PA Determining Multiphase Pressure Drops and Flow Capa

7/30/2019 PA Determining Multiphase Pressure Drops and Flow Capa

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Determining Multiphase Pressure Drops andFlow Capacities in Down-Hole Safetv Valves--A--- --- di

F. E. Ashford, SPE-AIME, Mene Grande Oil Co.P. E. pierce, SPE-AIME, Otis Engineering Corp.

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Introduction.A new relationship describing dynamic, multiphaseorifice pressure drops and fluid flow capacities has beenderived and tested with actual field data.The mathematical model relates dynamic orifice be-havior in both critical and noncritical flow regimes.Orifice pressure drops and capacities are related to perti-nent fluid properties and choke dimensions. Graphicalcorrelations are also presented to predict the ultimate(critical) capacity of an orifice for any given set ofdynamic conditions.To verify the model, a field test was designed and:arried out in a flowing oil well. Both orifice pressuredrops and fluid flow rates were measured in the well andthe information was compared with analogous data pre-dicted by the model, Comparable information was thenused to compute an orifice discharge coefficient thatenables calculation of actual orifice capacities fromtheoretical ones. The discharge coefficients are presentedfor 14/64-, 16/64- and 20/64-in. orifice diameters.The collected data reflect the behavior of an Otis En-gineering Corp. J-type 22J037 safety valve. However, themodel may be used to esrima?emultiphase pressure dropsthrough restrictive beans in safety valves of other internalgeometrical configurations.DiscussionThe increased need for more accurate settings on down-hole, self-contained, flowing safety devices (stormchokes) has prompted efforts by many oil-producing

companies to develop new multiphase orifice flow rela-tionships.Interest in antipollution devices, especially in offshoreoil. ; reducing areas, has also encouraged the major oilcompanies to re-evaluate old, established procedures forthe design of oil- and gas-well mfety valves,A review of the existing orifice flow literaturemT andanalysis of standard safety-valve design proceduresyielded the following facts concerning noncritical mul-tiphase orifice flow.1. Most orifice flow models do not adequately reflectthe compressible nature of actual oilwell multiphaseorifice flow. Consequently, models now in use do notadequately describe the dynamic behavior of orifice flow.2. The existing orifice flow relationships become lessexact as the dynamic conditions approach the criticalvalue; that is, at a given upstream pressure, no furtherflow-rate increase occurs through the orifice, regardlessof the pressure drcp across the orifice.Those who are involved in manufacturing down-hole,pressure-drop-operated safety valves are aware of theproblems associated with accurate prediction of orificeflow behavior. Most agree that a more rigorous mwhemat-ical model is needed to describe the mechanics of orificeflow under all oilfield conditionThe orifice relationships used by design engineers,fiough acceptable under certain flow conditions, are ques-tionable for applications falling outside these specifica-tions. A more rigorous procedure applicable to oilfield

m.

A new relationship describing dynamic multiphase orifice pressure drops and jluid jlowcapacities has been derived and tested with field data, The mathematical model relatesdynamic orifice behavior in both critical and noncritical jlow regions. Correlationsare presented for predicting the ultimate (critica[) capacity of an orijlce for any givenset of dynamic conditions.

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I SEPTEMBER, 1975 1145 s


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II,i

L.*

I-:-iFig. 1 Schematic storm-choke field test.

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conditions is needed to relate existing safety-valve pres-s re drops tothe flow rates of o~l,gas, and water thrGugh arestriction. Such anew orifice ii NWelationship has beendeveloped, The new development is an extension of thetheory initially presented by Ros and has definite advan-tages over other existing procedures.1. The model considers the adiabatic expansion of gasflowing simultaneously with oil and water through theorifice, using a polytropic expansion relationship.2. The model considers both free gas and solution gasflowing simultaneously with the oil in its liquid phase.3. The model incorporates an improved expression forthe liquid flowing per pound of fluid.4. The relationship predicts the pertinent critical prop-erties oi the orifice under set conditions.5. The model relates orifice pressure drops:0 oil, gas,and water flow rates and fluid properties.And orifice flow model must relate the cynamic pres-sure drop to fluid, as well as to orifice parameters. Oneapproach applied widely in the literature evolves from adirect application of the energy balance:

JPa

J2 11L//l144 ,,fdp= ...................(1)~rP1 u)

