33 open flow para pozos de gas

8/3/2019 33 Open Flow Para Pozos de Gas

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Chapter 33Open Flow of Gas WellsR.V. Smith, P e t ro le u m Co n su i t a n t *

IntroductionThe gauging or testing of gas wells arose from the needto measure the productive capacity of a well. The earliestresponse to this need was to open the well to flow to theatmosphere and then to measure the flow rate. However,it soon became apparent that such practices we rewasteful of gas, dangerou s for personnel and well equip-ment, and frequently damagin g to the reservoir. In addi-tion, such tests provided very little information forestimating production rates into a pipeline. As a result,the practice of gauging gas wells by opening th e well toflow to the atmosphere decreased and now is almostcompletely confined to stripper gas areas wherepressures are very low and the rates of flow are small.Pitot-Tube Gauging of Low-Pressure WellsThe pitot tube is one of the simplest instruments formeasuring the rate of flow of gas. As such, the pitot hasbeen used extensively to obtain an appro ximate gauge ofthe open-flow capacity of low-pressure gas wells. Thewell is opened to flow to the atmosphere through a flownipple, and the producing rate is measu red with a pitottube. Th e producing rate is influenced by the hydro statichead of the column of flowing gas and the friction be-tween the flowing gas and the walls of the flow string.Thus the observed rate of flow to the atmosphere may bea very close measure of the ability of shallow low-capacity reservoirs to deliver gas into the wellbore.However, it may be more nearly a measure of the flowcapacity of the flow string in the case of a well produ cingfrom a high-capa city reservoir. This is especially truewhere the flow is through a small-diameter flow string.

Historically, gauging of wells with pitot-tubemeasurem ents has been useful in the drilling and com-pletion of low-pre ssure gas wells. D uring the drilling ofmany w ells in the Hugoton field of Kansas, Oklahoma,and Texas, it was the practice to take pitot gauges after

Th e a u t h o r a l so wro t e t h e o r i g in a l ch a p t e r o n t h i s t o p c f n t h e 1 9 62 e d I t I o n

every bailer run or at the end of each 5 ft of formationdrilled. Upon completion, data were available to con-sttuct a chart showing a relationship between the rate offlow and depth. Th e chart is useful in determining thedepth of the major gas-producing zones. Such data werevaluable in planning remedial wor k that may benecessary during the life of the well. Pitot-tube gauge swere useful in determining rate-of-flow increasesresulting from each stage of acid treatment. In manycases the pitot-tube gauge after acid treatment provideddata from which the desired flow rates for a backpressuretest could be selected.Fig. 3 3.1 show s a pitot-tube and flow nipple arrange-ment that is suitable for gas measuremen t. The pitot tubeshould be made of %-in-ID pipe shaped to measure im-pact pressure at the center and in the plane of the openingof the flow nipple. The flow nipple should be at leasteight pipe diameters long, free from burrs or otherobstructions, and must be round. The impact pressuresare measured with water or mercury manometers or apressure gaug e, depending on the pressure to bemeasured.

The impact pressure is converted to rate of flow bysuitable equations or tables suc h as those pub lished byReid. Subsequent experimental work by the USBM * isin reasonable agreement with the Reid data. The equa-tions published by Reid were investigated by Binckley, 3who concluded that they were based on sound theoreticalprinciples. Reids equations and tables have been ad-justed to a pressure base of 14.65 p sia for the purposes ofthis handbook. The adjusted equations for impactpressures less than 15 psig are

~/,~=34 .81~& * K, . . . . . . (1)qa =1284d; Jh, , . . . . (2)

andy,C=183.2dt &, .___ _. _____. _. ___.. (3)


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33-2 PETROLEUM ENGINEERING HANDBOOK

TO MANOMETERORPRESSUREGAUGE CONNECTION

L=8di

Fig.33.1-Typical flow nipple and pitot tube for gasmeasurement.

whereqx = rate of gas flow, Mcf/D (14.65 psia andfjoF),dj = ID of flow nipple, in.,

h,. = height (manom eter reading), in. water ,h,, = height (mano meter reading), in. mercury , andpi = impact pressure, psig.

For impact pressures more than 15 psig, the adjustedReid equation is

q& ,=23 .89d ?p, , . . . . . . . . . . . . . . . . . . . . . . . . . . (4)where p, is impact pressure, psia. Values of rates offlow for various impact pressures are given in Table 33.1for a flow nipple with an ID of 1.000 in. Rates of flowin Table 33.1 were computed by Eqs. 1 through 3. Therange of impact pressure s is from 0.1 in. of water to 15psig. Rates of flow for impact pressures from 15 to 200psig were computed by Eq. 4 and are given in Table 3 3.2for a flow nipple with an ID of 1.000 in. Impact pres-sures measured on larger flow nipples can be convertedto rates of flow by multiplying the rate of flow fro m thetable corresponding to the impact pressure by the squareof the ID (in.) of the larger nipple.Rates of flow taken from Tables 33.1 and 33.2 or com-puted by Eqs. 1, 2, 3, and 4 are for gases with a specificgravity of 0.600 (air = 1 OOO ), lowing temperatures of

60 F, and for discharge into an atmospheric pressure of14.65 psia. Corrections can be made when desirable bymultiplying values from the equations or tables by thefollowing factors.

J.600

F,= - YRand

J 520FT= (460+ Tf) where

F, = specific gravity correction factor,YY = specific gravity o f gas being m easured,air= 1.000,FT = flowing-tem perature correction factor, andTf = temperature of flowing g as, F.

The atmospheric-pressure correction factor for valuesfrom Table 33.1 and Eqs. 1, 2, and 3 is

Fbar =J a-14.65 where Fbar is barom etric correction factor and pa is at-mospheric pressure, psia. The value of pressure used forp, in Eq. 4 is the absolute pressure and is com puted byadding the barometric pressure to the gauge pressure.The correction factor for barometric pressure for Table33.2 is

Fbar = Pi +Papi + 14.65 In ordinary usage, rates of flow are taken fro m pitottables or formulas without corr ection.Example Problem 1. Given an impact pressure of 27.2in. of wate r on a flow nipple with ID~2.441 in., deter-mine the rate of flow.Rate of flow from Table 33.1 for ID = 1 OOO = 182Mcf/D.Rate of flow for ID = 2.441 in. is

q,=182(2.441)2=182x5.958=1,080Mcf/D.Or, by Eq. 1, the rate of flow is

=(34.81)(5.958)(5.215) = 1,080 McfiD.Example Problem 2. Given an impact pressure of 65 psigon a flow nipple with ID=4.082 in. with discharge intoa barometric pressure of 13.2 psia, determine the rate offlow.Rate of flow from Table 33.2 for ID of 1 OOO nd at-mospheric pressure of 14.65 psia is 1,904 Mcf/D.For ID of 4.082 in. and barometric pressure of 13.2psia, the rate of flow is

qg = 1,904(4.082)*(65+13.2)/(65+14.7)=(1,904)(16.663)(0.9812)=31,100 Mcf/D.


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OPEN FLOWOFGASWELLS

Or by Eq. 4.qs =23X9 (4.082)*(65+ 13.2)

=31,100 McfiD.Backpressure TestingBefore the development of the backpressure method fortesting gas wells, the open-flow capacities of gas wellswere determined by actual open-flow tests. The flow-ing of wells at their w ide-open rate results in waste andpossible dam age to the well. In addition, the open-flow

33-3

test yields very little information regarding the capacityof a well to deliver gas into a pipeline system.The backpressure method o f testin gas wells wasdeveloped by Rawlins and Schellhardt. 9 Results of testson 582 wells as reported in their study and other work onmany wells reported elsewhere show that when the ratesof flow are plotted on logarithmic coordinates againstcorrespond ing values of (pi -p,,,,)-the difference of

squares of the shut-in pressure F R and the flowing sand-face (bottomhole) pressure (BHP) p,f-the relationshipmay be represented empirically by a straight line.

TABLE 33.1-RATES OF FLOW FOR IMPACT PRES SURES LESS THAN 15 PSIGMEASURED WITH A PITOT TUBE FOR FLOW NIPPLE WITH ID = 1 .OOO n. *

Impact Pressure qg, IO3 cu ft/D Impact PressureWater Mercury (14.65 psia Water Mercury

q,,103 cu ft/D(14.65 psia

(in.) (in.) psig and 60F) (in.) On.) (Psig) and60F)-~ -0.10.20.30.40.5

- -- -- -- -- -

11 .o 10.915.6 12.019.1 12.222.0 13.924.6 15.0

0.6 - -0.7 - -0.6 - -0.9 - -1.0 - -

27.029.131.133.034.6

1.25 - -1.36 0.10 -1.6 0.12 -1.6 0.13 -2.0 0.15 -

38.940.644.046.749.2

2.2 0.16 - 51.62.4 0.18 - 53.92.7 0.20 - 57.23.0 0.22 - 60.33.5 0.26 - 65.14.1 0.30 - 70.54.5 0.33 - 73.65.0 0.37 - 77.65.4 0.40 - 60.96.0 0.44 - 65.26.6 0.50 - 90.66.2 0.60 - 99.79.0 0.66 - 104.49.5 0.70 - 107.3

10.0 0.74 - 110.15.6 - 3096.0 3.0 3146.5 - 3277.0 3.5 3407.5 - 3526.0 4.0 3636.5 - 3749.0 4.5 3659.5 - 396

10.0 - 40610.2 5.0 41011.2 5.5 43012.2 6.0 44613.2 6.5 46614.3 7.0 466

16.317.719.020.421.624.527.229.932.6-

-------

---------------

0.60 -0.66 -0.90 -1.02 0.51.1 -

115121122130135

1.2 - 1401.3 - 1461.4 - 1521.5 - 1571.6 - 1621.8 - 1722.0 1.0 1822.2 - 1902.4 - 1992.6 - 2072.63.03.23.43.6

-1.5--

215222230237244

3.64.04.24.44.6

2.0-

250257263269275

4.85.05.25.45.6

2.5---

261267293296304

15.316.317.316.319.3

7.56.06.59.09.5

101112131415

502516522549564

20.422.424.426.526.5

560606634661677710

M u l t i p l y ra t e o f f l o w f ro m f a b le b y t h e sq u a re o f t h e d ia m et e r f o r f l o w n ip p le s w i t h I D smm than 1 ,DDO ,n


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33-4 PETROLEUM ENGINEERING HANDB OOK

TABLE 33.2-RATES OF FLOW FOR IMPACT PRESSURES.15 TO 200 PSIG, MEASURED WITH A PITOT TUBE

FOR FLOW NIPPLE WITH ID = 1 .OOO n. Impact

PressureW g)

1516171819

qg, lo3 cu ft/D impact(14.65 psia Pressure qg, 103 cu ft/D(14.65 psiaand 6OOF) W g) and 60F)

710 40 1,307733

z:1,426

757 1,546781 55 1,665805 60 1,785

20 829 65 1,90421 853 70 2,02322 877 75 2,14323 901 80 2,26224 925 90 2,50125 948 100 2,74026 972 110 2,97927 996 120 3,21828 1,020 130 3,45729 1,044 140 3,69730 1,068 150 3,93532 1,116 160 4,17434 1,163 170 4,41236 1,211 180 4,65138 1,259 190 4,890

