Distingtiished ,Author Series ,y~l~’llq

n‘w%%?+%+~:,- ...” Nodal Systems Analysis ofX..?“*:?-,..

Oil and Gas Wells.7 ~+:“,‘: By KermitE. Brown,SPE, and James F, Lea, SPE

Kermit E. Brown is F. M. Stevenson Professor of Petroleum En9ineerin9 at the U. ofTulsa. Since 7966 @wh has served es head of the Petroleum E“gineerhg Dept., vicepresident of research, and chairman of the Resources Engineering Div. He has conductedmany courses m gas lift, nwltiphase flow, and inflow peiformamx a“d served as aDistinguished Lectwsr dud”g 1969-70. Brow” holds a ES deg,ee in niech?”icaf a“dpetroleum engineering from, Texas A&MU. and MS and PhD deg!ees from the U. OfTexas, both in petroleum engineering. Brown sewed as the SPE faculty advisor for the U.of Tulsa student chapter during 1982-83. He also sewed on the SPE board during1969-72, the Education and Pm fessio”alism Committee during 1966-67, and theEducation and Accreditation Committee dud”g 1964-66 a“d was Balco”es Sectimchairmanduring 1964-65. He is currently o“ the Public Service Award Committee,James F. Lea is a research associate in the Production Mechanics Group of AmocoProduction Co,, in Tulsa, He works on computer hnplen?entation of existing design andanalysis methods for a,fiificial lilt md improved application techniques. Previous~, heworked with Pratt & Whitney Aircrati and .%” 0;/ Co. and taught engimseri”g science atthe tmiwrsity level. Lea holds BS and MS degrees in mechanical e“gi”eering and a PhDdegree in thermal{ fluid science from Southern Methodist U., Dallas.

Summary

Nodal 1 analysis, defined as a systems approach to theoptimization of oil and gas wells, is used to ev61uatetboruughly a complek producing system. Everycomponent in a producing well or all wells in aproducing system can be optimized to achieve theobjective flow rate most economically. Ml presentcomponents—beginning with the static resemoirpressure, endkg with the separator, and includinginflow performance, as weU as. flow across thecompletion, up the tublig string (inChIdlng 811Y

downhole restrictions and safety valves), across thesurface choke (if applicable), thrbugh horizontal flowlines, and into the separation factilties-are tiulyzed.

Introduction

The objectives of nodBI aualysis are as follows.1. To determine tlie flow me at which an existing

oil or gas yell wifl produce considering wellboregeometry and completion limitations (first by naturalflow).

2. To determine under what flow condhions (whichmay be related to time) a well will load or die.

3. To select the most economical time for theinstallation of afiticial lift and to assist in the selectionof the optimum lift method,

4. To optimize the system to produce the objectiveflow rate most economically.WYW 19s5societyof PetroleumEwi.eefs

OCTOBER 1985

5. To check each component in the well system todetermine whether it is restricting the flow.mteunnecessatiy.

6. To permit quick recognition by the operwor’smanagement and engineering staff of ways to increaseproduction rates.

Theie are numerous oil and. gas wefls aruund theworld that have not been optimized to achieve anobjective rate e~lciently. In fact, many may have beencompleted in s“cb a m~er tit their maximumpotenti81 kite cannot be achieved. Also, many wellsplaced on anificial lift do n6t achkve the efficiencykey shtiuld.

The pruductioi optimization of oil and gas wells bynodal systems analvsis has contributed to improvedcompletion techniques, pfiduction, and efficiency formany wells. @thou h this type of analysis was

i.proposed by Gilbert m 1954, it has been usedextensively in the U.S. only in the last few yeari. Oneprincipul ieason for tbk was the changing of allowableproducing. rates, and another has been the developmentof computer technology that allows rapid calculation ofcomplex algorithms and provides ea.sify understooddata.

Past conservation practices in the U.S. more or lessrestricted operaors t6 2- and 2 IA-in. [5.08- and6.35-cm] tubing and 4 shots/ft [13.1 shots/m] forpmfomting. The use of larger tubing (41Aand 51Ain.

175I

&P, = P, - Pwf, = LOSS IN POROUSMEOIUM

AP2 = Pw’,-Pwf = LOSS AcROSS COMPLETION

A% = k -%. = “ “ REsTRlcTl ONdP4 = PKv-Po~v = “ “ SAFETY VALVE

AP5 = Pw~-PD~c = ‘t “ SURFACECHOKE

AP6 = PO$C-P5,P= “ IN FLOWLINE

AP7 = Pwf -Pwh = TOTAL LOSS Ilq TUBING

nPs = Pw~-P,ep = “ ‘r “ FLOWLINE

Fig. l—Possible pressure losses in complete system.

[11.43 and 13.97 cm]) and 16 shots/ft [52.5 shots/m]is common today.

Although the increase in flow rates in hlgh-productivity wells has popularized nodal analysis, it is,nevertheless, an excellent tool for low-rate wells (bothoil and gas) as well as for all aititicid lift wells. Someof the greatest percentage increases in production rateshave occurred in low-rate oil wells (from 10 to 30 B/D[1.59 to 4.77 m3/d]) and low-rate gas wells (from 50Ilp to 100 to 200 Mscf/D [1416 Up to 2832 to 5663 stdm3/d]). Numerous gas wells have needed adjustmentsin tubitg sizes; surface pressures, etc., to prolong theonset of liquid Ioadlng problems. Nodsf analysis cmbe used to estimate the benefits of such changes beforethey am made.

