SPE_articulo Omana Multiphase Flow (1)

5/25/2018 SPE_articulo Omana Multiphase Flow (1)

1/16

SOCIETY OF PETROLEUM ENGINEERS OF AIME6200North Central Expressway mmSPE 2682Dallas, Texas 175206THIS IS A PREPRINT --- SUBJECT TO CORRECTION

Mult i phase Flow Through ChokesBy

R. On&&, Member AIME, Compsii{aShell de Venezuela,C. Houssiere,Jr., Member AIME, The U. of SouthwesternI.misiana,and Kermit E. Brown and Jmnes P. BriKL, Members AlME, and Richard E. Ihompson,The U. of Tul

@ Copyright 1 9American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc.This paper was prepared for the bbth Annual Fall Meeting of the Society of Petroleum Enginof AIME, to be held in Denver, Colo., Sept. 28-Ott. 1, 1969. Permissionto copy is restricted

abstract of not more than 300 words. Illustrationsmay not be copied. The abstractshould conconspicuousacknowledgmentof where and by whom the paper is presented. Publicationelsewherepublicationin the JO~RNAL OF PETROLEUM TECHNOLOGYor the SOCIETY OF PETROLEUMENGINEERS JCURNAusually granted upon reauest to the Editor of the appropriatejournalprovided agreementto givproper credit is made.

Discussionof this paper is invited. Three copiesof any discussion shouldbe sent to theSociety of PetroleumEngineersoffice. Such discussionmay be presented at the above meeting awith the paper, may be consideredfor publicationin one of the two SPE magazines.

AEYI RACT During both vertical and horizontal flthe well productionmay encounterrestrictExperimentalfield tests were conducted in the form of valves, pipe size reductionto study the multiphase flow of gas and liquid and/or purposely placed orificesor chokes[gaa-watersystem] through a smaii.-sizedchoke Theiatter restrictionsare placed at the

in a verticalposition. The resulting flow wellhead or at the bottom of the well withpatterns were photographedthrough trans- the object either to measure the flow rateparent nipples placed immediatelyupstream or to control the flow rate by imposing aand downstreamfrom the choke. backpressureon the formation. The choke oorifice can be used to predict the resultiA correlationrelating flow rates [gas upstream pressure associatedwith the newand water], upstreampressures, gas-liquid desired flow rate or a correct choke size mratios smd orifice sizes waa derived from the be selectedfor a particular flow rate. Thexperimentaldata and is presented in this assumes, of course, that a suitable correlapaper. The correlationhas a limited range is available.of applicationand is valid for criticalflowconditions. It should be useful for choke The use of chokes in dual installatiosizing for both downholeand surface systems. allows the productionof two zones at bottothrough one string of tubing. The two zone

INTRODUCTION are commingledat the bottom through a dualflow choke. This procedure eliminatestheMultiphase flow of gas and liquid occurs need of producinfjt~ zones through two aepfrequently in the petroleum, chemicaland arate strings.2) very significantcor-related industries. In the petroleum industry siderationis that the correct size of chokgas-liquidmixtures are transportedznroughA,--. to be used to allow t}ierequired flew r=tevertical and horizontalpipes from the from each zone must be accuratelyknown. Ureservoir to the wellhead, from the wellhead this premise the various regulatorybodiesto the gaa-liquidseparatorand to the stock pemit dual,installation to be producedtank. The refinery receives the mixture which through one string of tubing.undergoes further traveling from distillationand separatingunits to final storage. To study the multiphaae flow of gas anwater in a verticallyplaced choke, controlReference and i~ustrations at end of paper.


2/16

MULTIPHASE FIOkfield data were taken at the facilitiesofUnion Oil Co. of CaliforniasTiger I.a,goonField located near Delcambre,La. The dataobtained during the experimentaltests wereused to develop the correlationpresented inthis paper. Dimensionalanalysiswas appliedto determinethe groups involved in the cor-relation which was derived with the use ofmultiple-regressionanalysis techniques.STATEMENT OF TBXORY AND DEFINITIONS

~es of Flow EncounteredFig. 1 shows the three types ofobserved--mist,bubble and slug. NO flowattemptwas made to establisha correl~tionfor ea-~type of flow. Rather, the whole flow rangewas taken into account in the final correla-tion.