Eq, 1 relates the loss in pressure volume energy to anincrease in the kinetic energy across the orifice.While this approach is theoretically oriented and doesnot consider friction losses or heat transfer in the vicinityof the bean, it does offer an excellent point on which tobase future development in the orifice flow area.Following the theory of Eq, 1 and writing anotheruseful expression involving the orifice fluid velocity, 142,and the fluid specific volume, vf2,yields an expression forthe orifice mass flow rate:

IIgw = CA t .) .3.0 .,, .,. .....# ,#t#. o.). (2)vr2

The Appendix presents the development for the solutionof Eq. 1 and subsequent final form of W. 2. The finalform of the generalized multiphase orifice flow equationscan be written as

q.= C3.51d:cw,h,, . . . . . . . . . . . . . . . . . . . . . . . (3)where

a,~ = (B. + F,ro)-z .and

P1O=

K )n11-1q ~, Z,(A \ R,)(I CT) + 198.6P,(I e)n- 1

[T]ZI198.6 + (R Rg)r)PI 1

[ 112(Yo + 0.0002 ]7Y,,Rs+ Fuwyw)x (YO+ 0.000217 yoR + F,r.yw) C in Eqs. 2 and 3 is the orifice discharge coefficient. Thisparameter is proportional to the orifice size as well as tothe fluid properties. It is included in the relationship toaccount for nonidealities not considered in the derivationof the expressions for U2and vf2.

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The evaluation of C is important in any practical appli-cation of Eq. 3 to subsurface safety valve design. Thisconstant relates theoretical to actual orifice flow dataand enables the prediction of down-hole orifice pressurelosses under known set conditions.A field tes~designee, to evaluate safety-valve behaviorwas conducted by Gulf Research and Development Co.,Gulf Oil Co. U.S., and Otis Engineering Corp. The testwas designed specifically to (1) compare the predictedtheoretical orifice pressure drops from known od and gasflow rates with those measured in the well; (2) comparethe predicted theoretical fluid rates through the bean fromknown pressure drops with those measured in the weli;and (3) use the data from Eq. 2 to evaluate a series oforifice discharge coefficients for various bean sizes.Test ProcedureA flowing oil and gas well was selected for the field test.The well was producing from a depth of about 12,000 ft.An Otis F-type safety valve was instakd originally in alanding nipple at 3,500 ft. Production of oil and gas wasthrough a 2-3/8 in, nominal tubing.The test procedure was composed of two principalparts:1. The F valve was removed and the well was flowed toensure adequate response from the formation.2. An Otis J-type 22J037 safety valve was installed inthe hmding nipple at 3,500 ft, with 16/64-, 14/64-, and2@64-in. beans installed sequentially. A pressure bombattached directly to the J valve was located below thecurrent orifice. and a pressure bomb above the orifice wassuspended by a wireline. These bombs recorded flowingupsfream and downstream pressures existing across theorif!ce, A temperature recorder was also attached belowthe upstream bomb tomeasure the flowing temperatures atabout 3,500 ft, A low-pressure test separator of 1bbl totalliquid capacity was used to meter the liquid production,while gas volumes associated with the produced oil weremeasured using a 2-in. meter run.Fig. 1 shows a schematic of the equipment as it wasinstalled in the test well. Each bean size installed in the22J037 valve constituted a separate series of tests, duringwhich an attempt was made to flow the well at the threeseparate stabilized rates (200, 375, and 550 B/D), Fig. 2indicates a cross-section of the well with the safety valveand pressure bomb installed below the valve and the upperpressure bomb suspended by a wireline.Tests ResultsSukQurface Safety-Valve Pressure-LossMeasurementsA total of three rates was achieved for the 16j64-in. beansize. These rates ranged from 559 B/D at 478 GOR to 334B/D at 429 GOR. Rates imposed on the well for thisorifice size began with the highest, Fig. 4 indicates therecorded pressures downstream from (above) the safetyvalve at 3,500 ft. The times corresponding to Conditions1, 2, and 3 in Fig. 4 are shown in Table 1. The pressurestabilization downstream from the choke was not alwayscomplete because of the short time allocated to each rate(30 to 60 minutes). However, two rates did show fairstabilization where the pressure was pulsing; underCondition 2. an average pressure was obtained by balanc-ing the areas on the pressure vs time graph during the time