One”of ,jhe most impommt aspects of nodal analysisis to recognize wells that should be producing at rateshigher than their current rate. Therefore, it can serveas an excellent tool to verify that a problem exists andthat additional testing is necessacy. For example,assume that a well is producing 320 B/D [51 m3 /d] ofoil. Applying nodal analysis .to this well shows that itis capable of producing 510 B/D [81 m3/d], Thisdifference may be attributed to several factors, butnodal analysis can determine which component iirestricting the rate or can .detetine that iricomect dataare the cause of tbe higher predicted rate, A basicrequirement for weli analysis is the ability to detinethe current inflow performance relationship (IPR) ofthe well. Accurate well test data must be obtained andthe proper IPR applied for successful analysis, Then

1752

models of other welf components can be used tocomplete the p=dicted well pe,ffocmsnce.

Fig. 1 shows ,components that make up a detailedflowirtg wefl system. Beginning with the reservoir andprocecdin~ to tie separator, the components are (1)resemoir pressure, (2) well productivity, (3) wellborecompletion, (4] tubing string, (5) possible downitolere@ctive device, (6) tubing, (7) safety valve, (8)tubing, (9) surface choke, (10) flowline, and (11)separator.

To optimize tie system effectively, each componentmust be evaluated separately and then as a group toevaluate tbe entire well producing system. The effectof the chang&of any one component on the entiresystem is ve~ impomant and can be displayedgraphically yitb well analysis. Some aspects Of theIPR component are covered in Appendix A; discussionof myltiphase- flow pressure-drop correlations forpipelines is found in Appendix B,

The most common positions for nodal analysisgraphlcd solutions are listed below.

1. At the center of the producing intefial, at thebottom of the well. This isolates the well’s inflowperformance.

2. At the top of the well (wellhead). This isolatesthe flowline or the effects of surface mressure onproduction.

3., Differential pressure solutioris (Ap) across thecompletion intecwi to evaluate the effect of thenumber of perforations on production in gravel-packedor standard completion wells.

JOURNAL OF PETROLEUM TECHNOLOGY

\

c~q...

oRATE +

Fig. 2-Constructed IPR curve.

4. Solutions at the separutor, especially with gas-liftwells. This isolates the effect of separator pressure onproduction.

5. Other solution positions for graphical solution areat surface chokes, safety valves, tapered stringconnection points, and dowuhole restrictions.

The user must understand how pressure-flowcomponents of the weIl are grouped to form agraphicul solution at a node point. For example, if thesolution is plotted at the bottom of the well (center ofcompleted intmvat), then the reservoir and thecompletion effects can be isolated completely from theenthe piping and production system.

Caution should be taken in ne~lecting even 200 to300 ft [61 to 91 m] of casing flow fmm the center ofthe completed interval to the bottom of the tubing.Because of lower velocities, the larger pipe may not beflushed out with produced fluids. This large section ofpipe still can be neady full of completion fluids (waterturd mud), even though the well may be producing100% oil. Numerous flowing-pressure surveys haveverified this occurrence. A major company recentlysurveyed a will producing 1,600 B/D [254 m3/d] ofoil up 2~-in. [7.3-cm] tubing. Because of a dogleg,tubing was set 1,000 ft [305 m] off bottom in the11,000-ft [3353-m] well, Both water and mud werefound in the 7-in. [17.8-cm] casing below the tubing,even though rbe well produced 100% oil. CleaningWk well resulted in an increase of the rate to morethan 2 ,0i30B/D [318 m3/d] of oil. This points out onetype of practical limitation of nodal analysis whentubing-pressum-drnp calculations are used to calculateaccurately a bottomhole flowing pressure (BHFP).Here, the unalysis showed that the rate should behigher and, hence, served as a diagnostic tool thatprompted the mnning of a prsssure traverse. Irr manycases, the anafysis predicts what should be expected,and the operator is advised to look for problems if thewell is producing below that prediction.

OCTOBER 1985

+BHPor.

AP

c

x TUBINGINTAKE

CURVE

uRATE +

Fig. 3—Constructed tuping intake curve,

Specific ExantpIes

A liited number of examples are presented here;numerous examples, however, appear in theliterature. I-5

Two specific subjects have been selected forexample solutions.

1. The effect of the downhole completion on flowrate is illustrated. An example solution for both agravel-packed well and a stundtwd perforated well ispresented. Procedures to optimize the completions srecmttined.

2. Quick recognition of those wells with a greaterpredicted potential thatr the present production rate iscovered. These situations may be caused by arestriction in one of the components in the system.

Gravel-Packed Oti and Gas WeIls

A paper presented by Jones et al. 4 seemed to be thecatalyst that started operators looking more closely attheir completions. This paper nlso suggests proceduresfor determining whether a well’s inflow capability isrestricted by lack of area open to flow, by skin causedby mud infiltration, etc.

Ledlow and Granger3 have prepared an excellentsummary of background material on gravel packing,including detaifs on mechanical running proceduresand selection of gravel size.

The nodaf aua.lysis procedure for a gmvel-psckedwell, illustrated with a sequence of figures, ispresented here. The appropriate details, additionalreferences, and equations can be found in Ref. 3.

The foflowing procedure is vtild for either an oil orgas well with tie solution node at bottomhole. ‘‘

1. Prepare the node IPR curve (Fig. 2). (This stepassumes no Ap across the completion. )

2. Prepare the node outflow curve (tubing intakecurve in Fig. 3), which is the surface pressure plus thetubing pressure drnp plotted as a function of rate.

1753

3API AP2 AP3

Tw

/

\

(AP=O

RATE +

Fig. 4—Transfer Ap.

3. Transfer the differential pressure availablebetween the node inflow and node outflow curve onthe same plot (FQ. 4) to a Ap curve.

4. Using the appropriate equations, 3,4 calculate thepressure drop across the completion for various rates.Nnmerous variables have to he considered here,includ]ng shots per foot, gravel permeability, viscosityand density of the fluid, and length of the perforation

tunnel for linear flow. Add this Ap curve on Fig. 4, asnoted in Fig. 5,

5. Evsluate this completion (Fig. 5) to detemninewhether the objective rnte can be achreved with anaccepted differential across the grnvel pack. Companyphilosophies on accepted Ap values differ. Areasonable maximum allowable Ap that has givengood results rnnges from 200 to 300 psi [1379 to ‘206gkl%t]for single-phase gas or liquid flow. Mostoperatom will design for smaOer Ap’s for multiphaseflow across the pack.

