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SPE 14121

Production Optimization Using a Computerized Well Modelby J.F. Lea, Amoco Production Co., and K.E, Brown, U of TulsaSPE Membars

CW@Jht1SSS.Sooii ofPetroleumErI@neefeTM PSFUwssprewued lt theSPEwzs InwmstbnalMsethgonPetroleumE@teeringheldinseiiing,CMnaMarch17-20.1SSS.~ matwidis-m~timmsti. pmmidoa tocopyisrestrktadtoanabshct ofnotIWSIthan300wrds. WriteSPE.P.O.BoxS33S2S,RWwdson.loses 7Z@23WS.Telex720SSSSPEDAL

Many oil and gas weLls may be producing at rates 5. To analyze each component in the wel 1 system towhich appear to be optimum but which actually con- determine if it is restricting the flow ratetain unnecessary restrictions to flow. These wells unnecessarily when compared to the flow capaci-can be anaLyzed using modelling techniques to eval- ties of the other system components.uate all components of l producing well system.Often this procedure will identifypossiblemodifi- 6. Overall, this permits quick recognition by thecations in the well which if made will result inlarger flow rates. This method described is often

operatorsmanagement and engineering staff ofways and means to increase production rates.

referred to as Modal* AnaLysis. All componentti This is l very important feature of being ablestarting lt the static reservoirpressurelnd ending to graphically display the wells performanceat the separatorare evtluated if present. This mayinclude inflow performance,flow acroas the compLe-

with production optimization or Nodal* Anal-

tion, flow up the tubing string including lny down-ysis Techniques.

hole restrictions,safety valves, flow across the Thre lre numerous oil lnd gas wells lround thesurface choke (if lpplicable) and flow through hori- world that have not been optimized to achieve anzontal flow lines and into the separation facili- objective rate in an efficient manner.ties.

In fact,many may have been routinelycompleted in a manner

The objectives of well analysis are ls follows: such that their maximum potential rate cannot belchieved. Also, many of the wells pLaced on lrtifi-1. To determine the flow rate lt which l well wiLl

cial lift lre not lchieving the efficiency that maybe possible.

produce with a given wellbore geometrylnd com-pletion (first by natural flow). The production optimization of oil and gas

2. To determine under what flow conditions l wellwalls using computerized well modeLs has contributed

will cease to produce. This can be related toto improved completion techniques, better lffi-eiency, lnd higher production with many wells.

time as the reservoirdepLetes.This

type of anaLysis was proposed in a classic paper by

3. To select the most economical time for theGilbert* in 1954, however its use has not beenextensive until recent years. One principal reason

installation of lrtificial lift and to aasist for this was the changing of aLlowable producingin the selectionof the best artificial lift rates. Another reaaon has been the developmentofmethod. computer technology allowing rapid calculation of

4. To optimize the well conditions and geometrycompLex algorithm lnd lasily understood input lndoutput .

system in order to most economically producethe objective flow rate. Past conservationpractices in the U.S. led to

the use of 2 (5.08 cm) lnd 2-1/2 (6.35 cm) tubinglnd 6 shots per foot for perforating. Larger tubing(4-1/2 (11.43 cm) and 5-1/2 (13.97 cm)) and 16

References lnd illustrations at and of paper.shots per foot lre not uncommon today when higher

~radamark of FLopetrol-Johnston/Schlumberger-usedrates lre allowed.

by permission. J. Mach selected the word Uodalwhich was first used in the SPE paper 8025.1

77

2 PRODUCTIONOPTIMIZATION USING A CONPUTSRIZEDWELLHODEL 14121.

Although allowing increased flow rates in high 2. At the top of the well (wellhead). This iso-productivity wells has popularized well optimiza- Lates the flow line or the effects of surfacetion, it is, nevertheless, an excellent technique tobe used on low rate wells (both oil and gas) lad on

preBsure on production.

lll lrtificial lift wells. Some of the greatest 3. Differential pressure solutions (Ap) across thepercentage increases in production rates haveoccurred in low rate oil wells (from 10 to 30 bbl/D

completion interval in order to evaluate the

or 1.59 to 4.77 ts3/D) and low rate gas wells (fromeffect of the number of perforation on produc-

50,000 scf/D (L416 m3/D) to 100,000-200,000 scf/Dtion in l gravel pack or standard completion.

(2832-5663 q3/D)). Numerous gas wells have had 4. Solutions lt the separator - This is importantldjustments in tubing sizes, surface pressures, with gas lift wells.etc.~ to prolong the onset of liquid loading prob-

Thi8 isolates the effect

lams. Optimization techniques can be used to esti-of separator pressure on production.

mate the benefits of such proposed changes before 5. Other Locationa for graphical solution can bethey lre made. at:

One of the most important aspects of well anal- (a) Surface chokes,ysis is to offer recognition of those wells that can (b) Safety valves,produce lt rates higher than the current rate. (c) Tapered string connection points, orOptimization techniques can serve ls an excellent (d) Downhole restrictions.tool to further verify that a problem exists lndindicate that additional testing is in order. For It is very important that the user understandsexample, assume that l well is making 320 bbl/D(51 m3/D) of oil.