interval when the rate occurred. During the tests, it be-came apparent that the location of the flow-skirt/pressure-bomb assembly downstream from the safetyvalve was sufficiently removed from the orifice so thatmeasurements of actual vena confracta orifice pressureswere not obtained. The upstream pressure bomb wasplaced as close as possible to the actual location of theorifice in the safety valve; however, because of mechani-cal limitations, it was physically impossible to measuredownstream orifice pressures at a pressure-tap locationcioser than that achieved during the tests. The distancefrom the sensing unit to the bean seat was ~7.5 in. (asindicated by the schematic of the valve assembly). Thedownstream pressures shown in Figs. 3 through 5 are,therefore, the best possible measurable approximationsto actual vend contracta pressures.Fig. 3 shows a plot of the downstream pressures ob-tained for the 14/64-in. bean. A critical part of this opera-tion was the attempt to close the 22J037 valve. Closurewas achieved by flowing the well at a rate sufficiently high(600 B/D) to incui the necessary pressure drop across thesafety-valve orifice and close the valve. Fig. 6 reflects thevarious downstream pressure responses to the ratechanges, As can be seen, the rates fluctuated between261and 596 B/D, at which time valve closure occurred. Therate of 508 B/D, that existed for about 10 to 15 minutesimmediately after the valve closed reflected thu fluidexpansion from the wellbore to the test separator.Valve closure was verified after the well was shut in bythe inability of the wireline fishing tool to retrievs thevalve. This condition occurs when a safety valve hasclosed. High pressure from an independent source wasrequired to pressurize the 2-3/8-in. tubing to 1,000 ps:g toequalize the pressure across the valve and reopen thechoke. The valve was then retrieved using the normalwireline operations,Fig. 5 presents the results for the 20/64-in. bean sizeand the three corresponding rates for Conditions 1,2, and3. The flowing temperature surveys revealed the fluid

,Low,w. s I I L

.w.s. 04 , ,[ > . : ~ -,., .0..0,,s .2,0,7 ,Arrfv VA.., 3502 ,.ow.sr . . . *.( s,,, ) 3495.now ,,, AT 34s

T. MP,.. nJn, ,0. , 35h3 ,,,,.,0 q,*,.* mu,~ IPST* CA. ** C,*,,J$w=

Fig. 2 Weli schematic for upstream and downstreamstorm-choke pressure measurements.SEPTEMBER, 1975 1147


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temperature just below the orifice to be about 156F.Thistemperature was used as a constant throughout the subse-quent computations. Unfortunately, the upstream pres-sure bomb failed to operate properly during the days whenthe 14/64- and 1tV64-in. beans were run. During the20/64-in. tests, however, upstream pressures were ob-tained. These recorded pressures are shown inFig. 7. Thiscorrelation subsequently was used to obtain the corre-sponding upstream pressures for each of the 14/64- and16/64-in. orifice rates. This procedure was not precise,but was necessary under the circumstances.Fig. 7 indicates the increase of the flowing upstreamsafety-valve pressure at 3,500 ft as a function of increasedtubing oil rate. However, the upstream pressures recordedduring the test did not reflect stabilized conditions in thevertical string. For this reason, a decrease in the flowingtubing pressure yielded an increase in the production rate,along with an increase in the upstream safety valve pres-sure. The presence of the increased fluid rate in the vicin-ity of the safety valve during the flow tests was not trans-mitted to the producing horizon at 12,000 ft. Thus, de-creased upstream safety-valve pressures for increased oilrates, reflecting stabilized conditions, had not occurred inthe test well. The existing rates and pressures did, how-ever, yield measureabie pressure drops across the orificeinstalled in the safety valve. As long as the pressure dropsreflected the existing rates, the mathematical orifice rela-tionships could be tested.

;1 .,> ,, ,.,.LI.I \ ! i+

i-P7=Ej ..................,..I I,, -- ---- .-. .: ., . ..]_ +--1,,I, . ...c.. .:_--L--u. . . . .....