4

o \

RATE +

Fig. 6—Evaluation of various shot densities.

4BHP

flP

(“cl

RATE +

Fig. 5—Construct Ap across gravel pack.

6. Evaluate other shot densities or perhaps otherhole sizes until the appropriate Ap is obtained at theobjective mte (Fig. 6). Perforation efficiency shouldbe considered at thk time. A good review onperfoiatiug techniques, which poiuts out such factorsas the number of effective holes expected and the.effect of the number of holes and hole sizes on casingstrength, was presented by Bell. 6

7. The Ap across the pack can be included in theIPR curve, as noted in Fig. 7.

Example Problem—TypicaI Gulf Coast Well WithGraveI Pack. Below is a list of given data.

~, = 4,000 psi [27.6 MPa],D = 11,000 ft [3352 m] (center of perforations),k = 100 md (penneabfiity to gas),h = 30 ft [9.1 m] (pay interval),

h, = 20 ft [6.1 m] (perforated interval),

RATESPOSSIBLE

RATE +

Fig. 7—Gravel pack solution by including Ap completion inIPR curve.

1754 JOURNAL OF PETROLEUM TECHNOLOGY

4

3 -

q

&-

;2 -

L8m Pr = 4000 Psl

DEPTH = 11,000

1 - K = 100 MD

1 I I 1 I 1 1 I00 20 40 60 80 100 120 140

RATE, MMCFD

Fig. 8—IPR curve for gas well—gravel-pack analysis.

40/60-mesh gravel-packed sand,640-acre [259-ha] spacing,8~.in. [21.9-cm] casing; 1()%-in. [27.3-cm]

drilled hole,Tg = 0.65,screen size = 5-itr. [12.7-cm] OD,gas-sales-line pressure = 1,200 psi [8273 Wla],short flowline.

This well is to he gravel packed. The tubing sizeand the number of shots per foot are to he evaluatedwith an undcrbalanced tubhrg-conveyed gun. It isassumed that there”is no computable zone restriction

RATE, MMCFD

Fig. 1O—AP available fmm sandface to tubing intake.

OCTOBER 1985

8r /

IOo,

70

RATE,MMCFD

Fig. 9—Evaluation of tubing sizes.

around the perforation because of unconsolidatedforrrmtion-that is, sand flows immediately into allperforated holes until properly prepacked.

Procedure.1. The IPR curve is prepared with Darcy’s law, and

the additional turbulence pressure drop4 is included(Fig. 8).

2. Tubing sizes of 2%, 31A, and 41A in. [7.3, 8.89,and 11.43 cm] are evaluated at a wellhead pressure of ““1,200 psi [8272 kpa], which is needed to flow gas intothe sales fine. From analysis of Fig. 9, 41A-in.[11.43-cm] tubing is selected. Note that, if market

RATE, MMCFD

Fig. 1l—Ap across gravel pack at 4, 8, 12, and 16 shotslft.

1755

RATE, MMCFD

Fig. 12—Completion effects included with lPR—gravel-packed well.

RATE, MMCFD

Fig. 1S-Effects of wellhead pressure-gravel-packed well.

conditions permitted, much figher rates cotdd beprojected with adequate sand control.

3. The Ap is transferred, as noted in Fig. 10. This isthe Ap available across the gravel pack.

4. The Ap across tie pack for 0.75-in. [1.905-cm]-diameter holes with 4, 8, 12, and 16 effective shots/ft[13. 12,26.2, 39.4, and 52.5 effective shots/m] (Pig.11) should be calculated with Jones et al.’s equationsm with modifications of these equations adjusted to titfield data.

5. Figs. 11 and 12 show the final two plotsindicating that 16 shots/ft [52,5 shots/m] are necessaryto obtain a Ap of about 300 psi [2068 kPa] at a rate df58.5 MMscf/D [1.7x 106 std m3 /d]. Additionalperforations could bring thk AP below 200 psii1379 kPa~. - ~

6. To bring tik well on production properly, onemore plot (such as FQ. 13) should be made withseveral weffhead prcssmes so that Ap across the packcan be watched through fhe observation of rate andwellhead pressure. Thk procedure is described byCrouch and Packs and Brown et al. 3

Nodal Atwdysis To Evafuate a StandardPerforated WeU

In 1983 NfcLeod7 published apaper that promptedoperators to examine completion practices on normallyperforated wells. Although numerous priorp~bli@tio”ss-10 discussed this topic and Companiesbad evaluated the problem, Wk paper sparked newinterest. A modification of dds procedure is presentedin Ref. 3.

The procedure is similar to that offered for gravel-packed weUs, except that the equations used for thecalculation of pressure drop acmsa the completionhave been altered to model flow through a perforation

iT56

surrounded by a low-permeabfity zone. They stillincorporate basic concepts suggested by Jones et al. 4for gravel-packed weUs.

ExztnpIe ProbIem and Procedure fora Perforated Weff

Iu thk section, a sample oil well with a low GOR, alow bubblepoint pressure, and assumed single-phaseliquid flow across the completion will be anutyzed.The reason for thk selection is that current technologyhas offered solutions only for single-phase flow (gas orliquid) across such completions. When two-phase flowoccurs across either a gravel-packed or a standardperforated well, relative permeability effects must beconsidered. Additional turbulence then occurs ingrovel-packed weUs and creates more energy losses.