200 5,129M u l t i p l y ra t e o f t l o w f ro m t a b le b y t h e sq u a re 0 1 t h e

d iameter fo r Row n ipp l es with IDs mere than I .000 in

The backpressure method o f testing w ells requires thata series of flow rates and corresponding pressuremeasurem ents be obtained un der stabilized conditions orat certain fixed time intervals. Testing un der stabilizedpressure and rate-of-flow conditions or according to afixed t ime interval has become known as multipoint orflow-after-flow backpressure testing.As the original ba ckpressu re or multipoint meth odcame into general u se, it became evident that the methodof testing was applicable to those wells that approachedstabilized producing conditions within a relatively shor ttime. However, performance characteristics could not bedetermined by this method for wells that approachedstabilized producing conditions slowly over a con-siderable p eriod. This character istic of slow stabilizationhas been associated generally with wells producing fromreservoirs with low permeability and resulted in thedevelopment of the isochronal method of backpressuretesting by Cullender. 4

The procedure used to obtain the necessary perfor-mance data for the isochronal testing method is to openthe well from a shut-in condition and allow the well toflow without disturbing the rate by changing themechanical adjustment of chokes o r valves for a specificperiod of time. The well is then shut in and allowed toreturn to a shut-in pressu re com parable with that existingbefore the well was first opened, after which the well isagain op ened at a different rate of flow. In isochronaltesting, each rate of flow starts from a comparable shut-in condition, whic h provides a means o f maintaining asimple pressure gradient throughout the drainage area ofthe well during testing. The isochronal meth od of testing

99, lo3 cu ft/DFig. 33.2-Multipoint test showing bottomhole performance for

Well 0.

is especially suitable for determining the perform ancecharacteristics of wells producing from reservoirs withlow permeability.High-Pressure Gas and Gas-Condensate WellsAll the instructions for testing w ells in this chapter app lyto gas wells that produce a single-phase gas into thewellbore or to wells that are predominantly gas wells andthe fluid flowing in the reservoir has a high in-placegas/liquid ratio (GLR). However, these methods fortesting ga s wells have been ap plied to high-ratio oil wellswith some degree of success.The chief difference between testing m ethods fo r high-pressure gas and gas-condensate wells and low-pressurewells is the care used in taking the data and methods usedin compu ting the results. T he effec t of liquids is usuallymor e pronounced in high-pressu re than in low-pr essurewells. Consequently, special care should be used tomeasu re GLR s in high-pre ssure wells. Often it isnecessary to determine the GLR at each rate of flow dur-ing a backpr essure test. If the ratio was not constant dur-ing testing, the well probably was accumulating liquid inthe wellbore during testing or unloading liquid. In eithercase the test is probably not acceptab le and the wellshould be cleaned by flowing at a high rate and retestedat rates of flow high enough to keep the well free ofliquid.Temperature effects during testing of high-pressurewells may be troublesom e in interpreting test results. F orexam ple, Well B (Fig. 33.2) has a shut-in w ellheadpressure of 4,173 psia at a wellhead temperature of117F. M aximum wellhead pressure was observed 3minutes after the well was shut in. If wellhea d pressurehas been observed for an extended period of time, thewellhead pressure would have decreased to about 4,140psia. The decrease in wellhead pressure is caused by thecooling of the gas in the well. In general, better tests canbe obtained on such large-capacity wells if the testing isdone after a preflow period. The preflow period shouldbe run long enough to bring w ellhead tem peratures to anormal operating range of temperature. Wellhead


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OPEN FLOW OF GAS WELLS

temperatures should be recorded during testing atperiodic intervals so that actual measured temperaturescan be used in computing subsurface pressure s bymeth ods outlined under E xamp le 3 in the section oncomputing subsurface pressures.Official TestingOfficial testing of gas wells for state regulatory bodies isusually a multipoint test of short duration. In addition tothe multipoint test, a single rate of flow fo r a period of 24to 72 hours is required in some cases. The tester is re-ferred to the test manuals of the various states, p rovincesof Canada, or appropriate countries for exact procedures,and no attemp t is mad e here to outline official testing.Backpressure EquationsIn either multipoint or isoehronal backp ressure testing,the rates of flow and the corresponding values of the dif-ference of squares of the average formation (reservoir)pressure pR and the sandface pressure [bottomhole flow-ing pressure (BHFP)] p,,f are plotted on logarithmiccoordinates and a straight line is drawn throug h th epoints. Th e equation for the relationship is

qg =C(F ,2 -p,J), . . I . , . . . . . . . . . . . . . . . (5)

where the performance coefficient is represented by Cand the exponent of the backpressure curve by n. The in-dustry by common usage has referred ton as the slopeof the backpressure curve, even though n is thereciprocal of the mathem atical slope of the line. H ere n isreferred to as the exponent of the backpressure curve.Eq. 5 is an empirical relationship for both the multipointtest and the isochronal test and has resulted from thestudy of results of many tests. Values of the exponentvary for individual wells in the range of 0.5 to 1 O. Teststhat result in exponents less than 0.5 or more than 1 Oshould be rerun. Exponen ts of less than 0.5 resultingfrom multipoint tests may be caused by the slow-stabilization character istics of the reservoir or by the ac-cumulation of liquids in the wellbore. Exponen ts greate rthan 1 O may be caused by the removal of liquid from thewell during testing o r by a cleaning of the formationaround the well, such as the removal of drilling mud orstimulation fluids. A lso, a multipoint test run in decreas-ing rate sequence may have an exponent of more than1 O for wells in slow-stabilizing reservoirs. Erratic ex-ponents in isochronal testing are caused by either ac-cumulation or cleaning of liquids from around th e well.Erratic alignment of data points from multipoint orisochronal testing is usually ca used by changes in actualwell capacity during testing. Such changes m ay becaused by accumulation of liquids or the cleaning of thewells. The effe cts o f the liquids in the well on multipointtesting have been given in detail by Rawlins andSchellhardt.Eq. 5 represents the capacity of a well to deliver gasinto the wellbore, and it is useful esp ecially in evaluatingreservoir conditions. The capacity of a well to delivergas at the wellhead may be represented by

qy =c(p,\? -pl,2)i, . . (6)

33-5

where C, the performance coefficient, and n, the expo-nent, a re different from tho se in Eq. 5 for a given w ell.pr s and ptf represent wellhead shut-in (static tubing)pressure and working (flowing tubing) pressu re on theflowing-gas column at the wellhea d, respectively. Eq. 6is useful especially in estimating the capacity of a well todeliver g as into a pipeline under spec ified co nditions.Gas Well Inflow Equation,Pseudosteady StateReservo ir eng ineers have realized fo r many years that in-terpretation of multipoint and isochronal tests by meansof Eq. 5 gave no insight into the effect of reservoir or gasproperties on the rate of flow into a well. Thus, Eq. 5prove d inadequate for reservoir engineering purpo ses.An equation that describes th e pseudo steady-state flowof gas into a well h as been presented in the literature. 5-8It is

qe =703 x 10-6k,h(& -pwf2)

CL 8TRZ(lIl reh, -0.75+s+FnDq,) . . (7 )where

qg =k, =h=

PR =pWf=Pg =TR =

z=re =rw =

s=F nD =

If we let

gas-production rate, lo3 cu ft/D,permeability, effective to gas, md,formation thickness, ft,average reservoir pressure, psia,flowing bottomhole pressure, psia,gas viscosity, cp,reservoir temperature, R,compressibility factor of gas,effective drainage radius, ft,wellbore radius, ft,skin factor, andnon-Damy flow factor.

703 x 10 +kgh(&$ -p,) =PgTZ Cl ,

andIn r,lr,-0.75+s=C2,

Eq. 7 becomesq#= c1

C2 +F,,q, or

F,,Dq; +CzqR -C, =O.From this we get

-C2 +dC,2 +4F,,,C,9g = . .2Fn1, (8 )The maximum rate of flow [open-flow potential (OFP)]is given when Ct is a maximum-that is, whenp,f = 0.Eq. 7 incorporates the properties of the reservoir and thegas and can be extended to noncircular areas as given inRef. 5.


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Determination of Absolute Open Flow (AOF)The terms calculated absolute open flow (CAOF) andOFF are the rate of flow in thousands of cubic feet of gasper 24 hours that would be produced by a well if thepressure a gainst the face of the producing formation inthe wellbore were zero. The value of the OFP is usuallydetermined graphically by plotting rate s of flow qgagainst the correspondin g values of a,$ -p wf2. Th estraight-line relationship between qg and jji -pwf2 isextended so the rate of flow qg corresponding to thevalue ofp,$ can be read by extrapolation. Then qs is theAOFP of the well in cubic feet per 24 hours. The AOFcan be computed from Eq. 5 or read directly from plottedrelationships.In wells producing from reservoirs with lowpermeability, the repor ted AOF must be identified fur-ther by the time involved in the test and the type of test.For example, the OFP of such a well as determined by a3-hour multipoint test (each rate of flow lasting 3 hours)would be less than that determined by a 2-hour multi-point test. The open flow determined by an isochronaltest of 3 hours would be different from that determinedby a multipoint test. A good exam ple of the relationshipbetween AOF and type of test is given by Cullender.4Reported OFPs on wells in low-permeability reservoirsare more or less meaningless without an indication of thetype of test involved.Determination of the Exponen t nThe calculation of the exponent n is based on Eq. 5 andthe relationship

II=1% g2 -1% 481

log@j -p& -log(J,If -p&, . . .Values of qg and correspond ing values of pi -p,,f* ,either actual experimental points or values read from thestraight-line relationship, are substituted in Eq. 9. Usual-ly the data points do not fall exactly on a straight line; s othe best practice is to read values of qg and jji -pwf2directly from the straight line.Determination of the Perfor manc e Coefficient CAfter the value of the exponent n has been determined,the value of the performance coefficient C may be deter-mined by substitution of a correspond ing set of valuesfo r qg and a,$ -pwf2 and the value of n into Eq. 5. Thevalue of C is found by solution of the resulting equation.Graphically the value of C may be determined by exten-sion of the straight-line relationship to jj,$ -t,f2 = 1and reading the corresponding q! . When jr~ -pwf2 isunity, C is equal to qg . In practtce , a determination ofthe value of C is seldom necessary for routine analysis ofbackpressure tests.Prepa ration of Well for TestingThe wellbo re should be cleaned of liquids by flowing at ahigh rate to a pipeline for a period of 24 hours. If the welldoes not have a pipeline connection, it may be blown tothe air for a short period of time, provided blowing isconsidered safe. Extra precautions should be taken onnew wells to remov e drilling mud, solids, and stimula-tion fluids from the wellbore. The well should be shut in