how pressure-flow components of the well are groupedApplying well imdelling lnalysis

to this well shows it capable of 510 bbl/Dto form l graphical solution at an analysis point or

(81 m3/D). This difference may be attributed tonode point. For example,. if the solution is

several factors. The objective of production opti-graphically displayed for bottomhole conditions(center of completed interval), then the reservoir

qization methods is to find out that component ofthe well that is restricting the rate below the max-

and the completion effects can be completely iso-

i~ pssible. ~~wever, it ISZy also be found thatLated and lnalyzed separately from the entire well

incorrect data is ihe cauae of the predicted higherpiping lnd production system.

rate. A basic requirement for well analysis is tobe lble ta definz the currentwell inflow perfo-

Caution should be taken in neglecting aven 200to 300 ft (60 to 90 m) of casing flow from the

ante relationship (IPR). Accurate weLL te$t datamust be obttined and the proper IPR model appLied

center of the completed interval to the bottom of

for successful analysis. Then mathematical modelsthe tubing. The larger pipe, due to lower veloci-ties, may not be flushed out with produced fluids.

of other well components can be used to complete the It can be quite unexpected to still find this largepredicted well performance. section of pipe still partielly full of completion

Fig. 1 shows components that make up a detailedfluide (water and mud) even though the well may be

flowingwell system. Startingfrom the reservoirproducing near 100% oil. A major company recently

and proceeding to the separator, the componentspressure surveyed a well producing 1600 bbL/D(254 m3/D) of oil up 2-710 (7.3 cm) tubing.

shown here are (1) reservoirpressure,(2) well pro-ductivity, (3) wellbore completion, (4) tubing

Because of l casing deviation, tubing was set1000 ft (305 m) off bottom in the 11,000 ft (3353 m)

string, (5) possible downhole restrictive device,(6) tubing, (7) safety valve, (8) tubing,

well. Both water lnd mud were found in the 7

(9) surface choke, (10) flowline, and(17.8 cm) casing below the tubing lven though the

(11) separator.well produced 100% oil. A cleaning out of this wellincreased the rate to over 2000 bbl/D (318 m3/D) of

In order to optimize the system, each componentoil. Thie shows one type of Limitation of well

must be evaluated separately and then the entireanalysis using tubing preesure drop calculations toestimata l flowing bottomhole pressure. In this

group of components combined to evaluate the totalwell producingsystem. The effects of changing any

case, the analysis showed that the rate should be

one component on the entire system is very importantgreater and hence served es a diagnostic tool. This

lnd can be graphically dispLayed using well anal-prompted the running of l pressure traverse. In

ysis. Some limited discussion on the IPR componantmany cases this is typical where well lnalysis pred-

is covered in Appendix A, lnd multiphase flow pres-icts what rate should be possible, and the operator

sure drop correlationsfc pipe~ *-s discussed inis advised to Look for problems if the well is pro-

Appendix B.ducing well below a predicted production rate.

The most coimmon Locations for production opti-sxAnPLes

mization graphical solutions are: A l~mit?~ f ezamples lre presented,howevera num

1. At the bottom of the well at the center of the ature. 5.es llso appear in che liter-

producing interval. This isolates the weilsinfLow performance. Two subjects i.~.e been selected for examples:

78

14121 JAMES F. LEA ANDKERMIT E. BROW 3

1. The effect of the downhole completion on flowrate is illustrated. ti example solutionforboth l gravel packed well and a standard perfo-rated well is presented. Procedures to opti-mize the completions lre outlined.

2. Quick recognition of those wells having agreater predicted potential than the presentproduction rate is covered. These situationsmay be due to l restriction in one of the cowponents in the system.

cRAVEL PACKED OIL ANDGAS HELLS

A paper presented by Jones, BLount and Glazeseemed to have been the catalyst to start operatorsto look more closely at their gravel packed comple-tions. This is an excellent paper for study lndalso suggests proceduresfor determiningwhether ornot a wells inflow capability is restricted by lackof area open to flow or a skin effect due to mudinfiltration, etc. For backgr~und materiaL, see thesunz8ary by Ledlow and Cranger.

A graphical procedure for analysis of a graveLpacked well with l sequence of figures, is presentedhere. Additional details, references and equations,etc., can be found in Reference 3.

The following procedure is for either an oil orgas well with the solution plotted at bottomholeconditions:

1.

2.

3.

4.

5.

6.

Prepare the node inflow cuwe (IPR curve,Fig. 2). (Assumes no Ap across completion.)

Prepare the node outflow curve (tubing intakecurve, Fig. 3). This is the surface pressureplus the tubing pressure drop plotted ls afunction of rate.

Transfer the differential pressure lvailablebetween the node inflow and node outflow curveon the same plot (Fig. 4) to a &p curve.

Using the appropriate equations,34 calculatethe pressure drop lcross the completion forvarious rates. Numerous variables have to beconsidered here including shots per foot,gravel permeability, viscosity lnd density ofthe fluid, length of the perforation tunnel forlinear fl~w, etc. Add this Ap curve on Fig. 4as noted in Fig. 5.