Fig. 3 Storm-choke test well downstream safety-valveflowing pressures,

Test AnalysisThe results of the pressure drop/flow-rate data are alsopresented in Table 1. Average oil rates and solutionGORs for each subsurface bean test are shown, alongwith the corresponding orifice size. The solution GOR at1,200 psia was fixed at 120scf/STB by an analysis of thereservoir fluid. Errors incurred by different upstreampressures were slight. The gas gravity was 0.6 (air = 1),while the oil gravity was 0.89 (water = 1).The ratio of gasspecific heat at constant pressure to the specific heat atconstant volume was 1.275.The measured pressure drops for all bean sizes areusually lower than those predicted byEq. 3 (with C = 1 ~)for the same fluid rates. The necessary placement of thedownstream pressure recording bomb in its testing posi-tion during the flow tests probably incurred some error inthe measurements of actual vena coturucta orifice pres-sures. Thus, in the area where the pressures were re-corded, these flowing pressures had partially recovered totheir downstream values. Most calculated pressure dropsare a reasonable estimate of the approximation measured,except for the 16/64-in,, 334 B/D test, which yielded ameasured pressure drop of only 13 psi. in view of thelarger pressure drops measured for almost the same ratesthrough the 20/64-in. bean size, the 334 B/D, 16/64-in,point was discarded in the analysis of the data. The aver-age absolute percent error for the predictions was 33.7.

r.... .

,,M

i: , ,., 3

i w,* . .-. i- :.. L- :,~ i --nqq.., . - .I t. . . . . . . . .. . . .. . . . . ~ .. , ,, . ,. . . ,,.l-,~iil! -.-< .. A m. >.0 >.. -0. . . . .. .. .. . . . . . .

Fig, 5 Storm-choke test well downstream safety-valveflowing pressures.

I I ! ,!? I I ,,., L ,.,

Fig, 4 Storm-choke test well downstream safety-valve Fig, 6 Storm-choke test well upstream safety-valveflowing pressures, flowing pressure.I 1148 JOURNAL OF PETROLEUM TECHNOLOGY


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TABLE1 STORMCHOKEFIELDTESTPRESSUREDROPCOMWRISONSub-surfaceBeaean ChokeOiarneter

Vod datapm

(MUM in.)f

1414141414202020

oilFlowRatef70 mesa(B/0)559484334261427m382596232;4

Frcd&sd(MScflsm)0.4780.4440.429

Sdlon Measun?dFlowingressure(MScfl (psia)STB) Upstream Ownstream0120 1,015??5 1,1351,1B3 1,175

Prylreremp$rossMeasuml Calculated21180 i%13 54

PressureropPercentError-10.0+ 53.8

0.4% 1,171 1,125 +39.10.4% 1,205 1,015 1$ 1: + 3.20.391 1,202 1,102 100 138 +38.00,417 1,197 1,120 124 +61.00.344 1,230 l,04a lZ 283 +55.50.5010.416CM04

1,161 1,145 -25.01,1!s) 1,165 ;: ;: -$01,225 1,1s0 45 58 +2a9

When these measured pressure-drop data were used tocompute theoretical oil rates through the storm choke, theagreements between computed and measured flow rateswere much better. Excluding the last rate for the 16/64-in.run, the absolute average percent deviation from themeasured rates was 12.89. This shows that the orifice-fluid relationship tmly is rate sensitive; that is, themechanical operation of the valve occurs in a behaviorrrlregion where small changes in fluid rates incur largerchanges in :he orifice pressure drop. While the pressuredrop across the valve does indeed actuate the closingmechanism, the term rate sensitive applies mainlybecause of the extreme sensitivity of this pressure drop tototal fluid rates, Table 1 also shows computed orificedischarge coefficients, along with the predicted fluidrates. This coefficient is the required constant that, whenused in the orifice relationship, will yield actual oil flowrates from theoretically computed ones; that is,~o. act.al = 40,calc x C.

Fig. 8 isa plot of the computed discharge coefficient vsorifice size, While no data are available to lend suppori toextrapolation of the correlation below 14/64 in. or above20/64 in., the information presented does yield an in-dication of the range of C values expected for orificesizes other than those tabulated. No correlations were at-tempted for describing the discharge coefficients as afunction of fluid properties.The absolute values of the predictions of pressure drops

(__tr+-- ---//

IIm . . . . . .. ; .; fay/.,9 ., .. -.. . . .. - . ,. . . .1i.o.q .,.,U.X, . , ,, .