for 24 hours or longer to equalize the reservoir pressurein the vicinity of the well. W ells with slo w pressure-buildup characteristics should be shut in 48 to 72 hours,if possible.While the well is shut in, the gas-mea surement equip-ment should be prepared for use. If the gas is to bemeasured with an orifice m eter, the meter should becalibrated, the diamete rs and condition of the run andplate verified, and the differential pen should be zeroedin accorda nce with good m eter practice. If a critical-flowprover (se e later section on gas measurem ent) is used, itshould be placed in a vertical position at the wellhead ordownstream from the separator so that the gas will flowup and away from the test area. If a separator is used,control the rate of flow with a production choke andmaintain pressure on the separator w ith a critical-flowprover or backptessure regulator w hen an orifice meter isused. If a separator is not used, control rate of flow andpressure at the wellhead with the critical-flow prover.Always install thermom eter wells at the wellhead and atgas-measuring equipment so that temperatures may bemeasured with a thermometer or calibrated recordingdevice. The thermom eter wells should be filled withwater or oil to obtain accurate temperature measurement.Shut-In PressureAll shut-in or flowing pressure s sho uld be measu red witha dead-weight or piston gauge, because spring gaugesare usually not accurate enough for backpressure tests.Determine and record the pressure at the end of the shut-in period, prepa re the well for testing, and redeterminethe shut-in pressure as a check on the first measurementand to obtain the rate of pressure buildup. Report eachpressure and time the well was shut in prior to eachpressure measurement. After the second pressuremeasurem ent, either the isochronal o r multipoint testmay be started.Subsurface pressures in gas wells may be measureddirectly with pressure gau ges or computed fromwellhead pressures. Subsurface-pressure gauges are veryuseful in wells wher e liquids accum ulate in the wellboreduring shut-in. However, the use of subsurface gaugeslimits the rates of flow during the backpr essure test tovelocities that will not lift the gauge in the flow string.The use of subsurface gauges is limited to rather lowrates of flow in 2%-in. OD tubing, but there is practical-ly no limitation on their use in 7-in. casing. The use ofsubsurface gauge s in the annular spaces of dual comple-tions is practically impossible. In cases where large-capacity wells are being tested, correction must be madefor the effect of hysteresis on gauge readings, or the BHPmust be measured at each rate of flow by a separate runof the gauge.The accumulation of liquid in the wellbore is probablythe most serious cause of erroneous calculated BHP s.Other sources of error are uncertainties in temperaturegradients and specific gravities of the fluids flowing inthe well. Before a backpressure test is begun, specialcare should be taken to remove the liquids from thewellbore by flowing at rates large enough to lift the liq-uid. If possible, each rate of flow used in thebackp ressurc test should be large enough to lift con-tinuously any liquid that may move into the wellboreduring production. Temp erature gradients can be


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OPEN FLOW OF GAS WELLS 33-7

established for a new area only by actual measurem ent.Usually a flowing-tem perature gradient can be estimatedby assuming a straight-line gradient betw een flowingwellhead temperature and bottomhole temperature.Uncertainty in the specific gravity of the fluid flowing inthe well can be eliminated to a large degr ee by carefulmeasurem ent of gas/hydroc arbon liquid ratio and deter-mination of the specific gravity of the separato r gas,separator liquid. and stock-tank liquid.Multipoint Test and ExampleA four-point multipoint test of constant duration for eachrate taken in increasing rate sequence is normallysatisfactory for establishing the perform ance of a well. Inthe case of high-liquid-ratio wells or high-flowing-temper ature conditions, a decreasing-rate-sequen ce testmay be used if an increasing-rate-sequence test wouldnot result in alignment of points. In the case of high-liquid-ratio wells, the low flow rates will not clean thewellbore of liquids that accumulate during production. Inthe case of wells with exceptionally high flowingtemper ature, it may be desirable to start the test at thehighest rate of flow that will result in more nearly con-stant wellhead tem peratures during the test rather thanstarting at the lowest rate of flow. How ever, a test indecreasing-rate sequence should not be run unless it isknown th at an increasing-rate-sequence test will not givea satisfactory test.The four rates of flow for the test should be evenlydistributed over the test range. For average- to low-capacity gas wells, the first rate of flow should lower thepressure at the wellhead about 5%) and the pressurereduction for the fourth rate should be 25 %. The rate offlow required to reduce the working pressure to 5% forthe first test rate can be approximated from pressurereadings obtained while the well is being cleaned beforethe well is shut in. These recomm ended pressure reduc-tions may not be possible for large-capacity wells withlarge flow strings.After the well is opened for the first rate of flow, thetest rate should be continued for 3 hours but no morethan 4 hours. Each succeeding flow rate should be for thesame period of time. During each flow rate, the wellheadworking pressure and temperature, meter or proverpressure and differential, and tempe rature should bereported at the end of each I5-minute period, If separatorand tanks are used during testing, the rate of liquid ac-cumulation, both hydrocarb on and water, should bereporte d. If a critical-flow prover alone is used, thepresence or absence of liquids in the gas stream shouldbe noted and reported . The specific gravity o f theseparato r gas or the specific gravity of the gas flowingfrom the critical-flow prover should be measured andreported, or a gas sample should be taken for analysisand calculation of the specific gravity. Mo re represen-tative gas specific gravities can be obtained after the wellhas been flowing at least an hour.Table 33.3 is an actual copy of the field data sheet fora multipoint backpre ssure test for Well A in the GuymonHugoton gas field in Texas County, OK.* The form onwhich the data are reported has proved convenient forrecording test data. The times at which each plate was Th u s t e s t, u se d m t h e 1 9 6 2 e d l f i o n o f t h e h a n d b o o k wa s ru n m a n y ye a rs a g o I t s t i l l

s t a n d s a s a c la wc m u l t l p o in t t e s t e xa m p le t o d a y

changed and when the well opened on each rate of flowwere carefully reported. The remarks column givesthe results of the specific-gravity measurem ent and thecondition of the flow with regard to whether the well wasproducing water. All the observations record ed in Table33.3 are necessary for accurate analysis of test results.Computation of the results of a backpressure test on agas well involves the following steps.I. Compute rates of flow and pressures at the face ofthe producing formation from pressure and volumeobservations made at the wellhead.

2. Determine values of p,: -prf2 and p,$ -p,+f* andrates of flow corresponding to these pressure factors.Then, PR and pwf are calculated at the midpoint of thesandface in wells without tubing. If the well has tubing,they are determined at the entrance to the tubing, provid-ed the entry to the tubing is no more than 100 ft from themidpoint of the sandface.3. Plot values of q8 and corresponding values ofPR -pwf2 and pt: -pti2 on logarithmic coordinates.4. Determ ine values of the exponent n and the perfor-mance coefficient C of the flow equations

qg =C(Pl? -Pwf2Yand

4x =c(P,.? -Pff2Y*.For most routine analyses of backpre ssure tests. deter-mination of the value of C is not necessary.5. Determine the CAOF. Computations for rate offlow and pressures at the producing formation are ex-plained in separate sections.

A convenient form for reporting the results of a multi-point test is illustrated in Table 33.4 for the test datataken on Well A and reported in Table 33.3. Table 3 3.4show s general w ell information, a summ ary of test data,calculation of rates of flow, d ata for determining com-pressibility, and the difference of squares o f pressuresfor wellhead and bottomh ole conditions. The calculatedOFP of 25,000~10~ cu ft/D was determined in Fig.33.3 where the rate of flow is the abscissa and PJ -p w,2(in thousands) is the ordinate on logarithmic coordinates.The data points wer e connected by a straight line and ex-trapolated to a value of PJ -p,,,f2, where p&f2 is zero.In this case, the value is j~i = 230.9 (thousands). Thecorresponding rate of flow is 25,000 x lo3 cu ft/D. TheAOF of 25,000~ lo3 cu ft/D for Well A is for a 3-hourfour-point test. If the test were for a lesser-time four-point test, the resulting AOF would h ave been more than25,000 x lo3 cu ft/D.The exponent n was determined by taking values of qsandpd -pwf2 from the straight line in Fig. 33.3 and Eq.7 as follows.

qs , lo3 cu ft/D p, $ -p wf2 (thousands)20,000 168

4,ooo 16.8log 20,000-log 4,000 log 5.00 0.699

n= =-=-log 168-log 16.8 log 10.0 I .ooo=0.699.


8/23

33-a PETROLEUM ENGINEERING HANDBOOK

TABLE 33.3-FIELD DATA SHEET FOR MULTIPOINT TEST (WELL A)

Co m p a n y L e a se Well No. -L o ca t i o n re m a ca rn t y . o k u h a2 P ro ve r n M e t e r Ru n P Ta p s

DhTE WELLHEAD WORKING PRESSURE METER OR PROVER REMARKS6 - I W ? Tb g . Cs iq . A n ; & u s Te y .Tim IHrr, Psi0 W p * iq D i f . , O r i f i ceI u* l l hu t lo fo a dam I I II /

L I I I I IPAGEL OF JDATA BY J. i t . J .

The performance coefficient C was determined from theexponent n=0.699, Eq. 5, and one of the corresponding 33.4 where qg and corresponding pt: -ptf* values atevalues of qg and j12 -pd* as follows. plotted on logarithmic coordina tes. The straight line hasbeen extended to show a wellhead OFP of 22,000 X lo320,000 = C(168)0.699 cu ft/D. The exponent is 0.672 and C is 621. Thebackpressure relationship corresponding to Eq. 6 is

C = 20,000/(168)~699log C = log 20,000-0.699 log 168log c = 4.3010-1.5555

c = 557.The value of 557 may be checked bstraight line on Fig. 33.3 top2 -p,,,, z- extrapolating the- 1 and readingthe corresponding value of qs . Note that the value ofC=557 is for qg in units of lo3 cu ft/D and forjr2 -pg* in units of thousands.The backpressure equation for the results of the multi-point test on Well A given in Table 33.4 and illustratedin Fig. 33.3 is

The wellhead Performance of Well A as determined bythe test results given in Table 33.4 is illustrated in Fig.

qR =627(pr,2 -P~~)O.~*.This wellhead perfo rmanc e equation for Well A, il-

lustrated in Fig. 33.4, is a measure of the ability of WellA to deliver gas at the wellhead through 5 %-in. casing asindicated by the multipoint test given in Table 33 .4. Therelationship is influenced by the size of the flow stringand hydrostatic head of the gas column as well as theproductive capacity of the well.An example of the bottomhole performance as in-dicated by a multipoint test is given in Fig. 33.2 fo r anextremely large-capacity well. Well B (Fig. 33.4) had ashut-in pressure~R of 5,169 psia at a depth of 10,658 ftand a wellhead pressure of 4,173 psia. The calculatedOFP was 280,000x10 3 cu ft/D. The correspondingwellhead p erformance for Well B producing through2X-in.-OD , 6.5-lbm/ft tubing is illustrated in Fig. 33.5where the data points for the test are plotted as circles.


9/23


TABLE 33.4--RESULTS OF MULTIPOINT BACKPRESSURE TEST (WELL A)

COMPANY LEASE - WELL N0. IADDRESS DATE 6-17 19kDISTRICT FIELD ~goton RESERVOIR UwotaLOCATION Tens CmmtJ, OkldwmCASING SIZE5 WT.x I D 5 .012 SET Al 269 PERF 2665-2620TUBING SIZE- WT.--- ~ -.0 SET AT PERF.PRODUCING BOTTOMHOLESECTION FROM 2Lb5 TO 2620 I i 2542 TEMPERATURE 90 Ca 25fQ

DATE OF PRODUCINGELEVATION - COMPLETION A THROUGH TBG.: CASING IF, o.wl6105 BAROMETER 13.2 p* I ACRES -REMARKS:

P, . uB.5 DrioP, 201 15x10 j- Pa Le3.5 Pb230.92xlO

Potmtb l 25 .m IO C fm Co m m I t d o nn 0 .699 co m p a n yO t h e rs

qg, lo3 cu ft/D

Fig. 33.3-Multipoint test showing bottomhole performance forWell A.

3001------

I01 1 II,,,, I 11000 10,000 30,cQo

qg, IO3 cu ft/D

Fig. 33.4-Multipoint test showing wellhead performance forWell A.


10/23

3-

3-

3-

:0I0 10,000 IO C

q9, lo3 cu ft/DFig. 33.5-Multipoint test showing wellhead performance forWell 0.