Applicationof Other Methodsme formulaof &lMerb7 [Eq.1] and Roi+[Eq. 2], as adaptedby Poettmann and Beck6 infield units, were applied to the experimentaldata with results shown in Table 4.p. - . 435 R0546qtr [1:dl.09 * -

where Ptf = tubinghead pressure, psigR= gas-liquid ratio, Mcf/STBq = gross liquid rate, STB/Dd= bean size, l/~ in.

86,4ooCAtf = 5.61t 0.07657g~

J273.6 p 0.4513~Rt 0.7660. 1 + 0.5 mL] R+ 005663 [2]

where R =

L =

and plfi=Yg =~:P=T.

Rs., s

B. =~L =

o.oo504T z[m-Rsl . . . . ..[31pBo

1 mLPg ; L = ~..... . [4]l+R~L

density of crude, lb/cu ft at 60Fand 14.7psiaspecific gravity of gas [air = 1.00]producing GOR, scf/Doil, STB/D

pressure, psitubing temperature,R [assumedtobe 85F]~O~J~i~~~yof g~~ in ~H~~~~~ tubingpressure and 85%, scf/bbl formation volume factor of crude at&..l.


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R. OM&l, C. HOUSSIERE, JR.,SPE 2682 KEFU41TE. BRWN, JAMES P. BRIIL and-RICH&D E. THOMPSON

1. At a preset pressure a variable chokewas adjusted and the liquid rate determined asthe maximum liquid rate at the given pressure.2. The gas rate was set by a variablechoke and the gas meter noted until stabiliza-tion was obtained at the desired pressure.These rates were precalculated.3. Both liquid and gas rates were re-checked and adjusted.4. The cumulativemeter readingswerestarted.

5. Visual observationswere made andmotion pictures taken.6. Pressureswere read and recorded sev-eral times to ensure that stabilizationhadbeen reached.~. Temperatureswere recorded.At a gi~e~ the the ~e~~nd set Qf.

cumulativemeter readings were taken.9. After the single-phaseflow calibra-tion was completed for all chokes,a liquidrate was circulatedat the preset pressure and

gas introducedto give a precalculatedgas-liquid ratio. Steps 3 to7 were repeateduntilthe maximum gas-liquidratio was obtained.The preceding routine was followed foreach test. The fluids used were gas md waterThe physical propertiesof the water were: spe-

cific gravity, 1.01, surface tension 66.0dynes/cm, and viscosity 1.01 cp at 800F. Thecompositionand fluid propertiesof the naturalgas are given in Table 1.After the tests were concluded,the chokeswere gauged for size with the results shown in

Table 2. Some chokeswere found slightlyundersizedas comparedto the nominal size, andthese correctionswere accounted for in thefinal correlation.DEVELOPMENTOF CORRELATION

DimensionalAnalysisThe physical model utilized in this study

is the choke shown in Fig. 4, amd the dimen-sionlessgroups related to the choke through-put are listed below in both cgs and fieldUnits.Governinggroups:

) 0.5 ~L 0.5Nd = d% ()120.872d ~ . . [5]N L)

~ ~ 0.25= sL ~0.25. 1.9~vsL(5)

VL . [6]

Sg(:c)oas N---= V-.. -vg 1.9.38 -.(Q\025. [?]sg~cf)NR=- . . . . . . . . . . . . . . . [8]NVL

t0.25NL= ) ()1 0.250.15726~L~

PgNp=~ . . . . . . . . . . . . . .[Io~ 0.5

ml ()P~~ = 1.74 104+ .[pa] .5Dependent group:

~5g3 0.25()

1.25()