Evaluatethis completion (Fig. 5) to determineif the objective rate can be achieved with anlccepted differential lcross the gravel pack.Opinions differ some on accepted Ap values. Areasonable maximum lllowable Ap that has givengood resuLts is from 200 to 300 psi for singlephase gas or liquid flow. Most operators willdesign for lower Aps for multiphase flwlcrosa the pack.

Evaluate other shot densitiesor ~rhaus otherhole sizes until the lppropriate hp is-obtainedlt the objective rate (Fig. 6). Perforationefficiencyshould be consideredat this time.

A good paper for review on perforatingtechniques was given by Bells pointing outfactors as the number of effective holesexpected and the effect of casing strengthhoLe sizes.

such

on

7. The Ap lcross the pack can be included in theIPR curve as noted in Figure 1.

EXAIIIPLEPROBLBN- Possible U.S. Gulf Coast Well withGravel Pack:

Given Data:

~r = 4000 psi (27576 kPa)Depth = 11,000 (3352 m)k = 100 md (.1 pm2)h = 30 ft (9.1 m) (pay intervaL)h = 20 ft (6.1 m) (perforated interval)g?avel pack sand: 40-60640 lcre (2589952 mz) spacing8-5/8 (21.9 cm) casing10-3/4 (27.3 cm) drilled holeyg = 0.65Screen Size - 5 (12.7 cm) O.D.Sales line pressure= 1200 psi (8273 kPa)Short flow line.

This well is to be gravel packed. Tubing sizeand number of shots per foot using l tubing conveyedgun fired underbalanced lre to be evaluated. Thelssumption is made here that due to the unconsoli-dated formationthere are no low permeability zonesaround the perforations. That is, sand immediatelyflows into lll perforated holes until proper~y pre-packed.

SOLUTIONPROCEDURE- Gulf Coast Well

10

2.

3*

4.

5.

The IPR curve is prepared using Darcys lawincluding the additional turbulence pressuredrop. (Fig. 8)

Tubing sizes of 2-7/8 (7.3 cm), 3-1/2(8.89 cm) and4-1/2 (11.43 cm) are evaluatedat a wellhead pressure of 1200 psi (8272 kPa)needed to flow gas into the sales line. Fromlnalysis of Fig. 9, 4-1/2 (11.43 cm) tubing isselected. Note that market conditions permit-ting, much higher rates could be projectedassuming ldequate sand control is possible.

Transfer the Ap es shown in Fig. 10. This isthe Ap lvailable lcross the gravel pack.

Using equations proposed by Jones, et ll.,calculate the Ap lcross the pack for .75(1.905 cm) dia. holee with effective shots perfoot of 4; 8, 12 lnd 16. (Fig. 11)

Figs. 11 lnd 12 show the final two plots indi-ca~ing that 16 SPF lre neeessary to obtain a Apof about 300 psi (2068 kPa) at a rate of58.5 HNSCF/D (1656603 m3/D). Additional perfo-rations could bring this below 200 psi(1379 kPa).

79

6. In order to properly bring this well on produc-tion, one more plot such as Fig. 13 should bemade with several wellhead pressures includedso that Ap across the pack can be watched byobserving rate lnd wellhead pressure. Thisprocedure is described by Crouch and Pack,s andBrown. 3

NODALANALYSISTO EVALUATEA STANDARDPERFORATEDHELL

In 1983 HcLeod8 published a paper that helpedto emphasize analysis of completion practices onnormally erfmated wells. Several prior publica-

!tionslOl 12 had discussed this topic, but thispaper seemed to have increasedinterestin thisarea. This procedureis presented in Reference3with some suggestedmodifications.

The procedure is similar to that offered forgravel packed wells, except that the lqu~tions usedfor calculating pressure drop lcross the perforatedcompletions have been lltered to model flow througha perforation surrounded by a low permeability zone.The basic concepts suggested by Jones, et al., forgravel packed wells are incorporated into the soLu-tions.

PROCEDUREANDEXAMPLEPROBLEIII- PERFORATEDWELL.

An oil well will be lnslyzed with l low GOR andhence low bubble point pressure resulting in flow ofa single phase liquid acrose the completion. Tech-nology has so far only offered soLutions for singlephase flow (gas or Liquid) across such completions.Uben two-phase flow occurs across lither l gravelpacked or l standardperforatedwell, relativepermeabilityeffects muet then be consideredalongwith ldditional turbulence and energy losses.

McLeod6 noted that most of the pressure drop ina gas well occurs across the compacted zone lt theperforation wall due to turbulence. lhs wo-ked a gaswell example in his paper showing that 90% of thetotal Ap lcross the completion was in fact due toturbulence lcross the lpproximate 1/2 (1.27 cm)thick compacted zone. Pressuredrop in oil wellcompletionsmay be found to be due to laminar orDarcy Losses. Refer to his paper and other refer-ences= for details.

To use HcLeods technique, the crushed zonethickness and permeability (k ) must be estimated aswell ls the perforation tunnef diameter lnd length(Lp).

Due to the many input variables required, thisanalysis technique can only be approximate and indi-cate trende. Future research in this area is neededto enhance the accuracy of solutions.