Data points represented as squares (Fig. 33.5) are flowtests of several days duration with Point 1 taken shortlyafter production started and Point 3 taken over a yearlater. Th e position of the data points in Fig. 33.5 in-dicated that the performance of Well B improved afterthe well was placed on production, which w as probablycaused by the removal of drilling fluids from the areaaround the wellbore.

The wellhead OFP of Well B was 41,000~ IO3 cuND, which was the approximate capacity of the tubing.A different wellhead performance curve would result ifthe tubing were changed in Well B. The wellhead perfor-mance for a different string of tubing can be calculatedby starting with the bottomhole performance curve inFig. 33.2 and calculating the pressure dro p caused byfriction for the different string of tubing.Isochronal Test and ExampleThe isochronal meth od of backpressure testing as de-fined by Cullender4 considers the perform ance coeff-cient C in Eqs. 5 and 6 to be a variable with re spect totime until the well stabilizes but a constant with respe ctto a specific time. Thus the backpressure performance ofa well producing from a reservoir with low permeabilityis a series of parallel curves. Each curve represents theperform ance of the well at the end of a given time inter-val. Isochronal perform ance curves for wells producingfrom reservoirs with relatively highe r permeability arcclosely spaced. For example, the isochronal curves forvarious times for Well B (Fig. 33.5) are for all practicalpurpo ses one curve, and Well B is said to stabilizerapidly.The isochronal method of testing permits the deter-mination of the true exponent n of the performance curvefor a given g as well. This is accom plished by the

PETROLEUM ENGINEERING HANDB OOK

establishment of a simple pressu re grad ient arou nd a pro-ducing w ell during the test period, which preven ts thevariation of the perform ance coefficient with time fromobscuring the true value of the exponent. The determina-tion of the relationship between perform ance coefficientand time permits the estimation of the rate of flow of agiven w ell into a pipeline over long perio ds of time.The term isochronal was adopted as being descrip-tive of the meth od, because only those conditions ex-isting as a result of a single disturbance of constant dura-tion are considered as being related to each other by Eqs.5 and 6. The expression single disturbance of constantduration is defined a s those conditions existing arounda well as a result of a constant flow rate for a specificperiod of time from shut-in conditions. Under actual testconditions this requiremen t is rarely satisfied. How ever,this condition may be approx imated by starting a well onproduction and allowing the well to produce without fur-ther outside or mechan ical adjustments in rate of flow.Thus a simple pressu re grad ient is established around th ewellbore as opposed to a complex pressure gradientresulting from a multipoint backpr essure test.The presentation of isochronal test data as a series ofparallel cu rves with a constant exponent n and a constantperform ance coefficient C for a specific time interval in-volves certain assumptions. The exponent of the perfor-mance curves for a gas well is assumed independent ofthe drainage area. It is established immed iately after thewell is opened . The variations of the perform ance coeff-cient with re spect to time are believed to be independentof the rate of flow and the pressure level under simplegradient conditions.

The procedure employed to obtain the necessary per-formance data for an isochronal test is to open a wellfrom shut-in conditions and obtain rate-of-flow andpressure data at specific time intervals during the flowperiod w ithout disturbing the rate of flow. A fter suffi-cient data have been obtained, the well is shut in andallowed to return to a shut-in condition comp arable withthat existing at the time the well wa s first opened. Thewell is again opened at a different rate of flow with databeing obtained at the same time intervals as before. Theprocedure may be repeated as many times as necessary toobtain th e desired number of data points.With the exception of starting each rate of flow fromshut-in conditions, the proced ure for running isochmn altests is the same as that for the multipoint test. Thenecessity for cleaning the well, calibrating the gas-measuring e quipment, and accurately measuringpressures and temperatures remains the same. At leastfour rates of flow should be taken; the lowest rate shouldreduce the pressure at the wellhead about 5% and thehighest rate of flow should reduce the pressure about25%.The results o f an isochronal test are com puted in thesame manner as those for a multipoint test. The datapoints are plotted on logarithmic coordinates as il-lustrated in Figs. 33.6 and 33.7. The isochronal curvesare drawn so that the points taken at a constant time forthe various rates of flow are joined by a straight line. Forexam ple, all the points on the line labeled Time, 3 hrin Fig. 3 3.6 represent the performance of Well A afterflowing at the various rates of flow for 3 hours fromshut-in conditions.


11/23


IO I III1000 l0,000 60,000

qg. IO3 cu WD

3oor--,0

; loo-.PziN^ctIN:

IO_ * I II1000 10,000 50,000

qg. lo3 cu ft/DFig. 33.6~lsochronal test showing bottomhole performance for Fig. 33.7~lsochronal test showing wellhead performance for

Well A. Well A.

The results of isochronal tests can be analyzed in twoways. One way is to use E qs. 7 and 8 and the propertiesof the gas to determine the properties of the reservoir andthe skin factor. The second way is to use the results as abasis for comparison of well performance at the time ofthe test with performance as measured previously or toset a base against which future performance is to becompared.The isochronal type curves shown on Fig. 33.6 can beused to estimate the pressures that would have beenobserved if the test had been a constant-rate drawdowntest. Test periods longer than the 3-hour periods on Fig.33.6 are much more desirable for this purpose. With thisinformation the k,h value for the reservoir and the totalskin value (s,=s+F,~q ~) are calculated as given inChap. 35. This results in several values for the total skin,s,, as a function of the rate of flow, qg , from which sand F,D can be obtained for use in Eq. 7 .6 The multi-point test can be analyzed to obtain k,h , s, and F,JJ asindicated by Ref. 7. A discussion of the performance-comparison method follows.A copy of actual field data for an isochronal test isgiven in Table 33.5 for Well A, which is the same wellused in the exam ple of a multipoint test.* Four rates offlow of 3 hours duration were used w ith each flow start-ing from shut-in conditions. Shut-in pressures reportedvaried from 359.6 psig after 48 hours for the first rate offlow to 357.6 psig, which was just previous to the fourthrate of flow. The results of the isochronal test are sum-marized in Table 33.6. Bo ttomhole and wellhead perfor-mance curves are illustrated on Figs. 33.6 and 33.7,respectively.

The isochronal test on Well A (Fig. 33.6) sho ws thatthe calculated OFP for a BHP of 399.1 psia was 5 1,500,41,500, 35,ooO, and 31,500~ lo3 cu ft/D at the end of0.5, 1 O, 2.0, and 3.0 hours, respectively. Thecalculated potential after 3 hours flow was only 61% ofthe potential after 0.5 hour of flow, A similar figure forthe wellhead performance of Well A is 66% (Fig. 33 -7)If Well A were opened into a pipeline with a constant

Th i s t e s t , u se d I t h e 1 9 62 e d l t l a n , wa s ru n m a n y ye a rs a g o . I t s t i l l s t a n d s a s ac la ss t c t so ch ro n a l t e s t e xa m p le t o d a y .

pressure, the rate of flow at the end of 3 hours w ould be66% of the rate of flow at 0.5 hour. Experimental datanot given here show that the production at the end of 72hours has decreased to about 48 % of that at 0.5 hour.The figures showing change-of-performance character-istics with time illustrate the need for isochronal test datafor estimating the delivery from a particular well into apipeline. Accur ate estimation of pipeline deliveries fromwells producing from reservoirs w ith low permeability ispractically impossible without isochronal test data.

Examination of the field notes under the Remarkscolumn in Table 33.5 indicates that Well A started toproduce water during the flow test taken on Dec. 20,195 1, which was the largest rate of flow. The effect ofwate r production on well perform ance is illustrated bythe irregularities in the correspond ing data in Figs. 33 .6and 33.7. Water production and accumulation of wateror liquids in the wellbore cause the performancecharacter istics of a well to deteriora te.Th e data represen ted as squares in Fig. 33.5 areisochronal points taken after Well B has been flowingfrom 5 to 30 days. Their close agreement with the datafrom the multipoint test indicates that the perform ance ofWell B does not vary appreciably with time. Well B pro-duces from a reservoir w ith high permeability and theradius of drainage is established quickly after the well isopened to flow.Comparison of Multipoint WithIsochronal TestEither the multipoint or the isochronal test is suitable forwells producing from reservoirs with high permeability.The isochronal meth od of testing is especially suitablefor testing wells in low-perme ability reservoirs.Howev er, for wells producing from extremely low-permeability reservoirs wher e the unsteady-state effectslast for days or even weeks, economic considerationsmay limit the testing to only one point of the isochronaltype (starting flow from a shut-in condition). Multipointtests should be limited to reservoirs whe re the unsteady-state effects are of very short duration. Otherwise theresults of the multipoint test are difficult to analyze.


12/23


13/23

OPEN F LOW O F GAS WELLS

qg. IO3 cu ft/D

Fig. 33.6-Comparison of multipoint with isochronal test forWell A.

seen that the coefficient obtained in each case can beconsidered the result of an effective time, wh ich hasno permanent significance because it is not equal to theelapsed time or to the elapsed time since the last changein flow rate.An examination of the multipoint and isochronal datapresented in Fig. 33.5 for Well B shows that there arecertain gas wells that stabilize so rapidly that there is nonecessity for obtaining isoch ronal perform ance data. Asthe time required for stabilization increases, the dif-ferences between data obtained by the isochronal test andthe multipoint test increase.Gas MeasurementOrifice MetersThe recommended specifications for orifice meters andmethods for computing rates of flow are those publishedby the American Gas Assn. 9 It should be noted that thebasic orifice factors are for a pressure base of 14.73 psia.Multiplying the basic orifice factors in Ref. 9 by 1.0055changes volumes to a pressure base of 14.65 psia. Basicorifice factors,for a pressure base of 14.65 psia havebeen published in the test manual of the CorporationCommission of the State of Kansas lo and the InterstateOil Compact Com mission. Critical-Flow ProversThe following method for measurement and computationof rates of flow for critical-flow prove rs is a modificationof the method published by Rawlins and Schellhardt.*The equation computing rates of flow frommeasurements with a critical-flow prover is

qg=p sFpFg FTFpv , . . . . . . . . . . . . . . . . . .(lO)where p, , is static pressure on critical-flow prover , psia.Basic orifice factors, F,, , for 2- and 4-in. critical-flowprove rs are given in Table 3 3.7. These fa ctors apply on-ly to plates designed according to USBM specifications.