= 1.84 qL: . [qL qL~

Effect of Holdup.A . . ..-a.a--a k..+me effect of hddiipwas GvuaAucAGu Uuucould not be predicted using available corre

tions from the literaturefor vertical andhorizontal.multiphaseflow in pipes. Forexsmple, from the values NVL and ~g and us~the Ros correlationfor verticalflow of gasliquid mixtures [Fig. 4, Ref. 5], a froth fltype is obtained. Using Fig. 3 [same referethe liquid holdup is -1 as comparedto 0.12from Eatons holdup correlation. The peu%uunecessary to determinethe holdup value were~f ~~~ ~ug~ ~f USU edfwnnnd ~~~~g+ corre343-.=. ---- . --- -.tion. Therefore,the effect of holdup was nincorporatedin the proposed correlation.

Final CorrelationWith the use of a multiple-regressionanalysis technique some groups were eliminat

and one group ~ = l/[l+Rl was added to obta suitable correlation. Thus NqL was corre-7-L-A..a.ba.?- *%. --d n- .-._h+.4*4mr? +1. AAuUCU WAIAJ J d> ~~p> lvpl -u WQ, UUU-J.LA* w..followingexpression:NqL =0.263NP-3.49~.3.19 ~o.657Ndl.~

DISCUSSIONAND STATISTICALANALYSISOF RESULThe above correlationwas derived for din the critical flow region as indicatedby

P2/Pl ratio- However, it was noticed that,..%--&L- -.-1..--4.-* - ---- 1 a - ..*A -..4-J.. D ..-Wlleu bale VUJJJJIEUL-J.C &iaD-.LAquAu L-UIJAU n w-mequal to or less than one, deviationslargerthan 10 percent were observed in the predictdata regardlessof the VdUe Of p /p~. The

zata for Rs 1.0 and p2/pl< 0.54 were grouwith subcriticalflow data, p2/pl> 0.546, bno correlationwas obtainedwith any of theparameters in ~. 13 or using p2/P1 as thedependentvariable.

The effect of viscosity is not includethe correlationbecause the viscosity numbernot correlatewith the other independentgroand because the average Reynolds number [he3 x 105] located the experimentaldata in th


4/16

4 MULTIPHASEFLOW THROUGHCHOKES SPE 2682turbulent region.

The predicted flow rates vs the measuredflow rates as well as the percent deviation areshown in Table 3. A Cartesianplot of pre-dicted vs actual production values is shown inFig. 5. 4--.1--,. . ..naa.,,-,+ liq~:~the correlatingfunction is shown in Fig. 6.STATISTICALANALYSIS OF CORRELATIONRESULTS

To check the accuracy of the derivedempirical correlationthe calculateddeviationsbetween the observeddimensionlessproductionand that predicted by the correlationwerelisted in Table 3. The percent error, thealgebraicpercent error or the bias, and thestandard deviationwere calculatedas follows.

%Error =[observedproduction - calculate[production]observedproduction

% ErrorN >number of observations.

The estimate of the standarddeviationcalculatedfor the samplewas obtained from:Standard Deviation =* Z[% error]2- N[%error]2QJ N-1The experiment? data was tested using theGilbert7 and the Ros methods. Table 4 showsa comparisonof errors for the Gilbert and theRos correlationsand the proposed correlationof the authors. The average percentthe standarddeviation for the threeare as follows.

PercentErrorGilbert 44.4Ros [a= 0.5] 29.0Proposed correlationa. all data - 1.15b. excludingsubcriticalan+.=&U._. - ~,~1c. Only subcriti-

error andmethods~~mdar~Deviation? 64f 36

? 15

? 1~.~cal No correlation

The errors were initially calculatedbyutilizing all the data. They were again calcul-ated, but all subcriticaldata and the valuescorrespondingto R < 1.0 were excluded. Asnoted in the preceding table, these values were

found to be -1.11 percent for the bias and:15.3for the standard deviation.LIMITATIONSAND APPLICATION