McLeod7 noted that most of the pressure drop canoccur across a compacted zone at the pe.tioration wallbecause of turbulence. He annlyzed a gas-wellexample and showed that 90% of the totaf Ap acrossthe completion, in fact, was caused by turbulenceacross the approximately IA-in. [1.27-cm] -thickcompacted zone. (.Eefs. 3 and 7 provide more details).

To use this technique, the crashed-zone thickness,e,, the pemneabllity, kc, the perforation-tunneldiameter, dp, and the length, Lp, must be ~own.

Obviously, because of the many input variablesrequired, the technique can only be approximate andiadicate trends. It is hoped that fature research in thisarea wiU lead to mom accumte models of pressuredrup through perfomtions shot in both over- andunderbalanced condkions.

Example Problem.

j, = 3,500 psi [24.1 MPa],D = 8,000 ft [2438 m],

JOURNALOFPETROLEUMTECHNOLOGY

3.0 -

2.5 -

~ 2.0 -L

&-; 1.5-n.Im 1.0-

DEPTH= 800L7,5- Pr = 3500

Pwh = 140 PSI

! 1 I 1 ( Io 1000 2000 3000 4000 5000 6000

RATE, BID

Fig. 14-IPR and tubing curves for peqorated oil well.

36°API [0.84-g/cm3] oil,Solution GOR = 180 scf/bbl [32 std m3 /m3],80-acre [32.3-h2] spacing,5Win. [13.97-cm] casing,8 k-in. [21.59-cm] hole,

Lp =”4-in. [10.16-cm] perforation tunnel (seeTable 6 of Ref. 7 for tabulated values),

e. around perforated tunnel = O.5 in. [1.27 cm],ph = 800 psi [5515 kPa],

h = 30 ft [9.1 m],hp = 20 ft [6.1 m],78 = 0.7,

T = 180”F [82°C], andp WA = 140 psig [965 kpa].

Procedure.1. Prepare the IPR ctt~e with Darcy’s law,

assuming no Ap across the completion.2. Plot the node outflow curve (tubhg intake) for

2x- 2%,, ~d 31h-in. [6.03-, 7.3-, and S.w-mnltubing, This dekmmines the pressure requited at thebottom of tubing for flow through the tubing. Steps 1(IPR) and 2 (tubing intake) a~ shown in Fig. 14.Assume 3 k-in. [8.89-cm] tubing is selected.

3., T~sfer the Ap curve, as shown in Fig. 15.4. Using the appmpriite equations fmm McLeod7

(and as discussed by Brown et al. 3), determine theAp’s across the completions listed. in Table 1.

An an~ysis of Fig. 16 shows the importance ofperforating undeinlanced. Of course, the best fluidsand techniques should be used.

Recognition of Components Causing RestrictedFlow Rates in a WeIl

Example ProbIem—Anafysk of Flowline Capacity.The following well is on gas lift.

OCTOBER 1985

3.0

[\.

DEPTH = 8000

2.5R = 3500 PslTUBING I.D. = 2.992”

+! \, I ,\lo 1000 2000 3000 4000 5000 6000

RATE, BID

Fig. 15—Transfer for Ap curve-perforated oil well.

D = 8,000 ft [2438 m],2~-in. [7.3-cm] tubing,

p, = 2,100 psi [[4.5 MPa],35°API [0.85-g/cm3] oil,50% water [yW= 1.07],solution GOR=300 scf/bbl [54 std m3/m3],sepamtor pressure =60 psig [413 kla],flowline len=@=4,000 ft [1219 m],well test 500 B/D [79.5 m3/d] at 1,740 psi [12 MPa],

pb = 2,400 psi [16.6 MPa],-yX = 0.7, and

tubing size = 2 Win. [6.35-cm] ID.

Sufficient gas pressure is available (2,000 psi [13.8MPa]) to inject gas near the bottom, and a totalgas/liquid ratio of 800 scf/bbl [143 std m3/m3] ismaintained for gas lift. The flowline might berestricting the rate. With nodal analysis, a graphicalsolution can be generated auicklv at the wellheadlocation. - ‘ -

Examination of the results in F]g. 17 indicates thatthe flowline is a restriction because the Dmssure loss inthe flowline (21%-in. [6.35-cm] ID) sho~s a significantincrease in pressure loss with rate and is angledsharply upward at the intersection point between thetwo cuwes shown. The intersection point of thepressure required at the flowline intake and the IPRpmsure minus the pressure drop in the well fromsandface to the wellhead is the point of predicted flowfrom the well.

A 3- and 4-in. [7.62- and 10.16-cm] flowline is thenevaluated on the same plot. As soon as the slope ofthe flowline intake pressure VS. rate becomes small(showing very little increase of Ap with rate), thin theflowline diameter is sufficiently large. The diametershould not be oversized because additional sluggingand head@ may occur. Some operators just add a

i757

TABLE I-SAMPLE COMPL5T10Ns FOR PERFORATED OIL WELLS

FeetNumber ShotslFt ?erforated—— —

1 4 20

2 a 20

3 4 20

4 8 20

parallel line instead of replacing the current line with alarger size,

Restriction Caused by Incorrect Tubing Size. Thetubing may be either too large ‘(causing unstable flow)or too small (reducing flow rate). This can berecognized immediately on a nodal plot and is asimportant in high-rote gas lift wells as in low-rate gaswells.

A weak gas well is chosen to show how todeterroipe when thetubingistoolar eand to predict

,?when loading will occur. The Gmy cy’relationis

=commended for use in the calculation of tubingpressure drops in gas wells that produce some liquids.

Example ProbIem–Weak Gas Well withLiquid Production.

P, = 3,200 psi [22 MP?],30 bbl/MMcf [168 x 10’6 m3 /m3] condensate,5 bbl/MMcf [28.1 X10-6 m3/m3] water,

D= 10,000 ft [304$ m],,4 = 15 ft [4.57 m],

3.0 -

DEPTH = 8000’

2,5 - TUBING I.D. = 2.992”R = 3500 PSI

5‘. 2,0 -&

.