The adjustment factor (Table 33.8) to correct for anassumed specific gravity of 1.000 to the actual specificgravity of the gas flowing through the prover may becomputed by

33-13

TABLE 33.7-BASIC ORIFICE FACTORS FORCRITICAL-FLOW PROVER (USBM plate design) F, - McflD

Base temperature, OF 60Base pressure, psia 14.65Flowing temperature, OF 60Specific gravity 1.000

2-in. Prover 4-k ProverOrifice Diameter Factor Orifice Diameter Factor

(in.) (F,) (in.) (FP)0.065690.14460.27160.62370.86081.1151.7142.4393.4954.3886.6389.694

13.3317.5322.4528.3434.8243.19

2% 136.93 168.3

1.0742.4144.3196.7299.643

13.1117.0821.5226.5731.9938.1252.0768.8088.19

110.6

F,= i, . . . . . . . . . . . . . . . . . . . . . . . . . . ...(n)7s

whe re yg is specific gra vity of the flowing gas, air =l.COO.Factors to correct for an assumed flowing tem peratureof 60F to the actual flowing temperature of the gas atthe point of measurem ent are given in Table 33 .9 andmay be computed by

52 0FT= -, __. _. . . . . . . . . . . . . . . . . (12)Tf

where Tf is actual flowing temperature of the gas,(F +460).The supercompressibility factor to correct for the ef-fect of gas compressibility is computed from the com-pressibility by

F,,\,= r i, . . . . . . . . . . . . . . . . . . . . . . (13)zwhere z is compressibility of the gas at ps and Tf or thepressure and temperature at point of measurement.Meth ods fo r estimating gas compressibilities are givenin Chap. 20.Calculation of Subsurface PressuresSpecific G ravity of Flowing FluidCalculation of either shut-in o r flowing pressures in gaswells requires a knowledge of the specific gravity of thefluid in the wellbore. In the case of a gas-conden satewell, the specific gravity of the separator gas and thegravity o f the stock-tank liquid are measured, and it is


14/23

33-14 PETROLEUM ENGINEERINGHANDBOOK

TABLE 33.8--SPECIFIC-GRAVITY ADJUSTMENT FACTOR

SpecificGravity0.5500.5600.5700.5800.590

0.0001.3481.3361.3251.3131.302

0.001 0.0021.3471.3461.335 1.3341.323 1.3221.312 1.3111.301 1.300

0.0031.3451.3331.321

0.0061.3411.3291.318

1.3101.299

0.004 0.0051.344 1.3421.332 1.3301.320 1.3191.309 1.3071.298 1.296

1.3061.295

0.0071.3401.3281.3161.3051.294

0.600 1.291 1.290 1.289 1.288 1.287 1.286 1.285 1.2840.610 1.280 1.279 1.278 1.277 1.276 1.275 1.274 1.2730.620 1.270 1.269 1.268 1.267 1.266 1.265 1.264 1.2630.630 1.260 1.259 1.258 1.257 1.256 1.255 1.254 1.2530.640 1.250 1.249 1.248 1.247 1.246 1.245 1.244 1.2430.650 1.240 1.239 1.238 1.2370.660 1.231 1.230 1.229 1.2280.670 1.222 1.221 1.220 1.2190.660 1.213 1.212 1.211 1.2100.690 1.204 1.203 1.202 1.201

1.237 1.2361.227 1.2261.218 1.2171.209 1.208

1.2351.2251.2161.2071.199

1.2341.2241.2151.206

1.200 1.200 1.1980.700 1.195 1.194 1.194 1.193 1.192 1.191 1.1900.710 1.187 1.186 1.185 1.184 1.183 1.183 1.1820.720 1.179 1.178 1.177 1.176 1.175 1.174 1.1740.730 1.170 1.170 1.169 1.168 1.167 1.166 1.1660.740 1.162 1.162 1.161 1.160 1.159 1.159 1.158

0.0061.339

0.0091.3381.3261.314

1.3271.3151.3041.2931.2821.2721.2621.2521.242

1.3031.2921.2811.2711.2611.2511.241

1.233 1.2321.224 1.2231.214 1.2141.206 1.2051.197 1.1961.188 1.1881.180 1.1791.172 1.1711.164 1.1631.156 1.155

1.1891.1811.1731.1651.157

0.750 1.1550.760 1.1470.770 1.140

1.154 1.1531.146 1.1461.139 1.1381.132 1.1311.124 1.124

1.1521.1451.1371.1301.123

1.1521.1441.137

1.1511.1431.1361.1291.122

1.150 1.1491.143 1.1421.135 1.134

1.149 1.1481.141 1.1401.134 1.1331.127 1.1261.119 1.119

0.780 1.1320.790 1.125

1.1291.122

1.128 1.1271.121 1.120

0.800 ,118 1.117 1.117 1.1160.810 ,111 1.110 1.110 1.1090.820 ,104 1.104 1.103 1.1020.830 .098 1.097 1.096 1.0960.840 ,091 1.090 1.090 1.089

,115 1.115 1.114 1.113 1.112 1.112,108 1.108 1.107 1.106 1.106 1.105,102 1.101 1.100 1.100 1.099 1.098,095 1.094 1.094 1.093 1.092 1.092,089 0.088 1.087 1.087 1.086 1.085

0.8500.8600.8700.8800.890

,085 1.084,078 1.078,072 1.072

1.0831.077I.0711.0651.059

,082 1.081 1.081 1.080 1.080 1.079

1.066 1.0651.060 1.059

1.0831.0761.0701.064 1.0641.058 1.058

,076 1.075 1.075 1.074 1.073 1.073,070 1.069 1.068 1.068 1.067 1.067

1.063 1.062 1.062 1.061 1.0611.057 1.056 1.056 1.055 1.055

0.900 1.054 1.054 1.053 1.052 1.052 1.051 1.051 1.050 1.049 1.0490.910 1.048 1.048 1.047 1.047 1.046 1.045 1.045 1.044 1.044 1.0430.920 1.043 1.042 1.041 1.041 1.040 1.040 1.039 1.039 1.038 1.0380.930 1.037 1.036 1.036 1.035 1.035 1.034 1.034 1.033 1.033 1.0320.940 1.031 1.031 1.030 1.030 1.029 1.029 1.028 1.028 1.027 1.0270.950 1.026 1.025 1.025 1.024 1.024 1.023 1.023 1.022 1.022 1.0210.960 1.021 1.020 1.020 1.019 1.019 1.018 1.017 1.017 1.016 1.0160.970 1.015 1.015 1.014 1.014 1.013 1.013 1.012 1.012 1.011 1.0110.980 1.010 1.010 1.009 1.009 1.008 1.008 1.007 1.007 1.006 1.0060.990 1.005 1.005 1.004 1004 1.003 1.003 1.002 1.002 1.001 1.001

yL = specific gravity of hydrocarb on liquidreferred to water, andVL = vapor volum e equivalent of 1 bbl (60F) ofhydrocarb on liquid, cu ftibbl.

The specific gravity and the approximate vapor volumeof the hydrocarbon liquid can be calculated from the APIgravity by

usually necessary to comp ute the specific gravity o f thefluid flowing in the wellbore. The shrinkage of the liquidbetween the separato r an d the stock tank is usuallyunknown and apparently can be neglected. The equationfor computing the specific gravity of the flowing fluid,ysJ, is:

R &Yg +4m3 YL-rff= ) . . . . .,L~Lwhere

R h L = gas to hydrocarb on liquid ratio, cu ft/bbl, and(14b)


15/23

OPEN FLOWOF GAS WELLS

TABLE 33.9-FLOWING-TEMPERATURE ADJUSTMENT FACTOR

33-15

5 6 7 8 9Observed

TemperaturelOFl 0 1 2 3 4

1.063 1.062 1.061 1.060 1.059 1.057 1.056 1.055 1.054 1.0531.052 1.051 1.050 1.049 1.047 1.046 1.045 1.044 1.043 1.0421.039 1.038 1.037 1.035 1.034 1.033 1.032 1.0311.028 1.027 1.026 1.025 1.024 1.023 1.022 1.0211.018 1.017 1.016 1.015 1.014 1.013 1.012 1.011

50607080so

0.9905 0.98960.9813 0.98040.9723 0.9715

1.008 1.007 1.006 1.005 1.004 1.003 1.002 1.0010.9981 0.9971 0.9962 0.9952 0.9943 0.9933 0.9924 0.99150.9887 0.9877 0.9868 0.9859 0.9850 0.9840 0.9831 0.98220.9795 0.9786 0.9777 0.9768 0.9759 0.9750 0.9741 0.97320.9706 0.9697 0.9888 0.9680 0.9671 0.9662 0.9653 0.9645

100110120130140

0.9636 0.9628 0.9619 0.9610 0.9602 0.9594 0.9585 0.9577 0.9568 0.95600.9551 0.9543 0.9535 0.9526 0.9518 0.9510 0.9501 0.9493 0.9485 0.94770.9469 0.9460 0.9452 0.9444 0.9436 0.9428 0.9420 0.9412 0.9404 0.93960.9388 0.9380 0.9372 0.9364 0.9356 0.9349 0.9341 0.9333 0.9325 0.93170.9309 0.9302 0.9294 0.9286 0.9279 0.9271 0.9263 0.9256 0.9248 0.9240

150 0.9233 0.9225 0.9217 0.9210 0.9202 0.9195 0.9187 0.9180 0.9173 0.9165160 0.9158 0.9150 0.9143 0.9135 0.9128 0.9121 0.9112 0.9106 0.9099 0.9092170 0.9085 0.9077 0.9069 0.9063 0.9055 0.9048 0.9042 0.9035 0.9028 0.9020180 0.9014 0.9007 0.9000 0.8992 0.8985 0.8979 0.8972 0.8965 0.8958 0.8951190 0.8944 0.8937 0.8931 0.8923 0.8916 0.8910 0.8903 0.8896 0.8889 0.8882200210220230240

0.8876 0.8870 0.8863 0.8856 0.8849 0.8843 0.8836 0.8830 0.8823 0.88160.8810 0.8803 0.8797 0.8790 0.8784 0.8777 0.8770 0.8764 0.8758 0.87510.8745 0.8738 0.8732 0.8725 0.8719 0.8713 0.8706 0.8700 0.8694 0.86870.8681 0.8675 0.8668 0.8662 0.8656 0.8650 0.8644 0.8637 0.8631 0.86250.8619 0.8613 0.8606 0.8600 0.8594 0.8588 0.8582 0.8576 0.8570 0.8564

VL=369+5yAP , +O.O4(y Apr)2, . . . .(14c) whereL = length of flowstring in well corresponding to

H, fitH = vertical depth in well, ft, and

98 = rate of gas flow at 14.65 psia and 60F,lo6 scf/D.

whe re yAPr is stock-tank oil gravity, API. The de riva-tions of Eqs. 14a and 1 4c were given by Smith. I2Equations for Computing Subsurface PressuresPressures at the sandface or at the inlet to the tubing inshut-in or flowing gas wells may be measured with BHPgauges or computed from wellhead pressures. However,most subsurface pressures in gas wells are calculated byequations. The most usable and realistic equationsavailable are those of Cullender and Sm ith, I3 whichhave been adopted by the Kansas Corp. Commission, theInterstate Oil Compact Commission, and the New Mex-ico Conservation Comm ission, and by the RailroadCommission of Texas fo r cettain fields. The equationswere revised* recently for use with programmablecalculators and small computers.

The revised flow equation for gas wells is

F*= 2-6665-fq,2di =(F q )* . . . . .r 1 Wa)and

J 4 log 7.4ri-72 , . . . . . . . . . .K (16b)where

f = coefficient of friction (friction fac tor),ri = internal radius o f pipe, in.,K = absolute roughness characteristic = 0.0006

in., andr/K = relative roughness.