As discussedpreviously the application of&l.. .-,..-al.++{. Iimi+afl +.fi ~~~ fQ~QUi~IJLJAD LULAGJ.-U.OE A.. -A.-U ramges.Pressure: 400 to l,ooo/psigFlow rate: 800 B/DmaximmumChoke size: 4/64to 14/64

An example of the applicationof the correlationfor choke sizing is given in Appendix B.CONCLUSIONS

1. The proposed correlationfor verticallyplaced chokespredicts flow rates accuratelyfora gas-water system provided that criticalflowconditionsare present.Q ~~~ n.++i..l +1- ~Q~@i~iQ~~ ~ tA~i~. . . A.--a. .-.corre;&.ion,p2/pl must be less than 0.546andthe volumetric-ga~-liquidratio R must be >1.0.3. Based on the results of this study, itappears that the correlationshould give betterresults for small choke sizes [4/64to 14/64]than any other method in use. Reliabilitywillprobably be less at larger flow rates [>800B/D] and consequentlylarger choke sizes[> 14/64th].40 The correlationis useful in sizingsmall chokes.5* Although the data was taken for a dualflow choke assembly in a verticalposition, thecorrelationshould be useful for sizing chokesat the surface as well as bottom-hole chokes.

NOMENCLATUREd=Nd =NL =

NPl =NqL =Np =Nvg =NVL ==G=R=T.vsL =Vsg =

a=7

choke dismeter, l/& in.diameternumberliquid viscositynumberupstream pressure numberliquid volume rate numberdensity or mass ratio numbergas velocity numberliquid velocity munberpressure, psigdimensionlessproduction numbervolumetric gas-liquidratiotemperature,Fliquid superficialvelocity,ft/secgas superficialvelocity, ft/sec

Greek Symbolsquality parameter [Ros]specific gravity


5/16

R. OM&*A, C. HOUSSIERE,JR.,EWE 2682 KERMIT E. BRCMN, JAMES P.7g = specific gravity of gas [air = 1.0]yL = specificgravity of liquidPg = viscosity of gas phase, cpPL = viscosity of liquid phase, cpP = density, lbm/cu Nu= surface tension of liquid-air interface,dynes/cmACKNCXUEDGMENTS

The authors wish to thank the followingcompaniesfor making this study possible:Union Oil Co. of California,Otis EngineeringCorp., Halliburton Co., Gulf Research andDevelopment,Dow Chemical Co., Trunkline Gasco., Foxboro Co., NationalTsmk Co., Continentsoil co., Pan American Petroleum Corp., Hydrilco., Cameron Iron Works, The Bettis Corp.,Black, Syvalls and Bryson, Oil Center Tools Co.Roots-Connersville,The Annin Co., SouthernFlow Measurement Co., pr~~sureProducts Co.,Cliff Mock Co. md Compania Shell de Venezuela,Maracaibo.

Also the authors wish to thank the Dept.of Petroleum Engineeringat The U. of Texas for---+ CC4-- to ,d~ethe ao+m ,.,hi -h ..,.. +nbam bylJ=~JJJ~-D~-~ U-- ...LU. C4. W-.LLCharles Houssiere while at that university.REFERENCES1.2.

3.

4.

5.

6.

7.

@&a, R. A.: MultiphaseFlow throughChokes,MS Thesis, The U. of Tulsa [1968].Brown, K. E.: Gas Lift Theory and PracticePrentice-Hall,Inc., Englewood Cliffs, N. J[19671 735-74o.Eaton, B. A.: The Predictionof FlowPatterns, Liquid Holdup and Pressure IossesOccurred D.ming ContinuousTwo-PhaseFlowin Horizontal Pipe Lines, PhD dissertation

The U. of Texas [May, 1964].Tunstsll, K. N.: ArtificialLift asApplied to the Multiple CompletionChokeAssembly, SouthwesternPetroleumShortCourse [April,1966].Ros, N. C. J.: An Analysis of CriticalSimultaneousGas-LiquidFlow Through aRestriction and its Applicationto Flow-metering,Appl. Sci. Res. [1960]9, Sec. APoettmann,F. H. md Beck, R. L.: Newcharts Develomed to Predict Gas-IAauidFlow. _=--Through Chokes,World Oil [March,196j].Gilbert, W. E.: Flowing and Gas-LiftWellPerformance,[1954]. Drill. and Prod. Prac., API

lZLandRTCHiRDE. THOMPSON


6/16

APPENDIXADATA AND TEST DATA RESULTS

11I~T ~CJ,.-.