SXANPLEPROBLEN- Perforated Oil Well

~r = 3500 psi (24129 kPa)80 lcre (323744 m2) spacingDepth = 8000 ft (2438 m)5-1/2 casing (13.97 cm)36 API oil8-1/2 hole (21.S9 cm)SolutionGOR = 180 scf/bbL (32 m3/m3)Lp =4 (10.16 cm)

(see Table 6, Ref. 6 for tabulatedvalues )

Crushed zone thickness aroundperf. tunnel =0.5 (1.27 cm)yg = 0.7P = 800 psi (551S kPa)hb= 30 ft (9.1 m)h = 20 ft (6.1 m)Pp = 140 psi~ (965 kPa)Tw~ 180F (82 C)

PROCEDURE

1. Prepare the node inflow curve (IPR curve) usingDarcys Law and lssumingno additionalApacross the completion.

2. Plot the outflow curve (tubhg intake) for2-3/8 (6.03 cm), 2-7/8 (7.3 cm) and 3-1/2(8.89 cm) tubing. This is the pressurerequired lt the bottom of tubing for flowthrough the tubing. Steps 1 (IPR) and 2(tubing intake) lre shown in Fig. 14. Assume3-1/2 (8.89 cm) tubing is selected.

3. Transfer the Ap curve ls shown in Fig. 15.

4. Using the appropriate lquations from NcLeod8(and ls discussed by Brown3), determine Apacroea the completions listedTable I.

Examination of Fig. 16 shows the effects ofperforating underbalanced on production. The bestfluids and perforating techniques should be used.

RECOGNITIONOF COMPONENTS CAUSINC RESTRICTEDFLOURATES IN A WELL

1. EXAHPLE PR08LSN - Analysis of Flow-LineCapacity:

The followingwell is on gas lift

~~t~ ~ ft (2438m)2-718 (7.3 cm) tubingP = 2100 psi (14477 kPa)56% water (S = 1.07)Well test: ~00 bbl/D (80 m3/D)

@1740 pai (12072 kPa)Solution GOR = 300 scf/bbl (53 q3/m3)P = 2400 psi (16545 kPa)S&rator Pressure = 60 psig (413 I@a)Cas gravity = .7Flowline: 4000 ft (1220 m)

2-1/2 I.D. (6.35 cm)

80

16121 JAHES F. LEA AWDKERMIT E. BROWW 5

Sufficient gas pressure is available (2000 psi, tubing curves crossing the IPR at a point to the13788 kPa) to inject gas near the bottom lnd a total left of the minimum for the Larger tubing. The 1.0GLR of 800 scf/bbl (143 m3/m3) is maintained for gas (2.54 cm) tubing shows stable flow.lift. It is suspected that the flowline isrestricting the rate. Uith analysis techniques pro- The same type of general observations can begreimsed, l graphical solution can be quickly gener- made for oil wells for various tubing sizes.ated lt the wellhead analysis location.

3. Uell Inflow and Completions Restrictions:Examination of the results in Fig. 17 indicate

that the flowline is indeed l restriction. This is It is very important for operator engineers andevident by noting that the pressL~re loss in the management to insaadiately recognize inflowflowline (2-1/2 (6.35 cm) I.D.) shows a significant restrictions. Some companies have arranged theirincrease in pressure loss with rate and therefore computerized well records to do such things asangles sharply upwards lt the intersection point call-up a group of wells in one field in the ordarbetween the two curves shown. The intersection of descending kh vaLues. In addition, all otherpoint (of the pressure required at the flowline available pertinent information can also be printedintake, and the IPR pressure minus pressure drop in out including the latest test data.the weil from the sandface to the wellhead) is thepoint of predicted flow from the well. By way of example, the following data was

printed out for an oil well.A 3 (7.62 cm) and 4 (10.16 cm) flowline is

then evaluated on the same plot. As soon as the EXAMPLE PROBLEH - Compare Predicted to Actual Oilslope of the flowline intake pressure vs rate Well Performance:becomes small, showing very little increaeeof Apwith rate, then the flowline diameter is suffi- k = 50 md (50x10-3pm)(from cores)ciently Large. It should not be oversizedsince h = 30 ft (9.14 m)(Logs)excessive slugging lnd heading may occur. some Caaing = 7 (17.78 cm)operators may add l parallel line instead of Tubing = 2-3/8replacing the current line with l larger size. API = 35

2. Restriction Due to Incorrect Tubing SizetDepth l 7000 ft (2134m)P = 2400 psi (16545 kPa)% = 250 psi (1723 kPa)The tubing may be either too large (causing Yg = .6?

unstable flow) or too smell (reducesflow rate). T= 170 F (76C)This can be ismadiately recognized on a nodal plot.This ie importantin high rate gaslift wells as well The Latest well teat shows this well producingla Low rate gas wells. 600 B/D (95 IS3/D) oil (no water) with l GOR of

400 SCF/B (71.2 m3/m3) (Hatural flow).A weak gas well is chosen to show how to recog-

nize when the tubing is too large and Loading will Question: Is this well producing near itsoccur. The Gray correlating is used and is recomr capacity? It is the engineers responsibility tomended for use in calculating tubing pressure dropa quickly recognize this wells potential and toin gas wells producing some liquids. recowsend: (1) ldditional testing, (2) a workover,