Refer to Ref. 12 for the background of Eqs. 15, 16a, and16b. The second term in the numerator on the right sideof Eq. 15 is the kinetic energy term that heretofore hasbeen set at zero because the computations were mademanually. Although the kinetic energy term can beneglected without appre ciable error in the majority ofcases, there is no need to do so when programmable

u yggdp1,ooo Y,L _sPI p Tz-2.082- d,% >

53.356 -pz H (~/Tz)~ IF*+-- L 1,000

. . . . . . . . . . . . . . . . . . . . . . (15)


16/23


TABLE 33.10- F, VALUES FOR VARIOUS FLOW STRING (K = 0.0006 in.)Nominal

Size d, d, Minimum(in.] (in.) (Ibmlft) (in.) N Rs f=,Tubing

1.315 1.80 1.049 139,000 0.095051%1%22/233%44%

4%

NominalSize

(2 ) d,(in.) (Ibmlft) (in.)~- - ~Minimum

N Fe Fr

696,000 0.002146681,000 0.002257784,000 0.001617778,000 0.001647773.000 0.001670

Casing5.000 13.00 4 .4 9 45.000 15.00 4.408

5% 5.500 14.00 5.0125.500 15.00 4.9765.500 15.50 4.9505.500 17.00 4.892 764;OOO 0.0017225.500 20.00 4.778 744,000 0.0018305.500 23.00 4.670 726,000 0.0019425.500 25.00 4.580 710,000 0.002043

5% 6.000 15.00 5.524 872,000 0.0012566.000 17.00 5.450 860.000 0.0013016.000 20.00 5.352 843;OO0 0 0013636.000 23.00 5.240 823,000 0.0014406.000 26.00 5.140 806,000 0.001514

6% 6.625 20.00 6.049 964,000 0.00099226.625 22.00 5.989 953,000 0.0010186.625 24.00 5.921 941,000 0.0010496.625 26.00 5.855 930,000 0.0010806.625 28.00 5.791 919,000 0.0011116.625 31.80 5.675 899,000 0.0011716.625 34.00 5.595 885,000 0.001215

6% 7.000 20.00 6.456 1.035.000 0.00083807.000 22.00 6.398 1;025;000 0.00085797.000 23.00 6.366 1,019,OOO 0.00086917.000 24.00 6.336 1,014,OOO 0.00087987.000 26.00 6.276 1.003.000 0.00090187.000 28.00 6.214 .992;000 0.00092537.000 30.00 6.154 982,000 0.00094897.000 40.00 5.836 926,000 0.001089

7h 7.626 26.40 6.969 1,125,OOO 0.00068727.625 29.70 6.875 1,108,OOO 0.00071197.625 33.70 6.765 1,089,OOO 0.00074237.625 38.70 6.625 1,064,OOO 0.0007837

1.660 2.40 1.380 189,000 0.046431.990 2.75 1.610 224,000 0.031052.375 4.70 1.995 284,000 0.017762.875 6.50 2.441 355,000 0.010503.500 9.30 2.992 445,000 0.0061804.000 11.00 3.476 525,000 0.0041844.500 12.70 3.958 605,000 0.0029854.750 16.25 4.082 626,000 0.0027554.750 18.00 4.000 612,000 0.0029055.000 18.00 4.276 659,000 0.0024425.000 21 .oo 4.154 638,000 0.002633

calculators or computers are used. E q. 15 is based on theassumptions that the flow is completely turbulent, thecoefficient of friction, f, is a constant, the compressibili-ty of the gas at base pressure and temperature conditions(14.65 p sia and 60F) is 1 OOO ,and only a gas phase isflowing.Eq. 15 has a subtle but important concept in the valueof the quantity H/L at the wellhead, where both Hand Lare zero. For a vertical wellbore, H = L and

NominalSize d, d, Minimum(in.) (in.) (Ibmlft) (in.) N fle F,

Casmg

7=/a7.625 45.00 6.4458.000 26.00 7.3868.125 28.00 7.4858.125 32.00 7.3858.125 35.50 7.285

1,033,OOO 0.00084171,199,ooo 0.00059111,216,OOO 0.00057101,199,ooo 0.00059131,181,000 0.0006126

8%8.125 39.50 7.185 1 ,I 63,000 0.00063498.625 17.50 8.249 1,353,OOO 0.00044388.625 20.00 8.191 1,342,OOO 0.00045208.625 24.00 8.097 1,326,OOO 0.00046588.625 28.00 8.003 1,309,OOO 0.00048018.625 32.00 7.907 1,292,ooo 0.00049538.625 36.00 7.825 1,277.OOO 0.00050898.625 38.00 7.775 1,268,OOO 0.00051748.625 43.00 7.651 1,246,OOO 0.00053949.000 34.00 8.290 1,360,OOO 0.00043829.000 38.00 8.196 1,343,ooo 0.00045139.000 40.00 8.150 1,335,ooo 0.00045799.000 45.00 8.032 1,314,OOO 0.0004756

9 9.625 36.00 8.921 1,473,OOO 0.00036239.625 40.00 8.835 1,458,OOO 0.00037159.625 43.50 a.755 1,444,OOO 0.00038049.625 47.00 8.681 1,430,OOO 0.00038889.625 53.50 a.535 1,404,OOO 0.00040639.625 58.00 8.435 1,386,OOO 0.0004189

9% 10.00010.00010.00010.75010.75010.75010.75010.75010.750

33.00 9.38455.50 8.90861.20 8.790

10 32.75 10.19235.75 10.13640.00 10.05045.50 9.95048.00 9.90254.00 9.784

1,557,OOO 0.00031781,47l,OOO 0.00036371,450,OOO 0.00037641,704,OOO 0.00025661,694,OOO 0.00026021,678,OOO 0.00026601,660,OOO 0.00027301,651,OOO 0.00027651,830,OOO 0.0002852

H/L=~l&(~/L)=l.ooO.+

In a deviated wellbore, H is less than L, and for ahorizontal pipeline, H = 0 , and as a result the term forthe head of gas drops out of Eq. 15. For a completeguide to the algebraic convention for H and L, refer toRef. 12.


17/23

OPEN FLOWOF GAS WELLS 33-17

TABLE33.11-F,VALUESFORVARlOUSANNULl (K= O.OOlin.)Casing

ID(in.) 1.900

4.154 0.0050824.276 0.0045764.408 0.0041074.494 0.0038384.580 0.0035934.670 0.0033614.778 0.0031094.892 0.0028724.950 0.0027614.976 0.0027135.012 0.002649 0.003235 0.004251 0.006883 0.012455.140 0.002438 0.002946 0.003809 0.005947 0.010125.240 0.002289 0.002746 0.003509 0.005343 0.0087385.352 0.002137 0.002545 0.003213 0.004770 0.0075065.450 0.002016 0.002385 0.002983 0.004342 0.006634

5.524 0.001931 0.002274 0.002825 0.004055 0.006074 0.010985.595 0.001854 0.002175 0.002684 0.003806 0.005601 0.0097835.675 0.001773 0.002070 0.002538 0.003552 0.005133 0.0086585.791 0.001883 0.001930 0.002346 0.003226 0.004552 0.007351 0.010175.836 0.001623 0.001880 0.002277 0.003111 0.004354 0.006924 0.009455

Tubino OD (in.12.375

0.0089010.006oa70.0053560.0049480.004583

2.875 3.500 4.000 4.500 4.750 5.0000.010930.0092680.0078670.0071190.006473 0.01250

0.004242 0.005886 0.010860.003880 0.005281 0.0092890.003544 0.004738 0.0079800.003390 0.004492 0.0074190.003324 0.004389 0.007187

5.855 0.001607 O.OO la59 0.002249 0.003065 0.004274 0.006755 0.0091765.921 0.001551 0.001790 0.002155 0.002911 0.004012 0.006215 0.0083015.989 0.001497 0.001722 0.002064 0.002764 0.003768 0.005726 0.0075286.049 0.001452 0.001665 0.001988 0.002643 0.003570 0.005341 0.006935 0.0095826.154 0.001376 0.001572 0.001865 0.002450 0.003260 0.004757 0.006057 O.OOa1326.214 0.001336 0.001522 0.001799 0.002349 0.003100 0.004466 0.005630 0.0074516.276 0.001296 0.001472 0.001735 0.002251 0.002947 0.004193 0.005235 0.0068376.336 0.001259 0.001427 0.001676 0.002161 0.002810 0.003952 0.004892 0.0063136.366 0.001241 0.001405 0.001647 0.002119 0.002745 0.003839 0.004734 0.0060748.398 0.001222 0.001382 0.001618 0.002074 0.002878 0.003724 0.004573 0.0058356.445 0.001195 0.001349 0.001576 0.002012 0.002584 0.003565 0.004352 0.0055086.456 0.001189 0.001342 0.001566 0.001998 0.002583 0.003529 0.004302 0.0054366.625 0.001099 0.001234 0.001429 0.001796 0.002266 0.003041 0.003639 0.0044866.765 0.001032 0.001153 0.001327 0.001651 0.002057 0.002710 0.003201 0.0038796.875 0.0009830 0.001095 0.001255 0.001549 0.001912 0.002486 0.002910 0.0034866.969 0.0009439 0.001049 0.001198 0.001469 0.001800 0.002316 0.002692 0.0031967.185 0.0008619 0.0009524 0.001079 0.001306 0.001577 0.001987 0.002276 0.0026557.285 0.0008273 0.0009120 0.001030 0.001240 0.001487 0.001857 0.002116 0.0024507.385 0.0007946 0.0008739 0.0009839 0.001178 0.001405 0.001740 0.001972 0.0022687.386 0.0007943 0.0008736 0.0009834 0.001177 0.001404 0.001739 0.001970 0.002266

Eq. 15 does not lend itself to mathem atical integrationwithout making assumptions regarding T and z, but itmay be integrated over definite limits by the trapezoida lmle.If we letI[ yk?qsLsPn p/Tz-2.082- di4 P 1Q=pnz( jp=s l , ooo& JPI H (P/Tz)* p,FZ+-- 53.356L 1,000

+...+(pn-p n-,)(I,+Z,-*)], . . . . . . . (17)then

(~3+~2)+...+(pn-pn-l)(zn+zn-1)], . . . (18)where Zt,Z2,Z3 . . . I, is the trapezoid al rule interval co r-responding to the respective pressure. If we make theassumptions that the kinetic energy term is zero or thatthe temperature, T, and the gas compressibility factor, z,are constant, the equations given in Chap . 30 of thishandbook can be derived. However, the numerical ex-amples that follow will make use of Eqs. 15 through 18.