1.001

1.002

1.003

1.004

1.005I=M

1.007

i.008

5.001

5.0U2

5.003

2.101

2 .0C12

2.003

2.004

2.006

2.007

CHOKE(6hTH)

4/64

6/64

8/64

10/64

11/6412/64

14/64

.1.rl.L*[O*

4/64

8/64

12/64

4/64

6/64

8/64

lo/64

12/64

14/64

PUS PDSPSI

1003.806.603.4C6.MOO .803.635.4U2.z:600.407.1002.w.600.407.1008.1004.:::400.1000.~~ .597.403.low .

939.950.9%.957.940.950.949.950.956.970.8ci)597.399.%5.799.609.400.970.800.599.396.933.79?.600.400.:::606.400.?2 :609.400.

295.276.28o.272.279.287.287.276.285278.275.285.276.286.285.288.281.282.283.287.278.285.s~~ .2&?290.117*A,.

295.505.8U .305.505.806.305.500.804.295.298301.;::303.307.299.306.306.307.;E :312.311.314.318.313.311.309.349.349.315.311.

DATATtE TDSDEG.F

70.076.071.069.067.077.076.578.067.075.576.076.064.072.076.075.074.566.574.078.579.570.0& Q80.080.0?O.Q

51.052.051.C51.053.053.053.055.058.079.074.067.o71.093.()85.0:.:87:086.085.088.097.095.093.067.095.091.0100.0&.o1040108.093.0&.o

69.074.071.068.666.075.075.576.067.574.574.074.063.o71.075.074.575.066.073.578.579.570.07g.Q79.079.0(58:Cl

51.052.051.051.053.0~>..53.055.058.058.057.059.070.057.559.070.068.051.060.069.078.061.066.073.059.060.063.oz::71+.081.074.073.0

~N oRIF Ps DIFF. TORINCH

3X.2503X.2503X.2503X.2503x.3753x.3753x.3753X.2503x.5003x.5003x.3753x.3753x.3753x.7503x.5003x.5003x.7503x.750g.;g3X:7503x.7507X.7503x.500

970.915.890.910.g:970.970.960.g.965:930.930.930.935.930.935.935.930.935.930.930.935

57.038.521.05;::57.021.037.059.040.571.024.025.018.054.019.038.o28.o16.039.058.o46.o26.o39.5

143.596.080.075.5115.0123.o132.0K8.594.0107.0lx.oU2.o107.0114.o328.0137.0105.0106.0)29.0139.5108.0132.0119.o129.o


7/16

DATA(Continued)

TEST NO.

3.001

3.OCQ

3.003

3.004

3.005

3.oo6

4.001

4.003

4.005

CHOKE(6@H)

4/64

6/64

8/64

10/64

2/64

14/64

4/64

8/64

,..12/64

Pm PDsPSI

700.970.%:627.905,976.978.980.607.709.973.;$ .610:918.970.967.&o.900.955.957.970.?80.967.935.965.951+987.987.986.985.992.996.897.900.907.915.919.%0.919.950.aZ97+ .934.950.971.976.

305.260.264.3CQ.294.295.293.286.302.300.296.293.291.305.298.296.296.295.31.9330.306.298.295.308.308.356.301.287.307.402.2::618.;Z :307.411.507.608.703.800.310.@,508.605.732.814.