(3) a change in tubing size, or (4) other action.BXAHPLE PROBLBW- Weak Gas Well with Liquid Produc-tion: A quick estimate of the PI (Productivity Index)

can be estimated from the product kh in Darcy feetPr = 3200 pai (22348 kPa)k = .12md (.12x1O 3PM)

lnd is

30 bbL/HMCF (1.7x1O-4 m3/m3) coi!denaate5 bbl/?DfCF (2.8x1O-5 m3/m3) waterDepth = 10,000 ft (3048m)

~= 50(30) . ~c5 bbl/D or ~.0345 &blm ~ kPa

pwh = 100 psig (689 ItPa)h = 15 ft (4.57 l)h = 1S ft (4057 n) MlA closer estimate can be made fromyi = .7 porno

lnd is

320 lcre (1294976 m2) spacinghoLe size = 8-1/2 (21.6 cm) (50)(30)

* (or .0359 ~aT = 200F (93C)~1000)(.8)(1.2) = 156 PS1 a, but

Wo skin affectarequires that v and B be known. One can recognize

gvaluate 3-1/2, 2-7/8, 2-3/8 lnd 1-1/2 (1.66I.D., (4.21 cm)) and 1 (1.049 I.D., (2.66 cm))

that l 35 API $rude l? 170F (76.6C) and with400 SCF/B (71 q3/m3) in solution will have a vis-

tubing for this wLI. cosity Less than one lnd chat the product of v Bwill be close to 1. Heavy crudes, of course, ~i?l

Note from Fig. 18 that all sizes of tubing lre have higher viscosities.too Lsrge except the 1.049 (2.66 cm) in this par-ticular caee. Unstable flow is indicated by the

81

--. .-. .------ ------ ----- ., .-.

6 PRODUCTIONOPTIMIZATIONUSING A COMPUTERIZEDWELL HUDEL 141Z1

ALSO a reasonable estimate at lower pressuresis that approximately 500 si (3447 kPa) is required

?to place 100 SCF/B (17.8 m /m3) in solution giving abubble point pressure of 2000 psi (13788 kPa).Standings correlation shows the bubble point, Pb, tobe close to 2000 psi (13788 kPa) for these condi-tions. This permits an estimate. of the maximum flowrate to be:

Obviously, this well has a rather seriouscompletion restriction. This well can also be ana-lyzed by plotting data in che form suggested byJones! et 41.4 They suggest plotting

J Pb 1.5 (2000)q = 1.5 (2400-2000) + ~ s on the ordinate vs q on the abscissa to evaluatemax = qb + 1,8 . 8 Sc

q = 600 + 1667 = 2267 bbl/Dor (360 m3/D)max

The IPR curve can be quickly drawn and thetubing performance imposed upon the sample plot(Fig. 19). The intersection shows a rate of 760 B/D(121 m3/D) of oil.

The question now arises - is this well worthspending sufficient money to determine why the rateis less than the predicted rate? The source oferror could be with two bits-of information. Is thepermeability of 50 md (5OX1O 3~m) (obtained fromcores) correct and~or is there a completion problem.In this instance the possibl~ additional productionappears to justify the expenditure to run a build-uptest to verify kh/poBo lnd to check for skin. Ahigh skin may indicate further testing is required.The skin may or may not be rate sensitive whichhelps decide if stimulation or re-perforating isrequired.

RESTRICTEDGAS HELL:

It is possible to fail to recognize the signif-icance of the exponent n for gae well IPR equa-tions obtained from G-point tests. It is notunusual to see exponents of .7 to .8 or Less in gaswells.

For example, the following equation waeobtained from a gas well after plotting data onlog-log paper.

.7= 0.0463[(5000)2 - Pwf2]qgsc , UCFD

The operator in this case had a market of 15 BINSCF/D(424770 n13/D). Note that this well has an AOFP of6984 HCF/D (197773 m3/D).

The follawing AOFPs exist for higher values ofn:

n AoFe (t41iscF/D) (m3/D x 10-5 at SC)

.7 7 (2)

.8 38 (11)

.85 90 (92)

.9 211 (60)1.0 1157 (328)

the need for op;~~ng more area to flow as comparedto stimulation.

EFFECTS OF WELLHEAD AND SEPARATORPRESSURE

Specific cases of gas wells and gas lifted oilwells may be influenced significantly by changes inseparator pressure andlor wellhead preesure.

A good plot for both oil and gas wells is adeliverability plot of wellhead pressure vs rate andin turn separator pressure vs rate. This type plotcan also show the loading or critical rate andoffers immediate selection of rates based on well-head pressures.

SUUHARYAND CONCLUSIONS

Well analysis is ln lxcellent method for indi-cating how to obtain the objective flow rate on bothoil and gas wells. A conmon comment is we justdont have lnough data to use this lnalysis. Thisis true in some cases, but it is lmazing theimprovements in wells that have been made beginningwith very little data. Analysis has llso promptedthe obtaining of ldditionaL data by properly testingnumerous wells.