The details of computations of a BHFP and a shut-inBHP by Eqs. 16a, 16b, 17, and 18 are illustrated by Ex-ample Problem 3 on Page 33-18. To utilize the equations,it is necessary to evaluate the factor F, for various flowstrings. The value may be determined by several corre-lations; h owe ver, the values given in Tables 33.10 and


18/23

33-16 PETROLEUM ENGINEERING HANDB OOK

TABLE 33.12-WORK SHEET FOR CALCULATION OF SUBSURFACE FLOWING PRESSURE BY EQS. 15,16a, AND 16bCompany Lease Well No. B Dateof Test

-^l g 0.615 %CO, 2.5 % N 2 PPC 679 T 361 EquationsUsed 15,16a,16bPC49 11.29s H 10,658 , 10,490 d. 2.441 in. Temperature Gradient 5F/1,000 ft10,658 ' 1.995

H L d P T-02.4413,913.0117

2 I AP0 0.8776 104.719 0

1,000 1,000 2.441 4,023.l 122 0.8894 104.346 110.11,000 1,000 2.441 4,023.3 122 0.8894 104.343 110.32,000 2,000 2.441 4.134.0 127 0.9012 103.992 110.73,000 3,000 2.441 4,245.0 132 0.9129 103.659 111.04,000 4,000 2.441 4,3X3 137 0.9244 103.337 111.35,000 5,000 2.441 4,468.0 142 0.9359 103.036 111.76,000 6,000 2.441 4580.0 147 0.9472 102.743 112.07,000 7,000 2.441 4,692.3 152 0.9584 102.464 112.38.000 8.000 2.441 4.805.0 157 0.9695 102.196 112.79,000 9,000 2.441 4,917,s 162 0.9805 101.943 112.9

10,000 10,000 2.441 5,031.l 167 0.9913 101.693 113.210,490 10,490 2.441 5,086.7 169.5 0.9966 101.583 55.610.490 10,490 1.995 5,086.7 169.5 0.9966 76.546 010,658 10,658 1.995 5,112.0 170.3 0.9989 76.446 25.3

33.11 were calculated by the methods published bySmith. *To compute subsurface pressures w here the well isequipped with tubing set without a packer, the preferredpractice is to calculate the flowing subsurface pressurefrom the wellhead pressure measured on the static gascolumn by means of the static column equations. If thewell has a packe r, it is necessary to calculate the flowingsubsurface pressure by means o f the equations for flow-ing gas columns.Dep ths for calculating or measuring subsurfacepressures in wells are determined in practice by theequipment installed in the well. W here a well isequippe d w ithout tubing or with tubing set withou t apacker, the proper depth for pressure determinations isthe distance to the midpoint of the productive sandface.If the well has tubing set with a packer, the pressures aredetermined at the entrance to the tubing provided the en-try to the tubing is no more than 100 ft from th e midpointof the productive sandface. Otherwise, appropriate cor-rections would be made to determine the pressure at themidpoint of the sandface.An explanation of the computational procedures usedin Tables 33.12 and 33.13 will be helpful before goinginto the details of the calculations. The recent advan cesin computing equipment or, mor e realistically, thedramatic decrease in the cost of computations have giventhe average engineer access at least to a handheld pro-grammable calculator or mom likely a microcomputer.Therefore, the emphasis in the past has been to simplifyequations by making assumptions regarding pr essure,tempe rature, and gas compressibility, but that has notbeen done here. Now the factor F, and compressibilityfactor, z, becom e subroutines, the results of which arenever seen by the user. In this case, Tables 33.10 and33.11 may seem redundant. The compressibility factorsgiven in Tables 33.12 and 33.13 were calculated by theequation of state published by Hall and Yarborough t4and Yarborough and Hall. l* The results of the computa-tions in Tables 33.10 through 33.13 have been rounded,

-23,01823,05923,06323,04923,03923,05223.04723104523.06523,04723,05211,302-

3,871

-23,01823,05946,12169,17092,209

115,261138,308161,352184.417207,464 207,473230,516 230,526241,818 241,822241,616 241.822245,689 245,695

Y,L0

23,05346,10569,15892,211

115,263138,316161,369184,421

Line123456789

IOII12131415

and the rules for rounding vary from one piece of com-puting equipment to another. The algorithm used forsolving Eqs. 15, 17, and 1 8 seems to work for all cases,but users may wish to devise their own algorithm.

Example Problem 3-Flowing Well. Details of themethod for calculating a flowing subsurface pressure forWell B are given in Table 33.12 .The wellhead flowing pressure for Well B was 3,913psia at a flow rate of 11.299 x lo6 cu ft/D. The annularspace between the tubing and casing w as packed off andfilled with mu d so that it is necessary to calculate theflowing subsurface pressure at a depth of 10,658 ft downthe flowing column of gas. Gas properties are thosegiven in Table 33.12 .The flow string measures 10,490 ft of 27/s-in.-OD,6.50-lbm/ft tubing with 168 ft of 2%-in.-OD,4.70-lbm/ft tubing at bottom of flow string. Also, H =L, or the flow string is vertical.Computation of the required pressure is done in twomajor steps because of the change in size of the flow

string at a depth of 10,490 ft. Computations are given inthe following steps.Step 1. Obtain the IDs from Table 33.10 and enter attop of Table 33.122% in. 0%D = 2.441 in.2% in. OD-ID = 1.995 in.Step 2. Determine the temperature gradient applicable tothe problem. In this example, the flowing temperature ofthe gas at the wellhead was 117 F, and the subsurface

temperature at 10,658 ft was 170F. The temperaturewas assumed to be a straight-line relationship between117F at H = 0 and 170F at H = 10,658 ft for atemperature gradient of 5F per 1,000 ft.


19/23

OPEN FLOW O F GAS WELLS 33-19

TABLE 33.13-WORK SHEET FOR CALCULATION OF SUBSURFACE SHUT-IN PRESSURE BY EQS. 15,16a, AND 16bCompany Lease Well No. 0 Date of Test

yg 0.615 %CO, 2.5 - 679N, PPC T 361 Equations Used 15,16a, 16bPC99 0 H 10,656 , 10,656 d N.A. Temp erature Gradien t 5Fll,000 ft

(4J)x WP) x 37.464 xH T Z I AP (1 +/n- l) u , +/ n-1) Y,L Line-

L d, PO0 ---ii 4,173.o 117 123.931.A. 0.6963 0 - - 0 1

1,000 1,000 N.A. 4,266.0 122 0.9071 123.753 93 .0 23,036 23,036 23,053 21,000 1,000 N.A. 4,266.l 122 0.9071 123.751 93.1 23,059 23,059 32,000 2,000 N.A. 4,359.3 127 0.9177 123.573 93.2 23,051 46,i 10 46,105 43,000 3,000 N.A. 4,452.6 132 0.9262 123.410 93.3 23,043 69,153 69,156 54,000 4,000 N.A. 4,546.1 137 0.9365 123.245 93.5 23,062 92,215 92,211 65,000 5,000 N.A. 4,639.7 142 0.9486 123.061 93.6 23,056 115,271 115,263 76,000 6,000 N.A. 4,733.4 147 0.9566 122.929 93.7 23,051 136,322 136,316 67,000 7,000 N.A. 4,627.2 152 0.9665 122.766 93.6 23,046 161,370 161,369 96,000 6,000 N.A. 4,921.l 157 0.9762 122.645 93.9 23,046 164,416 184,421 IO9,000 9,000 N.A. 5,015.l 162 0.9677 122.500 94.0 23,044 207,460 207,474 11

10,000 10,000 N.A. 5,109.3 167 0.9971 122.362 94.2 23,066 230,526 230,526 1210.658 10,656 N.A. 5,171.3 170.3 1.0033 122.266 62.0 15,166 245,694 245,695 13

Step 3. Enter w ellhead data on Line 1 where Hand Lare zero. Calculate f t from definition of I in Eq. 17.From Eq. 17. I is:

;-2.082(g)F2 + H (P& .

L 1,000;=(3913)/(577)(0.8776)=7.72747.Note that z was calculated by methods given in Refs.

14 and 15 (see also Chap. 20).2.082(ygq,2/dpp>= 2.082(0.615)( 11.299)*(2~l41)~(3913)

=0.00118.[p/~z-2.082(y,q,2/dpp)]=7.72629.

Using Eqs. 16a and 16b:

=2.6665(11.299)2/~(2.441)5. [4 log(2.441/O.ooO6) +2.27281] )

=340.425/24,200=0.014067,or, from Table 33.10:

F*=(F,qs)*=(0.01050~11.299)*=0.014075.This value of F* will be used later for comparison.

(p/Tz)*/1,CKIO=(7.72747)*/1,000=0.059714.

At the wellhead, where H=O and L= O for a verticalwellbore. H=L, thenH/L=lim (H/L)=l.OOO.H&L+0

For a deviated wellbore, H is less than L, and for ahorizontal pipeline, H = 0, and the term for the head ofgas drops out of the term for 1.

FZ+~(plTz)/l,OOO

=0.014067+(1.000)(0.059714)=0.073781.

ThenZ=(7.72629)/(0.073781)=104.719.

If the F2 value determined from F, (taken from Table33.10) is substituted above, I becomes 104.708, whichcompares well with 104.719.

Step 4. Determine trial Ap (Line 2) for a depth of 1.000ft by

Ml=37.484~7, XL 37.484(0.615)(1,000)

21, = 2( 104.719)=llO.l psi.

Step5. Comple te calculation of first trial 12 (104 .346)on Line 2 where the temperature is 122F, and the firsttrial pressure is 3913.0+ 110.1=4023.1 psia. At theseconditions, the compressibility factor, Z, is 0.8g9 4. Esti-mate the second trial Ap by:

&2 =37.484(0.615)(1,000) = 1 1o 3

104.719+104.346


20/23


Step 6. Com plete calculation of second trial 12(104.343) on Line 3 where the temperature remains at122 F, and the second trial pressure is 39 13 O+ 110.3 =4023 .3 psia. Under these conditions, the compressibilityfactor, Z, remains at 0.889 4. Estimate the third trial Ap by

*~3= 37.484(0.615)( 1,000) = 110.3.104.719-t 104.343Since the third trial Ap is the same to within 0.04 psi, thepressure at a depth o f 1,000 ft was determined by trialand error to be 3,913.0+110.3 = 4,023.3 psia. (Notethat the third trial was not entered in Table 33.12 .)

Step 7. Repeat Steps 4 through 6 to calculate the pres-sure at a depth of2,OO O ft. Only the final step was givenin Table 33.12.Table 33.13 illustrates the calculation of subsurfaceshut-in p ressures in a gas well by Eqs. 15, 16a, and 16b

by the same procedure used in Example 1. The only dif-ference is that for the shut-in well the rate of flow, qg , iszero and, as a result, the pressure loss caused by frictionis zero. Therefore, the inside diameter of the pipe has noeffect on the calculations.Size of Integration IntervalThe integration interval w as 1,000 ft in Tables 33.12 and33.13 for a moderately high-pressure well and, for theflowing example (Table 33.12), the rate of 11.299 x lo3cu ft/D gave an effective or average velocity of 14.7ft/sec near the wellhead . Also, the compressibility fac-tor, z, of the gas at wellhea d conditions is in that portionof the z vs. pressu re curve whe re z is very nearly a linearfunction of pressure . At this low velocity and the nearlylinear relationship of z with pressure, an integration in-terval of 1,000 ft is probably more than enough.Likewise, at low pressures where z is again almost astraight-line function of pressure and at low velocities,the integration interval could be extended to 3,000 ftwithout undue error. However, even moderate computa-tion facilities eliminate the necessity f or expanding theintegration interval to mor e than 1,000 ft.Application of Backpressure Teststo Producing ProblemsBack pressur e tests taken properly are useful in predictingdelivery rates into a pipeline and in reconditioningstudies. Fo r these purposes, either the multipoint or theisochronal test is suitable for wells producing from reser-voirs with high permeability such as Well B (Fig. 33.5).The isochronal-type test is necessary for an accurateanalysis of producing problem s for wells producing fromlow-perm eability reservoirs such as Well A (Fig. 33.7).Althoug h multipoint tests can be used, suc h analyses ar emuch more difficult.

Well performance at the bottom of the well is ameasure of the capacity of the reservoir to deliver gas in-to the wellbore and is useful in analysis of reservoirproblems. A wellhead performance curve is a measure ofthe capacity of the well to deliver gas into a pipeline andis useful in equipment and reconditioning problem s.Usually, an analysis of producing problem s can be com-pleted with wellhead backpressure data.