.,! Wm ..,, - ,,qwL

fig. 7 Storm-choke test well flowin upstreamrafety-valve pressure at 3,500 t.SEFtEMBER> 1975

Oil OischargeRate CoefficientCalc C/Omea,h?calc615 09089402 1.2039 *224 1.1652432 0.98935B 1.14251.2403M 1.2189270 0.8593363 0.9504493 1.1176

and oil rates using the newly developed relationship arenot precise. The state of the art of characterizing thebehavior of down-hole safety valves has not yet becomestandardized throughout the industry. Therefore, thereexists a need to collect more data reflecting noncriticalorifice flow. Special care should be exercised in placingthe downstream pressure recording device. This recordershould be placed as close as possible to the actual beanlocation to insure accurate measurements of verracontracta pressures, Although the appl~;at;on of theoreti-cal orifice relationships to actual field conditions does notyield exact information, the predicted results using anappropriate discharge coefficient are an improvementover those derived from relationships used previously.Graphical Presentation of TheoreticalPressure-Loss DataEq. 3 has been represented graphically for a sample ofinput parameters. A single curve or a family of workingcurves could be constructed to predict orifice behavior inany actual installation. The graph is shown in Fig. 9. Thefigure is for a bean size of 8/64 in. The solution GOR is200 scf/STB and the producing ratio is 600 scf/STB. Gasgravity, oil gravity, orifice temperature, and a specificheat ratio are held constant at 0,6,0,85, 150F,and 1.275,respective]y. The graph shows the predicted orifice oilflow capacity in barrels per day vs the downstream toupstream pressure ratio, c. Upstream pressures vary from1,000 to 8,000 psia. A WOR of 0.01 is also assumed.

,..,4..,** i ,,.,, &l! ....-.. :+!. . . . . .. . .,,.... .

.,. +

! . , ,, ., II,. ,0. I Iill! I

Fig. 8 Noncritical flow orifice dischalge coefficient.1149


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As indicated by the plot, the critical pressure ratio, cC,ispredicted for each curve. At this value of e and a givenupstream pressure, the orifice is unable to allow anyfurther increase in the oil flow rate, regardless of thepressure drop imposed across it. Stated mathematically,the condition occurs such thatd~o=O ~=edc . . . . . . . . . . . . . . . . . . . . . . . . . . ...(4)

The condition stipulated by Eq. 4 and depicted by Fig, 9can be satisfied by the relationship

[R(p,T)/n R(p,T) ~ (-%) 1.,5)(1q.)1= ,,+10.5 [1 + R(p, T) E;I]26~Thus, formultiphase orifice flow the critical pressure ratiois a function of the gas-liquid ratio, R(p, T), and thespecific heat ratio, n. The correct value of c, is the one thatsatisfies Eq. 5 for any R(p, T), and thus any value ofpressure and temperature occurring at the orifice. Theutility of the curve in Fig. 9 is that the value of e, can be

oOIL FLOW RATE -% ,POFig. 9 Three-phase orificefflolowates for noncritical orifice

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graphically obtained should the need arise.The graph of Fig. 9 predicts only theoretical rates, andthe appropriate value of the discharge coefficient shouldbe applied to the theoretical rate to achieve an actual rate.For bean diameters less than 14/64 in., a disdharge coeffi-cient of 1.2 is recommended, while for beans larger than20/64 in., a value of 0.95 may be used. These additionaldischarge-coefficient values, recommended from purelyan infuirive basis following extensions of the correlationof Fig. 8, are not supported by actual data.It is hoped that the procedure presented here will behelpful in providing flowing orifice information useful incurrent oilfield safety procedures, and perhaps will indi-cate areas in which improvements can be made.ConclusionsA noncritical, multiphase, orifice flaw relationship hasbeen found to yield the following information regardingthe flow ofoil and gas through anOtis 22J037 safety valvefitted with 14/64-, 16/64-, and 20/64-in. beans.1. For known pressure drops, theoretically computedoil rates can be expected to yield answers within 15 to 20percent of the actual throughputs,2. An orifice discharge coefficient computed for beansizes from 14/64 to 20/64 in. should aid in accurate] ypredicting either orifice oil rates from known pressuredrops or pressure drops acrossthe bean for any given rate.The discharge coefficients computed from mw-u~t~flow-ing data are the following.

Orifice DischargeSize (in.) Coefficient, C14/64 1.151016/64 1.05642oj64 0.9760

NomenclatureAGorifice cross-sectional area. ftzb = polytropic expansion equation constantB. = oil formation volume factor. bbl/STBC = orifice discharge coefficientde = choke diameter, 64th in.F,,.. = WORA. = gravitational constant. lb~ft/sec71b~n = specific heat ratiop, = t!pstream orifice pressure. lb/ftPZ = downstream orifice pressure, lb/ftzp,. = 14.7 lb/in.2q,, = gas f low rate. B/Dqo = 011low rate, B/D

qTF = totallowrate,/Dq. = water flow rate, B/DR = producing GOR, scf/STBR8 = solution GOR at p,, scf/STBT, = upstream orifice temperature. RT9C= 460 R