Another concern is that there is too much errorinvolved in the various multiphase flow tubing orflowline correlations, completion formulas, etc., toobtain meaningful results. Because of these pos-sible lrrors, sometimes it is difficult to get apredictive well lnalysis plot to show an intersec-tion lt the exact rate le the well is currentlybeing produced. However, even if current productioncannot be matched exactly, the analysis can show apercentage increase in production with l change, forinstance, in wellhead pressure or tubing size.Often these predicted possible increases are fairlyaccurate even without an exact match to existingflow rates.

Two detailed examples are given in this paperto show the effect of perforation shot density inboth gravel pac!ked and standard perforated wells onproduction.

Computerized well analysis has completelyaltered perforation philosophy in the U.S. and hasprompted ldditional open hole completions for bothgravel packed lnd nongravel packed wells. One ofthe most important lspects of Nodal type lnalysisis that it offers supervisors and managers a tool tolnow quick recognition of those components that arerestricting production rates.

14121 JAMES F. LEA AND KERMIT E. BROWN 7

REFERENCES

Although not discussed, this type of analysis 1. Hach, Joe, Eduardo Proano and Kermit E. Brown,is used to optimize all artificial lift methods. A Nodal Approach for Applying Systems AnalysisFlow rate lnd horsepower requirements for all lift to the Flowing and Artificial Lift Oil or Gasmethods can be predicted permitting easier selection Hell, SPE 8025.of a lift method.

2.Finally, complez pipe network systems such as

Gilbert, W. E., Flowing and Gas-Lift Well Per-formance, API Drilling and Production Practice

ocean-floor gas lift fields including gas allocation (1954), p. 126-143.to maximize rates and most economical gas rates canbe modelled using this procedure. 3. Brown, K. E., et al., Technology of Artificial

Lift Rethods Volume 4 Production OptimizationHowever, system analysis should not be used of Oil and Gas Wells by Nodal Systems Anal-

indiscriminately without recognizing the signifi- ysis, Pennwell Publishing Co., Tulsa, OK,cance of all plots and what each reLationship means. 1984.Engineers should be trained in understanding theassumptions that were used in developing the various 4. Jones, Loyal C., E. II!. Blount, and C. E. Glaze,mathematical models. to describe well components. Use of Short Term Hultiple Rate Flow Tests toAlso, it is necessary to be lbLe to recognize Predict Performance of Wells Having Turbu-obvious error and use practical judgment as lppLi-

Experience in different operating areas canLence, SPE 6133, SPE of AIllE, October 3-6,

cable. 1976.indicate the accuracy to be expected from variouscorrelations used in well analysis models. 5. Crouch, E. C. and K. J. Pack, Systems Analysis

Use for the Design and Evaluation of High-RateNOMENCLATURE Gas Wells, SPE 9424, SPE of AIMI, Sep-

Bo - Formation volume factor, bbl/stk tank bbltember 21-24, 1980.

6. !fcLeod, Harry O., Jr., The Effect of Perfo-GLR - Gas-liquid ratio, scf/bbL rating Conditions on Well Performance, JPT

Cm - Gas-oil ratio, scf/bbloil(January1983).

7. Firoozabadi,A., lnd D. L. Katz, An Analysish- Height of pay interval, ft of t(ighVelocityGas Flow Through Porous

Media, JPT (Pebruary 1979), p. 211-216.hp - Height of interval perforated, ft

8. Bell, W. T., Perforating UnderbalancedIPR - Inflow performance relationship Evolving Techniques, JPT, (Ott. 1984)$

k,kf - Permeability, formetion Pa-ability, ISAp. 1653-1662.

9. Gray, H. E., Vertical FLOWCorrelation in Gaskc - Permeability of crushed zone lround perfora- Wells, User Manual for API 14B, Subsurface

tion, md Controlled Safety Valve Sizing Computer pro-

L - Length of perforation tunnel, in.grea, App. B, (June 1974).

P 10.P- Presaure, psi

Locke, S., An Advanced Method for Predictingthe Productivity Ratio of l Perforated Well,JPT, (ikCo 198i), p. 2481-2488.

Wh - Wellhead pressure,psi11. Hong, K. C., Productivity of Perforated Com-

b - Bubble point pressure, psi pletions in Formations With or Without Damage,JPT, (Aug. 1975), p. 1027-1038.

- Gas flow rate at standard correlations, HSCFD%8C 12. Klotz, J. A., R. F. Krueger, D. S. PYe, Effect

qgof Perforation Damage on Well Productivity,

- Liquid flow rate, bbi/D JPT, (~Oo 1974), p. 1303-~314.

s - Water gravityw 13. Vogel, J. V., Inflow Performance Relationship

for Solution Cas Drive Wells, JPT,T- Temperature, F (Jan. 1968), p. 83-93.

Ap - Pressure difference,psi 14. Fetkovich,M. J., The Isochronal Testing ofOil Wells, SPE 4529, 1973, by If. J. Fetkovich.

Yg -Caa gravity (air = 1.0)Standing, H. B., Inflow Performance Relation-

Oil viscosity, cp1s.