Production RateEstimation of the steady produ ction rate of a well into apipeline opera ting at a relatively constant pressure re-quires both test data and a general knowledge of the pro-ducing character istics of the well. For exam ple, anestimate is required of the capacity of Well A (Fig. 33.7)to deliver gas into a pipeline operating at a pressure sothat pts * -ptf * in thousands equals 20 . Starting fro mshut-in conditions, the delivery rates would be 6,950 ,6,000, 5,150, and 4,730x103 cu ft/D. The rate at 72hours would be 3,340 x lo3 cu ft/D from data given inthe text. The steady reduction rate would be about2,000 to P2,400x10 cu ft/D. Although theoreticalmeth ods have been published for estimation of stabilizedproduction rates, they would require more data than isavailable for the well.Well B (Fig. 33.5) would produce about 4,300~ lo3cu ft/D into a pipeline when

PlS2 -prf* =500

as long as the well remained in good condition. Actually,the performance of Well B increased during productionand the rate of flow would have increased. The perfor-mance of Well B did not deteriorate with time.Estimation of the sustained production rate of a par-ticular well against fixed pipeline conditions requires ageneral knowledge of well performance and a definiteknowledge of the performance characteristics of the par-ticular well. The accuracy of such estimations is depen-dent to a large extent on the amount of proper test dataavailable for study.Causes of Deterioration in PerformanceThe principal causes of deterioration in gas-well p erfor-mance are hydra tes, liquids, cavings, deposition of salts,equipment leaks, foreign objects, and damage to the pro-ducing form ation. Any one or a combination of thesecauses m ay result in loss of productive capacity and indecreased income. Th e determination of the cause ofdeterioration in perform ance and the recomm endation ofremedial measures require a history of the performanceof the particular well.

The tests illustrated in Fig. 33.8 f or Well A give ahistory of the performance between the date (June 17 ,1947) of the multipoint test and the date (Dec. 17, 1951)of the isochronal test. The performance indicated by thefirst point of the multipoint test (q8 =4,92 8x lo3 cuft/D) is the same as that of the isochronal test. T hus it isconcluded that the performance of Well A was main-tained for about 4% years. N othing occurred that harmedthe well. Sim ilar conclusions regarding Well B are in-dicated for the time interval represented by the data onFig. 33.5.A regular progr am of testing g as wells is essential toplanning remedial action.HydratesThe formation of gas hydrates in the flow string or in thereservoir m ay cause a well to cease flowing. The authorknows of no remedial action to remove hydrates from theproducing formation excep t that of allowing the naturalheat of the reservoir to melt the hydrates. The formationof hydrate s in the flow string ma y be prevented by use of


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qg, IO3 cu ft/D

Fig. 33.9-Effect of tubing installation on performance of WellC; Points 1 through 4 are before tubing installation,Point 5 is after.

qg, lo3 cu fVDFig. 33.10-Effect of obstruction in tubing on performance of

Well D; Points 1 through 6 are before removal,Point 7 is after.

bottom hole chok es, injection of chemicals such as thealcohols or glycols into the flow string, or by the installa-tion of downh ole heating equipment. The accumulationof hydra tes in the flow strings m ay be alleviated to someextent by elimination of obstructions in the flow string,use of prop er valve sizes at the surface, elimination ofsharp bends in surface lines, and prop er placement ofchokes in surface lines. Remedial action consists inlowering of hydrate-formation temperatures bychemicals or by maintaining the tempe rature of the flow-ing gas above the hydrate-formation temperature.Heating of the flow string in a well is usually ac-comp lished by the circulation of hot oil in the casingaround the tubing o f the well. How ever, it must be em-phasized that hydrate troubles are very easily confusedwith liquid troubles in low-tem perature wells. A carefulstudy should be made of flowing temperatures in a wellbefore recommendations are made for hydrateprevention.LiquidsMo st perform ance difficulties in gas wells are caused bythe accumulation of liquids in the wellbore. Liquidtroubles may be caused by hydrocarb ons (condensateand etude oil), salt water , or brines com ing into thewellbore from the producing formation, brines fromforeign sources through casing leaks, or fresh water. Oc-casionally, the production of formation water or crudeoil may be eliminated by plugback operations. Liquids inwellbores may be remo ved by tubing strings of prop erdesign, siphon strings (tubing with jet holes or gas-liftvalves), and plunger lifts. Periodic flowing of the well athigh rates to the pipeline may eliminate liquid troubles.Rem edial action for wate r troubles requires an iden-tification of the source of the water . T his is done bywater analyses. If it is decided from analyses that thewater is native to the formation, there is a choice be-tween plugback work and water removal by variousmeans. Salt water that is foreign to the producing forma-

tion or fresh water in excessive amounts indicates a cas-ing leak that should be repaired. However, moderateamounts of fresh water usually condense in the flowstrings of gas wells. F resh w ater that occurs naturallyshould not be confused with fresh water from a foreignsource.CavingsCavings that consist of shale and pieces of the formationare usually mo st troublesom e in openho le completions.The presence of cavings in wells without tubing can bedetermined easily by comparison of measured depth withdrilled depth . Rem edial action consists of cleaning ou t,installation of liners in openho le, and acid wash es wher ethe formation is soluble in acid.Unconsolidated sand is troublesom e in many GulfCoast wells. Sand may damage the performance of awell in addition to causing severe dam age to equipmen t.Remed ial action consists of cleaning out, installation ofspecial liners, or consolidation treatment for theformation.Deposition of SaltsSalts (sodium chloride or other chemical compounds)may be. deposited in the flow strings or wellbores of gaswells. Sodium chlo ride and water-soluble salts oftenmay be removed by water or light acid washes. Occa-sionally it is necessary to replace the flow string withclean pipe. Heavy crude oil (not a salt) may be remo vedFrom the flow string and to a limited extent from the faceof the wellbore by washing with kerosene.Casing and Tubing LeaksCasing lea ks usually permit the migration of gas intoanother formation, but occasionally in low-pre ssureareas water may come into the wellbore through leaks.The migration of gas into another form ation is wasteful.Casing leaks, d epending on their size in relation to well


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33-22

capacity, cause deterioration in well perform ance.Positive identification usually can be mad e with subsur-face temp erature surveys or special techniques suppliedby service companies.Tubing leaks, w here there is no packer, tend to defeatthe purpose o f the tubing. Liquid rem oval becomes dif-ficult if the hole in the tubing is large. Small leaks in tub-ing are usually the result of corrosion. In wells wh ere theannular space is pack ed off, tubing leaks may allow cas-ing pressure s to build up to dangerou s levels.Foreign ObjectsForeign objects su ch as swab rubbers, stud bolts, orpieces of metal may remain in the flow string of a wellafter completion. Such objects should be removed fromthe flow string because th ey can seriously affect thedelivery capacity of a well. Th e remova l of foreign ob-jects ftom the upstream side of chokes is common.Examples of Remedial OperationsThe effect of water pro duction and the installation of tub-ing on the performance of Well C in the Texas H ugotonfield is illustrated in Fig. 33 .9. T he curve (n=0.86 0)shows the 3-hour isochronal test results taken im-mediately after completion. Numbered points are72-hou r isochronal tests taken at yearly intervals, excep tfor Points 4 and 5, which were immediately before andafter installation of tubing. Point 1, taken after comp le-tion, and Point 2, taken about a year after comp letion,represent g ood performance. Points 3 and 4 show poorperformance with the result that Well C was producingabout 30 % of its assigned allowable. A study of Well Cindicated that salt water wa s causing the poor perfor-mance. A string of 1 g-in. tubing with a X,-in. jet hole100 ft from the bottom of the tubing was installed. Thewell was then produ ced continuously throug h the tubingstring. At the time Point 5 was taken, the performance ofthe well had not only been restored but it had been im-prove d over wh at it had been originally, which is shownby the relative positions of Points 1, 2, and 5 withrespec t to the 3-hour isoch ronal curve. Conclusionsregarding Well C are that there was a minor w ater prob-lem from completion through the time that performancedata were taken for Points 1 and 2 (Fig. 33.9). Watermovement into the wellbore h ad seriously damaged theperformance of the well at the times Points 3 and 4 weretaken. The installation of tubing after Point 4 perm ittedthe removal of water from the well and even allowed thewater saturation to be reduce d in the formation aroundthe wellbore. The position o f Point 5 indicates better72-hou r perf orman ce than the well had originally as it iscloser to the 3-hour isoc hronal curve than Points 1 and 2.An example of the effect of a tubing obstruction on theperform ance of a well is illustrated in Fig. 3 3.10 fo rWell D, where the performance points (indicated bycircles with and without numbers) were taken at intervalsof a month after start of production. Well D was an ex-tremely high-capac ity well as indicated by the position ofthe original m ultipoint test. As the numbered points wer eof long-time-flow duration, it was though t that positionof Points 1, 2, and 3 indicated some sort of liquidblockage in the reservoir. However, the tubing appearedto be free of liquids when the well wa s shut in andpressures were normal. Water-gas and condensate-gas

PETROLEUM ENGINEERING HANDBOOK

ratios were normal. Thus it was concluded that liquidswere not the source of trouble. After Points 4, 5, and 6were taken, it was decided to blow the well. Shortly afterthe well was opened, a swab rubber and several pieces ofmetal were blown from the well. Afterward, the perfor-mance of Well D returned to normal, as indicated by thepositions of Point 7 and later perform ance points that arenot numbered on Fig. 33.10.Space does not permit a complete description of recon-ditioning proced ures. How ever, it is hope d that this briefoutline does illustrate the importance of adequ ate perf or-mance tests in the maintenance of well productivity andplanning reconditioning procedures.Nomenclature

C = performance coefficientdi = internal diameter, in.f=F=F, =

F =;; =

Fpu =F, =FT =h, =h, =

H=

I=K=L=

n=P

Pi =PI =

Ppc =PR =

Ps =Ptf =

Pts =Pwf =

qg =ri =

R gL =

coefficient of friction (friction factor)term in Eq. 16aspecific-gravity adjustment factornon-Darcy flow factorbasic orifice fac tor for critical-flow prove r,lo3 cu ft/D at 14.65 psia, 60 F, specificgravity = 1.000supercom pressibility adjustment factorfactor defined by Eq. 16aflowing-temperature adjustment factorheight (mano meter reading), in. mercuryheight (mano meter reading), in. watervertical depth in a well, ft (in untubed wells

H is the vertical depth to the midpoint ofthe productive formation; in tubed wellsH is the vertical depth to the entrance tothe tubing)

terms in Eq. 17absolute roughness characteristic, in.length of flow string in well correspondingto H, ftexponent of the backpressure equation orslope of the backpressure curvepressure, psiaimpact pressure on a pitot tube, psigimpact pressure on a pitot tube, psiapressure , pseudocritical, psiaaverag e pre ssure in the reservoir at verticaldepth Hstatic pressure on critical flow prover, psiaflowing pressure at wellhead measured on aflowing column of gas, psiashut-in pressure a t wellhea d, psiasubsurface (bottomhole) flowing pressure inthe wellbore at vertical depth H, psiarate of flow, lo3 cu ft/D or lo6 cu ft/D(14.65 psia and 60F)internal radius of pipe, in.gas to hydrocar bon liquid ratio, cu ft/bbl

T = temperature, OF+460Tf = temperature of flowing gas, OF+4 60


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Tpc = temperature, pseudocritical, OF+460TR = reservoir temperatureI, = vapor volume equivalent of 1 bbl (60F) ofhydrocarb on liquid, cu ft/bbl

z = compressibility factor for gasA = difference between two values

78 = specific gravity of separator gas or gasbeing measured, air = 1 .000yg = specific gravity of the flowing fluid, air =1.000-ye = specific gravity of hydrocarb on liquidreferred to water

Key Equations in SI Metric Unitsqn =o. 1 533 d?p, . . . . . . . . . .

33 open flow para pozos de gas

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