; 1,5

s

: 1.0 -

.5 -

500 1500 2500 3500 4s00

RATE, B/D

Fig. 16—Production vs. various perforated completions.

Perforation kc as%ofCondition k, Formation

Overbalanced with 10filtered salt water

Overbalanced with 10salt water

Underbalancedwith 30

filtered salt waterUnderbalanced

With 30filtered salt water

320-acm [129-ha] spacing,T = 200”F [93”C],k = 0.12 md,

p~h = 100 psig [689 kf’a],hp = 15 ft [4.57 m],-yg = Q.7,

hole size = 8% in. [21.6 cm], andno skin effects.

Evaluate 3Y-, 234-, 2X-, and 1%-in. [8.89-, 7.3-,6.35-, and 3.81-cm] tubing (1.66-in. [4.21-cm] ID)and l-in. [2.5-cm] tubig (1 .@19-in. [2.66-cm] ID) forMS well.

Note in Fig. 18thataU sizes oftubing are too largefortbis particular caseexcept thel.049-in. [2.66-cm]-ID tubing. Unstable flow isindicated bythetubi”gcurves crossing the IPR at a point to the left of theminimnm forthelarger tubimg. The ?.O-in. [2.54-cm]tubing shows stable flow,

The same type of analysis can he made for oil wellsfor various tubing sizes.

500r 79

02~RATE, B/D

Fig. 17—Wel!head nodal plot—flowline size effects.

1758 JOURNAL OF PETROLEUM TECHNOLOGY

Well Inflow und Completion Restrictions. It is veryimportant for operutora, engineers, and managers torecognize inflow restrictions immediately. Somecompanies have arranged their computerized wellrecords to do such things as call up a group of wells inone field in descending-kh-vahe order. In addkion, allother available pertinent information, includlng thelatest test data, cm also be printed out.

Exsmple Problem. Compare predicted perfonnanm toactual oilwell performance.

k = 50 md (cores),h = 30 ft [9.14 m] (logs),

35”API [0.85-g/cm3] oil,casing = 7 in. [17.78 cm],tubing = 2X in. [6.1 cm],

D = 7,000 ft [2134 m],yg = 0.65,

T = 170”F [77”C],

p, = estimated2,400 psi [16.5 MPa], andpwh = 250 psi [1723 k%].

The latest well test shows thk well producing 600B/D [95 m3/d] oil (no water) with a GOR of 400scf/bbl [71.2 std m3/m3 ] (natural flow).

Determine whether this well is producing near itacapacity. It is the engineer’s responsibility to recognizethk well’s potential quickly and to recommendaddkional testing, a workover, a change in tubing, orother action.

A very quick estimate of the productivity index canbe estimated from the product kh in darcy-feet.

2.5 -

2,0 -

~

~- 1.5 -

xL

%1.0 -

,5 -

DEPTH = i 0,00WFwh = 100 PSIR = 3200 PSI30 B/MMCFD COND.

5 B/MMCFD WATER

7

I c , I 10 50 100 150 200 250

RATE, MCFD

Fig. 18—Tubing.diameter effects-weak gas well.

TABLE 2—AOFP,S FOR HIGHER VALUES OF n

AOFP

n (MMscf/D) [m3,,jx, o-5]

0.7 7 20.s 38 110.s5 90 920.9 211 601.0 1,157 32S

A closer estimate can be made from

kh (50)(30) BID=1.56 —,

KOBO = (1,000)(0.8)(1.2) psi

but it requires that PO and 30 are known. One canrecognize that a 35”API [0.85-g/cm3] cmde at 170°F~77°C] with 400 scf/bbl [71 std m3/m3] i“ solutionwill have a viscosity less than 1 and that the productpoBO will be close to 1. Heavy cmdes, of course, willhave high viscosities, and a larger value must be usedin estimating the productivi~ index.

Also, a reasonable estimate at lower pressures ia thatabout 500 psi [3447 kPa] is required to place 100scf/bbl [17.8 atd m3/m3] in solution giving abubblepoint pressure, pb, of 2,000 psi [13.8 MPa].Standkg’s 14 correlation shows the pb to be very closeto 2,000 psi [13.8 MPa] for these conditions. Thispermits a quick calculation of the maximum flow rate.

Jp~%ax=qb+=

..-1.5 (2,000)

= 1.5 (2,400-2,000)+ —1.8

=600+ 1,667

=2,267 BID.

30 r25 -

20 -

$

~- 15 -x&~ 10 -

5 -

.995”

I [ t [ ! ! I I00 500 1000 i 500 2000 2500

RATE, MCFD

Fig. 19—Predicted vs. observed oilwell performance.

OCTOBER 1985 1759

3.0

[~

7UU

2.5 a

,s~%:,fl::.9g5 , } , ;mjMy!’y,: ,>,

0 500 T000 1500 2000 2500 200 400 600 800 1000 1200

RATE, WD

Fig. 20—Wellhead pressure effects on rate—nodal plot.

The IPR curve can be drawn quickfy and the tobingcurve imposed on the sample plot (Fig. 19). Theintersection shows a rate of 760 BID [121 m3Id] ofoil.

The question of whether this well is worth spendingsufficient money to determine why the rate is less thanthe prdcted rate now arises. The source of errorcould be with two. bits of information. Is thepermeability of 50 md (obtained fmm cores) correct?1s there a completion problem? For this well, thepossibility of additional production justifies theexpenditure to ron a buildup test to verify M/yOBoand to check for skin. A high skin may indicate thatfarther testing is needed to determine whether a rnte-sensitive skin exists to decide whether stimulation orteperforating is required.