TLE TDSDEG.F

69.068.074.568.066.0?Z=Q74.560.564.568.071.()71.068.066.069.076.072.071.074.078.078.071.066.069.0z::67.o71.67.069.071.070.073.077.061.066.068.070.071.072.072.072.071J n,.,.77.078.062.065.0

68.06J.;68:066.070.070.060.564.568.070.067.068.066.069.0E::71.073.074.073.071.066.069.068.0W.o67.o71.0

67.069.071.070.073.077.061.066.068.070.071.0P.o72.072.0?&.~77.078.0&n.065.o

IJ3WORIF.INCH.5xl/8X.275.5xI/8.5xI/83X.250ax.2~o3X.2503X.250.5xIJ83X.2503X.2503x.3753X.250.5x1/83X.3753x.3753x.3753X.2503x.3753x.5003x.5003x.3753X.2503x.3753x.5003x.3753x.3753x.375

.5xI./8

.%1/8.5X1/8.%1/8.5xI-/8.5x1/83X.2503X.2503X.2503X.2503X.2503X.250.5X.075X.575w 376/.../,/3x.3753X.3753X.2~o3X.250

PsPSI1C20.1000lCQO.970.1005.1000.1000.995.1000.970.970.975.990.1012.965.960.960.960.950.;;;.950:960.960.960.950.960.950.

993.995%:1000.1010.915.915.92.930.930.935.935.---WY.91?Q945.955.nQ nyuu .985.

DIFF.INCH33.06.527.55.011.o42.056.0-.2;:;40.064.o38.o29.066.018.071.015.012.o28.036.o44.021.019.042.026.044.051.07.025.027.017.08.010.019.020.524.o24.527.021.58.519.0170U18.Q18.022.0cn nJ~. U30.0

D

1U

I13311111111111111

111111i1J1~1


8/16

TEST DATA RESULTS

TE S T N O

1.001

l.oce

1.003

1.004

1.0051.006

1.007

1.008

5.00.I

5.OCQ5.003

2.001

2 .0(2

2.003

2.004

2.006

2.007

LIQUIDRATEB/D

87.8073.1655.9934.10201.40167.uX29.3477.75381.63334.24260.76154.01572.19490.21383.15226.87581.07155.~468:61275.74827.36710.53544.0831:.9&.

;;.:.39:63371.73304.23li2.34670.34565.76Y4.81.-----------------------------------------------

GAS RATE (CF/D) GAS IJQUIDSURFACEURFACE INSITU

87657.574299.155291.352553.9194797.9161cQ2.71,205(8271939.5375278.4305207.J)2263(R36172005.71528: .81+471+(s(13566):0.5ly(sgl7LG}1193zUz-. ..565tY16.2414795.62S19J4908121J+3.1698556.6554152.7288596.8

1154.21198.71209.31103.52690.62684.52719.32462.85062.85095.55170.946go.41$128.27688.37831.06630.605(% 7,-,.9552.1977.;,I2104:8J-2339.9x2228.710004.2

---.-------------------------------------------.

RATION (CU.FT/B)INSITU PDs/PU3

-------------------------------------.--------.-

.304,554

.477.681.289.369.464.698.298.358.471.711.286.368.488.718.289

.29i.365.489.706.295.~~~.485.729.130

.325W&.329.544.851.39.534.843.315.384.516.766.324.390CIL.,-756:326.394.524.771.346.402.530.793.351.401.525.781.386.445.529.785

4/64

6/64

8/64

lo/64

n/6412/64

14/64

14/64

4/64

8/64

12/64

4/64

6/64

8/64

lo/64

@64

iL/64

-.