P. - ships for Damaged Wells Producing by SolutionGas Drive Reservoirs, JPT, (Nov. 1970),p. 1399-1400.

.83-

.8 PRODUCTIONOPTIMIZATION USING A COMPUTERIZEDWELLNODEL 14121

16. Eickmeier, J. R., HOWto Accurately Predict 30 l Dukler, A. E., et al., Gas-Liquid Flow inFuture Well Productivities, World Oil, Pipelines, I. Research Results, AGA-API Pro-04ay 1968), p. 99. ject UK-28, (Hay 1969).

17. Dias-Couto, Luiz Evanio and Hichael GoLam, 31. Dukler, A. E., and H. G. Hubbard, A Hodel forGeneral Inflow Performance Relationship for Gas-Liquid Slug Flow in Horizontal and NearSolution Gas Drive Reservoir, JPT, Horizontal Tubes, Ind. Eng. Che., Fund.,(Feb. 1982), p. 285-288. (1975) ~, No. b, p. 337-347.

18. Uhri, D. C., and E. H. Blount, Pivot Point 32. Eaton, B. A., et al., The Prediction of FlowMethod Quickly Predicts $lell Performance, Patterne, Liquid Holdup lnd Pressure LossesUorld Oil, (Hay 1982), p. 153-164. Occurring During Continuous Two-Phase Flow in

Horizontal Pipelines, Trans. AIME, (1967),19. AgarwaL, R. C., F. A1-Hussainy, and p. 815.

H. J. Ramey, Jr., An Investigation of WellboreStorage and Skin Effect in Unsteady Liquid 33. Cullender, II!. H., and R. V. Smith, PracticalFLow: 1. Analytical Treatment, SPE Journal, Solution of Gas Flow Equations for Wells and(Sept. 1970), p. 279-290. Pipelines with Large Temperature Gradients,

Trans. AIFIE, 207, (1956).20. Agarwal, R. C., R. D. Carter, and

C. B. Pollock, Evaluation and Performance 34. Poettmen, F. H., and P. C. Carpenter, The !hIl-Prediction of Low Permeability Cas Wells Stimu- tiphase Flow of Cas, Oil and Water Through Ver-lated by Massive Hydraulic Fracture, JPT, tical Flow String with Application to the(March 1979), p. 263. Design oECas-Lift Installations, Drill. and

Prod. Prac., API, (1952), p. 257-317.21. Lea, J. F., Avoid Premature Liquid Loading in

Tight Cas Wells by Using Prefrac lnd Postfrac APPENDIX A: INFLOWPERFORMANCETest Data, Oil and Gas Journal, (September 20,1982), p. 123. Inflow performance is defined ls the lbility of

a well to give up fluids to the wellbore per unit22. Hai-Zui, Heng, Eduardo Antonio Proano, Ismeil drawdown. For flowing and gas Lift wells it is nor-

U. Buhidma, and Joe M. Mach, Production Sys- melly plotted as stock tank barrels of liquid perterns Analysis of Vertically Fracture Wells, day (absciasa) vs bottomhole pressure opposite theSPE/DOE 10842, presented at SPE/DOE Symposium center of the completed interval (ordinate). Thein Pittsburg, PA, Hay 16-18, 1982. total volumetric flow rate including free gas can

llso be found using production values and PVT data23. Creene, Ii. R., Analyzing the Performance of to calculste a total volume into, for instance, a

Gas iieLIs, 25th Annual Southwestern Petroleum downhole plllllp.Short Course, Lubbock, TX, (April 20-21, 1978),Proc. pp. 129-135, 197B. Brown, et ll.3, has given detailed example

problems on most of the methods of constructing IPR24. Hagedorn,A. R., and K. E. Brown, Experimental curves. It should be remembered that nothing

Sutdy of Pressure Cradients Occurring During replaces good test data and that many procedures do,Continuous Two-Phase Flow in Smell-Diameter in fact, require from one to four different testVertical Conduits, JPT, (April 1965), pointe. A stabilized rate and corresponding flowingp. 475-484. bottomhole pressure as well as the static bottomhole

pressure is usually a minimum requirementfor estab-25. Duns, H., Jr., and N. C. J. Ros, Vertical Flow lishing a good IPR.

of Cas and Liquid Mixtures in Wells, Proc.,6th World Pet. Congress (1963), p. 451. IPR HETHODSFOR OIL WELLS

1. Flowing pressure above the bubble point.26. Orkiszewski, J., Predicting Two-Phase Pressure

Drops in Vertical Pipes, JPT, (June 1967), a) Teat to find the productivity index.pp. 829-838. b) Calculation of productivity index from Dar-

cys Law27. Beggs, H. D., and J. P. Brill, A Study of 2* Two phase flow in reservoir.

Two-Phase FLOWin Inclined Pipes, JPT, (Hay1973), p. 607-617. a) Vogels Procedurei3

b) Darcys Law knowing relative permeability28. Aziz, K., C. U. Covier, and if. Fogararasi,

Pressure Drop.inUells Producing Oil lnd Cast 3. Reservoir Pressure greater than bubble pointJ. Canadian Pet. Tech., (July-8ept. 1972), (Pr>P ) lnd flowing bottomhole pressure abovep. 38-48. tor be ow the bubble point.