Restricted Gas Well

Many operatora fail to tecognize the significance ofthe exponent n for gas-well IpR equations obtainedfrom four-point tests. It is common to see expcmentsof 0.7 to 0,8 .or less in gas wells. For exnmple, thefollowing equation was obtained from a U.S. @fcoast well after data were plotted on log-log paper.

c?gm‘@@W(5>oo02–PW2107Mcf/d.

The operntor of tiIs well had a market of 15MMscf/D [424x 10’3 std m3 Id]. Note that tbk wellhas an abso[ute o en-flow potential (AOFP) of 6,984

3PMcf/D [198x 10 m 3/d]. See Table 2 for AOFP’s forhigher values of n.

Obviously, this well has a serious completionrestriction. Sufficient data are nlready available to plotin the form suggested by Jones et al. 4 They suggestedplotting (p, 2 –p ~f 2)/qg,, on the onihwe vs. qg.c on

the abscissa to evaluate the need for opening more

1760

RATE, B)D

Fig. 21 —Pmduction vs. wellhead pressure.

area to flow than to stimniation. Refs. 3 aad 4 providemore details on this procedure.

Effects of Wellhead And Separator Pressure

Specific cases of gas wells and gas-lift oil wells maybe influenced signiftaotly by changes in separatorpressure andior welfhead pressure.

A good plot for both oil and gas wells is adeliverability plot of wellhead pressure vs. rnte and, inturn, separator pressure vs. rate. This plot a.tsocanshow the loading or critical rate and offers immediateselection of rates based on wellhead pressures. Thesample data used to construct Fig. 19 arc used toconstruct Flg. 20 at various wellhead pcessures. FromtMs graph, data are used to consmtct Fig. 21, whichdemonstrates dte well response as a function of surfacepressu~.

Summm_y and Conclusions

NodaJ analysis is an excellent tool for optimizing theobjective ffow rnte on boti oil aod gas wells. Acommon misconception is that often there areinsui%cient data to use thk analysis. Thk is tme insome cases, but mzmy amazing improvements havebeen made with very few data. The use of nodalanalysis has &so prompted the obtaining of additionaldata by proper testing of numerous wells.

Aaother common statement is that there is too mucherror involved in the vmious multiphase-flow tubing orflowfiie correlations, completion formulas, etc., toobtain meaningful resufts. Because of these possibleerrors, it is sometimes dficult to get a pmdlctivenodal plot to intersect at exacdy the same productionrate of the actual well. Even if current conditionscannot be matched exactfy, however, the analysis can

show a percentage. increase in production with a

change, for instance, in wellhead pressure. These

JOORNALOF PETROLEUM TECHNOLOGY

I

predicted possible increases often are fairly accufateeven without an exact match to existing flow rates.

Two detailed illustrations are given in this paper toshow .jhe effect of perforation shot density in bothgravel-packed and standard perforated wells onproduction.

Nodsl analysis has completely altered perforationphilosophy in the U.S. snd has encouraged higher-density perforating and use of open-hole completionswhen practical. One of the most important aspects Ofnodal tiysis is that it offers engineers and managersa tool to recognize quickly those components that an

restricting production rates.Although not discussed in this paper, nodal analysis

is used to optimize all artificial lift methods. 3 Ratepredictions, along with horsepower requirements forsll lift methods, cm be predicted, thereby permittingeasier selection of lift methods.

Finally, some ve~ complex network systems, suchas ocean-floor gas-lift fields (including gas allocationt.omsximize rates) and most economical gas rates, canbe pfedlcted with this procedure.

Nodd analysis, however, should not be usedindkcriminately without the recognition of thesignificance of all plots and the meaning of eachrslationsbip. Engineers should be tmined to understandthe assumptions that were used iR developing thevarious mathematical models to describe wellcomponents. Also, recognizing obvious ermrsndusing practical judgment are necessary. Experience indiffenmt opemting areas can indicate the accumcy tobe expected from various correlations used in nodalmzalysis well models.

NomenclatureB. = FVF, bbl/stb [m3/stock-tank m3]Cl = numerical cnefticientdp = perforation-tunnel diameter, in. [cm]“D = depth, ft [m]e. = .cmshed-cone tlickness, in. [cm].h”=height of pay interval, h [m]

hP =height of interval perforated, ft [m]J= productivity index, B/D/psi [m3/d/kPa]k= permeability

kc = penneabiity ofcmshed zone aroundperforation, md

kf = formation penneabllity, mdLP =length of perfora.tion tunnel, in. [cm]

p = pressure, psi [kPa]P_b ‘bubblepoint pressure, psi [kPa]p, = Kservoirpressure, psi [kPa]

pwf = BHFP, psi [~a]

P ~fi = wellhead pressure, psi [kpa]Ap = pressure difference, psi ma]qb = flOWrate at the bubblepoint, Mscf/D [103

std m3 /d]q~~ = msxirnum flow rate, B/D [m3/d]

cIe = liquid flow rate, B/D [mS/d]

T = temperature, “F [“C]yg = gas gravity (air= 1.0)y,, = water gfavityy. = oil viscosity, cp pa.s]