9/16

TESTDATARESULTS(Continued)

TEST NO LIQUIDRATEB/D3.001 17.9120.7934.9437.503.0U2 56.5342.3542.15

4)+3284.813.003 125.9882.2983.3084.423.004

3.005

3.006

4.001

4.003

4.005

169.63258.06121.23323.55238.84365.95155.58154.10154.13309.95453.59183.18184.35361.61362.2835.3834.2037.3442.3141.6637.76174.05167.28164.73;;; .:.150.35IY2.65386.38381.31292.88289.69268.11231.55

GASRATES U R FACE19450.413E 206.1O17657.387443.1842009.6879543.7291722.4639050.8116187.01759@ .0395751.21.165032.8166091.872C66.37109365.66215008.1399801.6841005.01135244.73268T72.08297497.4o118001.3051733.66165267;30230647.95168915.99182226.1968999.9716678.6917339.4513780.039476.5010560.6914541.7653315.9557375.4658216.836141o.1454799.6034991.474410.87107960.35111155.78111630.47125309.2192836.6566660.70

(CF/D)INSITU359.08485.88223.9495.80868511112.&1.182.47479.92o1.121634.721752.632111.55830.60342.872349.112986.801285.57Y28.40285P.333841.833975.041538.89653.662703.482981.642212.622323.79903.10207.21216.83173.63119.16132.99184.60725.64790.38799.88840.55748.6747-;$

1459:531508.391525.161684.381156.30833.54

GAS LJQUIDS U R FACE1086.281837,51505.35198.48743.141878. K?2;I- ; . ::190:876(x?.471..I63.641981.09782.85160.74423.791773.49807.81171.69369.581727.521930.2765.59166.91364.363259.11916.27503.93190.46471.405C6.94369.06223.97253.51;;; .OJ

342:99353.41400.16370.72232.7428.90352.37368.91381.15432.56346.26287.89

RATZO(CU.FT/B)INSITU tis/PIEl20.0523.376.412.5515.3626.2728.0510.832.3712.9821.3025.35g.842.@9.1024 6410.412.217.9024.6925.799.982,1.1.5.9616.28D .006.432.495.866.344.652.823.194.894.174.724.865.485.063.19.404.765.015,215.814.313.60

.447.279.277.325.481.337.311

.303.318.506.429.312.307.323.501.333.316.315.526.377.331.322.315.406.329.390.322

.311.321.416.522.624.628.511.354.352.46 ?.561.667768.875.344.441.551.642.737.836

14/64

4/64

8/64

lo/64

12/64

CHOKE GLR(VOI/VOL)4/64 :.::

1:141.4556/64 2.7364.6794.996l:g:

8/64 2.3113.7934.5141.752.3601.6214.3881.853.3941.4094.3984.5941.778.3761.0612.8992.1381.144.4441.0431.129.&8.5C 2.569.871.742.841.865.975.W.567.071.848.892. 271.036.768.641

12/64


10/16

APPENDIX B -- CALCULATIONPROCEDUREThe proposed correlationwill give adirect answer once the correspondingdimension-less groups have been determined. Therefore noiterativeprocedure is necessary. However, adigital computerwill speed the calculationprocess considerablyif a large amount of datais involved.The step-by-stepprocedure to solve thecorrelationis as follows.

-3.49 3.19%o.657Nd1-8e13]qL = 0.263 Np NPl1 Evaluate Pg at PI and [upstream.--a


11/16

Table 1 - Mass spectrometeranalysis of the

Mole SpecificComponent Per Cent a

HeliumNitrogenCarbon DioxideHydrogen SulfideMethaneEthanePropaneIsobutaneNormal ButanePentanesHexanes~eptane~+

0.61JJ0.050.460.02%.%4.141.300.410.310.240.60n Aleu U U

test gas.3

Viscosity(cp at 8cfF)

o o12

* Courtesy of Pan American Petroleum Corporation,Research Department,Tulsa, Oklahoma - after Eaton.

Table 2 - Choke sizes gauged after test.

Choke Size (Nominal) Deviation from Nominal Size(in.)

4/64 -.oce56/64 -.oo128/64 +.0008lo/64 +.000712/64 -.007614/64 -.0065


12/16

Table 3 - Actual versus predicted flow rate.