II = velocity of fluid. ftlsecv, = total fluid specific volume, cu ft/lb~v,. = liquid volume per pound of fluidz! = nonideal gas factor at T, and PIc = orifice downstream to upstream pressure

ratio, p2/plCe= orifice downstream to upstream ratio at Critics]

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CYIO= (BO+ WOR)-2y. = gas gravity, (air= 1.0)y. = oil gravity , (water = 1.0)yw = water gravityp, = gas density, lb/cu ft1 =upstream choke conditions2 =downstream choke conditions

AcknowledgmentSpecial thanks are extended tothe New Orleans Dist., GulfOil Co. U.S., and to Otis Engineering Corp. for fieldoperations conducted during the test procedure. GeorgeGrimmer, chief design engineer at Otis, was of greatassistance in on-site evaluations and served as a consultantfor the test operations.References1. Baxendell , P. B. and Thomas, R.: Calculat ion of Pressure Gra-dients in High-Rate Flowing Wells: J. Per. Tech. (Ott. 1961)1023-1028; Trans., AIME, 222.2. Ge.;r, G. E. and Rohrer, W. M.: Sudden Contraction Losses inTwo-Phase Flow, J. Hear Transfer (Feb. 1966) 1-9.3. Orkiszewski, J.: Predicting Two-Phase Pressure Drop in VerticalPipes: J. Per. Tech. (June 1967) 829-838; Trans., AIME, 240.4. Poettmann, F. H. and Beck, R. L.: New Charts Developed toPredictGas-Liquid Flow Through Chokes,Wor/dOil (March 1963)95-1OI.5. Ros, N. C. J. : An Analysis of Crit ical Simultaneous Gas/LiquidFlow Through a Restriction and Its Application to Flow Metering,Appl . Sri . Res . (1961) 9, Sec. A.6. Smith, R. V.: Steam Water, Critical Flow in a Venturi, NBSTechnical Note 608 (July 1971).7. Streeter, V. L.: Fluid Mechanics, McGraw-Hill Book Co., Inc.,New York (1958).

APPENDIXDerivation of the MultiphaseChoke EquationReferring to Fig. 10, the general energy balance can bewritten as

44rfd~+r %=0 +0 A-)PI It,lf the gas flowing through the orifice is assumed to ex-pand polytropically, then

p(v, v,.) = b , . . . . . . . . . . . . . . . . . . . . . . . (A-2)or,

b I/n()

v,= +V,, . . . . . . . . . . . . . . . . . . . . . . . . (A-3)PReplacing Eq. A-3 into Eq. A- I and expanding with111


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B.+ FWOv~= (where R, replaces R).~ + pWFWO+ 5.615 . . . . . . (A-12). . . . . . . . . . . . . . . . .The mass and fluid rates are related by

.BO+r*)(R)(+)~uol1 Rpo() + F ~OpW,0+ 5.615 J5.615wvLf=qtf~~ . . . . . . . . . . . . . . . . . . (A-13)The sum of the oil, gas, and water flow rate must be

qtf=qo+qg+qw.Thus,

,ti=,o[Bo+(~)f#) +FIS.o]. .. . ..A-14.When the expressions for the volumetric flow rate, qv,the mass flow rate, w, and the revised vahIe of vL, (Eqs.A-14, A-13, and A-1 2, respectively) are substituted in

Eq. A-7, the final expression for the orifice oil flowrate results:

q. = 3.51 Cd$alo/310, . . . . . . . . . . . . . . . . . . . . . (A-15)where

CXIO (BO+ FUJ-2.and

/3,0 ={[( )5 ,@-R-(lw+986(6)1[ TIZI (R _ R,)e-,l,,198.6 + P1 1}

1/2[yO+ 0.0002 17YgR,+ F,,.oy,,]x [Yo+ 0.0002 17Y,,R+ Fu.oyu.l

iTPTOrigina l manusc ript r eceivad in S-c ie ty o f Pet ro leum Eng in ee rs o ff ic e Aug . 5,

1974 . Rev is ed manuscr ip t r eceived JU e 5, 1975. Paper (SPE 5161) was firstp resent ed at the SPE-AIME 49t h An nu al Fall Meetin g, h el d in Hou st on, Oct. 6-9,1974. @ Copyright 1975 American Institute of Mining, Metallurgical, and Pet ro leum Eng in eers, Inc .

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PA Determining Multiphase Pressure Drops and Flow Capa

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