1,

2

3,

4

5

6,

7

8,

9

10

11

12

13

14

15

16

17

1s

19

20

21

22

Mach, J,, Pmano, E., and Brown, K.E.: “A Nodal Approach forApplying SYSteInSAndysiS to the Flowing and Artificial Lift Oilor Gas Well,,, paper SPE 8025 available at SPE, .Richardson,TX.Giiben, W. E.: ‘, Flowing and Gas-Lift Well Performance,” Drill.and Prod Proc. , API (1954) 126-43.Brown, K,E. et cl,: ‘&Prod.cdm Optimization of Oil and GasWells hy No&f Systems Analysis,>XTechml.g3 of Artificial Lf$Methods, PennWell Publishing Co., Tulsa (1984) 4.Jo”es, L.G. Bloum, E.M., and Glaze, C.E.: “Use of Shofi TermMultipleRateFlowTeststoPredictPerfmmmeofWellsHavingT.I+JUleme,>7paperSPE6133 presented at the 1976 SPE Amma3Technical Conference and Exhibiticm, New Orleans, Oct. 3-6.Crouch, E.C. and Pack, K.J.: ‘&SystemsAnalysis Use for theDesiS” and Evahafim of Higi-Ram Gas Wells,,, paper SPE 9424presented.at the 1980 SPE Annual Technical Confe=?ce and Ex-hibition, Dalfas, Sept. 21-24.Bell, W.T.: “Perforating Underbalanced–Evolving Tech-niques,, >J, Per, Tech. (Oct. 1984) 1653-62.McLead, 33.0. Jr.: “l%. Effect of Perforating Ccmditicmson WellPerformance,,> 3. Per. Tech. (lam 1983) 31-39.Locke, S,: ‘LAnAdvanced Method for Predicting fhe Prod. ctivitjRatio of a Pmfmated Well,,> 3. Per. Tech. (D,,. 19S1) 2481-S8.Hong, K.C.: “Productivity of Petiotated Completions in Forma-tions With or Without Damage,” J. Per. Tech. (Aug. 1975)1027-3% Tram; , AIME, 259.IGotz, I. A.,. Xmeger, R.F., and Pye, D.S.: “EffectofPerfomtionDamage cm WdJ Productivity,,, J. Per. Tech. (Nov. 1974)1303-1% Trans., AIME, 257.Gxay, H.E.: “Verticd Flow Comelation in Gas WeUs,” UserMaumi for API 14B, .Mbswface Conmiled Safety Valve SizinSCbmpurer Program, App. B. API. Dallas (June 1974).Vogel, J.V.: ..Inflow Performance Relationships for Soknion-GasDrive Well s,” J. Pet. J“ech. (Jan. 1968)S3-92 Trans.,AfME,243.Fetkovich, M,J.; ‘.Thc Isochronal Testing of Oil W.Us,’, paperSPE 4529 presented at tie 1973 SPE Annuaf Meeting, Las Vegas,seDL 30-oct. 3,Suindi”g, M.B.: “Inflow Performance Relationships for DamasedWells Pmd.cing by Solution-Gas Drive,, >J. Pet. Tech. (Nov.1970) 1399-1400.Eickmeier, J.R,: *’How to Accurately Predict Future Well Pm-

1968)99.H.: ‘<GeneralInflow Performance

ductilities,,, World Oil (May 1’Dia.-Couto, L.E, and Gobm, NRelationship for Solntion-Gas Reservoir Wells,” J. Per. Tech.(Feb. 1982, ?~~-~~Uhri, D.CPredicts Well Pdmmance, ,S Wmid Oil (Mw 1982) 153-64

-., .-. —.-.. and Blount, E.M,: ,&Pivot Poim Methcd Quickly

Aga@ R.G., A1-H.ssainY, ‘?., and Ramey, H.J. Jr.: ‘.A. In.vemgmon of Wellbore Storage md Ski” Effect in Unsteady Liq-uid Flow: L Amdvtical Treatment. ” Sot. Pet. Em. J. (Sect.1970) 279-9Ll T,&?., AIME, 249.’Agarwaf, R, G., Carter, R.D., and PoRock, C.B.: “Evaluationand Performance Predictim of Low-Permeability Gas WellsS&mdamd by Massive Hydraulic Fracture,,3 J. Per. Tech. (March1979) 362-72 Trans. , AIME, 267.Lea, J. F.: C-AvoidPremamm Liquid fmadi”g in Tight Gas Wellsby Using Pmfrac and Pomfrac Test Da%” Oil ??d Gas J. (Sept.20, 19S2) 123.Me”g, H. M .1.: “Production Systems Analysis of VerticaUyFmctured Wells,’, paper SPHDOE 10S42 presented 81the 1982SPFJDOE Unconventional Gas Recove~ Symposium, Pittsburgh,May 16-18,Greene, W.R.: ‘,Analyzing the Performance of Gas Wells,”Pm,, , 1978 .%utiwestem Petmle”m Shmt Cows., Lubbock, TK(APril 20-21) 129-35.

OCTOBER 19S5 1761

23. Hagedorn, A.R. and Brown, K.E.: ‘?3xperimentd Study ofFmssure Gradients Occurring During Continuous Two-PhaseFlow in SmaJJ-Diameter Vertical Conduits,”. J. Pet. Tech. (April1963J 475-S4 Trans. ANE, .234.

24. Dins, H. Jr. andRos,N.CJ.: “VerticalFlowofGasandLiquidM,xturesin Wells,,, Pro.., gixti World Pet. Cong. (1963) 451.

25, Orkiwcwsti, J.: ‘Wedicdng Two-Phase Prass.re Drops in Ver-tical P,pes,,, J. Pet. Tech. (J.ne 1967) 829-38; Trans., A2ME,240.

; 26, Beggs, H.D, and Brill, J.P.: “A Study of Twc-Phase Flow in In-clined Pipes,, >J. Pet. Tech. (May 1973) 607- 1.% Tram., .41ME,255,

27, Aziz, K., Govicr, G.W., and Fogammsi, M.: ‘%essure Dmp inWells Producing Oil and Gas,,, J. Cd.. Pet. Tech. (July-Sepl.1972). 38-d8

28.

29,

30.

31,

. ..-.,..Dukkr, A, E. et .[.: ‘‘Gas-Liqoid Flaw in Pipelines, 1. ResearchResults, ” AGA-API Pmjmt NX-28 (May 1969).Du!der, A.E. and Hubbard, M. G.: “A Model for Gas-Liquid SlugFlow in Horizontal and Near Horizontal Tubes,” Ind. and Eng.Chen. (1975) 14. No. 4.33747.Eaton, i. A.’ et il.: “The Predction of Flow Paftems, LiquidHoldup and Ptessure Losses Occurring During Continuous TwG-Phme Flow In HorizontalPipelines,,, J. Pet. .Tt-ch. (June 1967)

m,. , A3ME, 240.M,H. and Smith, R.V.: “Practical Solution of Gas-

815-28; TraCuUen&r, hFlow Equations for Wells and Pipelines witi Large TemperatureGradients,’, J. l+v. Tech, (D... 1956) 281-8R Tmm., A2ME,207.