Ob. No..1234

:91011Q13141516

353637383940414243:;::

Actual16.7019.4032.5834.9652.6939.4539.2941.3478.90117.2776.7477.8278.90158.35240.50lx?.95... ..U>. M.222.66341.(%2144.84111X7A.L-T,.143.76289.14422.63170.78171.86337.2b337.7632.9631.8334.8039.4538.8535.18162.13155.65153.48143.22137.81139.97142.14285.90281.03272.93269.68249.69212.39

Predicted24.3917.1530.32;:.$37:53;;.;:79:12120.1986.6462.0793.54144.43192.0197.27is~..23211.96:%%.lzh N?-,- .193.*285.70364.3021.1.09228.34296.60407.8830.7630.6834.5438.8438.9636.37123.92127.37129.29125.93130.33148.72191.19263.43267.17271.05263.14230.46252.13

L_-46.06u.606.94-13.26-14,134.8510.75-13.06- 0.27-2.48-:0.:;-18:558.7920.1613.887L L lAu U L4.8011.150.316.771-,.-34.891:1913.80-23.60.32.86E .05

-20..756.693.610.751.55-0.27-3.3928.5618.i615.76w.065.43-6.25-34.517.854.930.682.427.69-18.70


13/16

Ob. No.1234

78910ILE1314

Table 4 - Percent error comparisonbetween Gilbert,correlationfor the same unit of production. ROSand

1516171819202122232425262728293031p333435363738394041424344454647

Bias:Standardev.:

Gilbert18.005.6829.8895.47-11.372.932.9160.6893.97-25.637.165.8855.3082.33-32.60- 1.1857.4289.09-26.528.108.9980.93109.490.5956.8979.3030.76----l.-JJy .4y32.8332.0543.71AK }11 .-r+59.0940.2515.08=.9513.7215.0925.0958.76387.9335.I.234.2936.oo30.5262.76109.56+ 44.4

+ 64.

Ros9.930.7310.3264.60-15.311.771.8355.7168.70-28.05-6.60-3.4251.9655.59-35.762.8857.5968.33-30.2914.4015.6784.1089.26-4.5268.5990.6028.81--- IriLuy.40x2.58X2.9716.03~~.~~41.2113.30- 1.30- 1.43- 0.492.7o9.9551.CE13.2.3122.6922.7224.6121.9348.1082.44

+ 28~ 36:;8

Correlation-46.1u.66.8-13.3-14.14.910.8-13.1- 0.3-2.5-12.520.0-18.58.720.113.9-16.64.81.1.30.36.834.9-1.113.8-23.6-y?.812.1-20.66.53.70.7~.~- 0.2-3.423.518.215.832.15.4-6.2-34.57.89.90.72.47.7-18.7

- 1.15&14.g8


14/16

ist

ELECTRONIC PRESSUREFOXBORO RECORDERS REAOouTsORIFICE METERREAOOUT

REAOOUTS

icENT131iL coNmoL HOuS[;.. .. ... VARIABLE

Bubble

Fig. 1 - Typesoffiowencountered.

slug

>

R

QUICK UNIONR R . PRESSURE ANO TEMPERATURERECORDERS

PLASTIC NIPPLE

ii

R

RCHOKE ASSEMBLY

PLASTIC NIPPLE

Fig. 2 - Test unit.


15/16

-.

L

HALCO

I

ILF41 1 ?iWINDOW FI 3 CHOKE L

F7 LWINDUW GAS

F2

A

9 \yI 3

78F = FOXBORO A = MAIHAK

Fig. 3 - Testingcontrolassembly.

mlFig. 4 - Choke and two-inch type S dual flow unit.


16/16

500

400

nl Xnr)1- .vEwa 200

100

0 100 200 300 400 5Q ACTUAL

Fig. 5- Predicted vs actualproduction.

ooo~-1ZW100t

;/:

/

e

L *

k r- /x.1/.

10 I 1I11I 1 I 1 I t 1 I 1111 I I30 100 1000 2000-3.49 N3.19Qd657 ~)8P P1

Fig. 6 - Dimensionless productionvs correlating function.

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