingeffectsdue to an elbow immediatelyupstream from it, then, CD = 0.85 should be used.
S1 Metric ConversionFactors
atm X 1.013 25A E+02 =bbl X 1.589 873 E-01 = ~afeet x 3.048* E-01 = m“F (“F-32)/l.8 E+OO = 0gal X 3.785 412
$E-03 = m
in X 2.54* EtOO = cmlbm X 4.535 924 E-01 = kgpsi X 6.894 757 E+OO = kPa~eonver~ionfactor is exact
WETABLE 1
Coefficients for the Gilbert-typeEquationfor ~o-Phaee CriticalFlow
Correlation A B c
Gilbert 10.00 0.546 1.84
Roa 17.40 0.500 2*OO
Baxendell 9.56 0.546 1.93
Achong 3.82 0.650 1*88
Pilehvari 46.67 0.313 2011
TABLS 2
Evaluationof correlationsUsing Air-WaterData
c = critical Standard Average Abeoluteg m subcritical devlatlon error average
(%) (%) error (%)Correlation
GilbertRoeAchongPilehvarlAahfordOmanaPilehvari
(c) 22.2 -71.7(c)
71.713.8 -25.2
(c)26.2
19.0 -5.8(c)
17.016.5 -18.5
[:;22.2
7.7 36.7 36.76.4 59.2
(a)59.2
40.9 -16.7 24.7
TABLE 3
Evaluationof Correlation Using Air-KeroseneData
c = critical Standard Aver?ge Absoluteg = subcritical deviation error average