32. Poeimmnn, F.H. and Cmpenter, P.G.: “The Muldpbase Flow ofGas, Oil and Water Through Verdcal Flow String wilh Appliw.-tion to the Designof Gas-Lift Installations,” Drill. and Prod.Pm,., API (1952) 251-317,

APPENDIX A

Inflow PerformanceInflow performumc is the ability of a well to give upfluids to the welJbore per unit drawdown. For flowingand gas-lift wells, it is plotted normally as stock-tunkbarrels of liquid per day (abscissa) vs. bottomholepressure (BHP) opposite the center of the completedintend (ordimte). The total volumetric flow rote,includlng free gas, can also be found with productionvalues and PVT data to cdcuIate, for instartce, a totalvolume into a pump.

Brown et al. has given detailed example probIemsfor most methods of constmcting IPR curves. Nothing,however, replaces good test data, and manyprocedures, in fact, do require from one to fourdlffemnt test points—that is, a stabl@ed rate andconesponding BHFP, as well as the static BHP, arcusually a minimum requirement for establiahlng agood IPR.

IPR Methods for Oil Wells

For flowing pressure above the bubblepoint, test tofind the productivity index, or cnlculate theproductivity index from Darcy’s law.

For two- base flow in a reservoir, apply Vogel’s?procedure 1 or Darcy’s law using relative

permeability data.For reservoir pressure greater thau bubblepoint

(P, >P~) and BHFp above or below the bubblepoint,use a combination of a straight-line productivity indexabove pb and Vogel’s 12 procedure below.

1762

.

The Fetkovich procedura 13 requifes a three-or fom’-flow-rate test plotted on log-log paper to determine snequation in the form of a gas-well backpressureequation with a coeffkient and exponent determinedfrom plotted data. This is equivalent to armlysis of anoil well with gas well relationships.

%audmg’s 14 extension of Vogel’s wmk accom3ts forflow-efficiency values other than 1.00. Jones et al. ‘s4procedure will determine whetier sufficient mea isopen to flow.

Futnre IPR Curves

The prediction of future IPR curves is critical indetermining when a well will die or will load up orwhen it shoufd be placed on artiticid lift. ThefoUowing procedures can be used (1) Fetkovich 13procedure, (2) combination of Fetkotich and Vogel’sequation, IS (3) Couto’s 16 procedure, and the (4) PivOt

point method. 17

Transient IPR Curves

Oil or Gas WeIIs. A time element allowing fheconstmction of IPR cmves for transient conditions canbe brought into Darcy’s law. This is important insome wells because of the long stabfiza.tion time. (SeeRef. 3 for discussions by several authors.)

Fractured Oil and Gus Wells. The constmction ofIPR ctnves for fractured oil or gas wells has beentreated in the literature by Agsfwal et al., 18,19Lea, 20and Meng. 21 Fractured wells can show flushproduction initially but drop off considerably in rate atfuture timex.

IPR Methods For Gas Weffs. GenemIIy, a three- orfour-flow-fste testis required for a gas weJl fromwhich a plot is made on log-log paper and theappropriate equation derived.

q=cl(P2–PL”fV

where q is the mte of flow, Cl is a numericalcoeftkient, characteristic of the particular well, p, isthe shut-in rcse~oir pressure, p .f is the BHFP, and nis a numerical exponent that is characteristic of thepsrticxdw weJL (See Ref. 22 for a discussion on gaswell pefionnance). Also, Darcy’s law can be used,and the turbulence terms should always be included6for all but the lowest rates.

Fructured and transient wells have Alsobeen treatedin the literature.

APPENDJX B

Muftiphase Flow Correlations

The use of multiphsse-flow-pipeline pressure-dropcorrelations is very important in applying nodalanalysis.

The corrclationa that am most widely used at thepresent time for vetical multipbase flow were—

JOURh’AL OF PETROLEUM TECHNOLOGY

developed by Hagedorn and Brown, 23 Duns smdRos, M Ros modification (Shell Oil Co., unpublished),Orkizewski, ~ Beggs and BriU,26 snd Aziz. 27 Thesecorrelations calculate pressure drop ve~ well in certainwells snd fields. However, one may be much betterthan the other under certain conditions, and fieldpressure surveys are the onfy way to find out. Withoutknowledge of a particular field, we would recommendbeginning work with the correlations listed in theabove order.

Horizontal MuIti haae-Flow Pipeline CorreIationa.?Beggs and Brill, 2 Dukler et al., 28 Dukler snd

Hubbard, 29 Eaton er al., 30 and Dukler using Eaton’sholdup28,30 nre the best horizontal-flow correlations.Again, we recommend to begin work using them inthe order given.

Vertical Gas Flow. The procedu~ by (ldlender andSmith 31 and Poettmann aud C~enter32 arerecommended for gas-flow calculation in wells.

Wet Gas Wefla. We recommend the Graycorrelation 11 for wet gas wells.

S1 Metric Conversion Factors

bbl X 1.589873 E–01 = m3cu ft X 2.831 685 E–02 = m3

ft X 3.048* E–01 = min. x 2.54* E+OO = cmpsi x 6.895757 E+OO = kPa

-conversion tam, i, exact. Jr’l-Origlml man”s+t (SPE 14714] r%,bed in the SOcieV d Peto[eum Engineef$ .f.tic, Aug. 19, 19S5,

. .

OCTOBER 1985 1763