29. Beggs, H. D., and J. P. BrilL, A Study of Use a Combination of a straight line produc-Two-Phase Flow in Inclined Pipes, Trans. AIME,(1973), p. 607.

tivity index above Pb and VogeLs13 procedurebelow.

. 4. $etkovich Procedure14

--- .84.. --- ---- ---- ---------- ----

14121 JAMES F. LEA AND KERHIT E, BROWN 9

l

A three of four flow rece test pLotted onlog-log paper is required to determine and See Reference 23 for a discussion on gas well

equation of a form Like a gas well back pree-performance. ALso, Darcys law can be used and the

sure equatio~ with a coefficient and exponent turbulence terms should always be included6 for all

determined from plotted data. This is equiva- but thelowest rates.lent to analysis of an oil well with familiargas well relationships. Fractured and transient wells have also beentreated in the literature.

5. Standingsls extension of VogeLs work toaccount for flow efficiency values other than APPENDIX B: !4ULTIPHASEFLOWCORRELATIONS

1.00. The use of multiphaee flow pipeline pressure

6. Jonee, et al.4, procedure co determine if suf- drop correlations is very important in applyingficient area is open to flow. Nodal Analysie.

FUTUREIPR CURVES The correlations that are most widely used acthe present time for vertical multiphase flow are asThe prediction of future IPR curves is critical follow3:

in determining when a welL will liquid Load and die, 1. Hagedorn and Brown24or should be placed on artificial lift. The fol-lowing procedures can be used: 2. Duna and ROS2S3. Ros Codification (Shell Oil Co., unpublished)

1. Fetkovich 16 Procedure 4. 0rkizewski262. Combination Fetkovich and VogeL Equationla 5* Beggs and Bri11273. 1 Procedure 6. Aziz2sCouto sf). Hobil Pivot Point tlethodis These are found to calculate pressure drop very

TRANSIENTIPR CURVESwell in certain wells and certain fields. However,

OIL OR GAS WELLS one may be much better than the other under certainconditions and field pressure surveysare the only

A time element can be brought into Darcys Law way to find out. Uithout any knowledge in a partic-

allowing the construction of IPR curves for tran- ular field, we would reconsnend beginning initialsient conditions. This is important in some wells work with the correlation as Lieted in the abovedue to the long stabilization time. See Reference 3 order.for discussions by several authors. lfORIZOWTALMULTIPHASEFLOWPIPELINE CORRELATIONS

FRACTUREDOIL ANDGAS WELLSListed below are the better horizontal flow

The construction of IPR curvee for fr-ztured correlations, and lgain we would recomsnend startingoil or gas wells has been treated in the Literature in the below order.

lgtzo, Lea21 and tleng. 22 Fractured wellsby Agarwal 1. Beggs and BriL129can show flush production initially which drops off 2. ~kLerso,31rapidLy as time proceeds. 3* Eaton32

IPR METHODS FOR GAS HELLS 4. Dukler using Eaton HoLd-up3032

Generally a three or four flow rate test ie VERTICAL GAS FLOWrequired for a gae well from which a plot is made onLog-log paper and the appropriate equation devel- The following procedures are reconsnended foroped: gas flow calculations in wells.

1. Cullender and Smith33= cl(P* - Pwf2)

%ec 2. Poettman and Carpenter34

WETGAS HELLSwhere:

%sc= rate of flow, MCFD

1. Gray correlating

c1 = a numerical coefficient, character-istic of the particular well

Pr = shut-in reservoir preseure, psia

P = flowing bottomhole pressure, psiaWfn = a numerical exponent, characteristic

of the particular welL

%5 --

TABLE I - COMPLETIONCONDITIONS

.

Feet Perforation kc as % ofNo. Shots Per Foot Perforated Condition kf Formation

1 4 20 Overbalanced with 10fiLtered salt water

2 8 20 Overbalanced with 10salt water

3 4 20 Underbalanced with 30filtered salt water

4 8 20 Underbalanced with 30filtered salt water

where: k = permeability of compacted zone around the perforation;k; = permeability of the formation.

p~hYmBOTTOMHOLERESTRICTIONAP3 = i ok(PUR-PDR) T UR

API * Pr-PWfs = LOSS INPOROUS MEDIUMAP2 = P~fs-P~f = LOSS ACROSS COMPLETIONAP3 = p@-Pi)~ s RESTRICTIONAP4 = Pm-POW = SAFETY VALVEAP5 = Pwh- p~~c = SURFACE CHOKE

A% = PDsc-Psep = IN FLOWLINE

iiP7 = pwf+wh = TOTAL LOSSIN TUBINGII

Ape * p~h-psep * FLOWLINE

Fig. l-Poaaible praeeure Ioaeee in compldo system.

0!)

.*

BHP

AWP

o

+BHP

:P

a

+BHP

orAP

,

00 RATE +

Fig. 2Constructed IPR curve.

RATE +

Fig. 4Trsnefer Ap.

RATE +

4BHP

A:

Fig. 3Constructed tubing intake curve.

4BHP

AWP

00 RATE +

Fig. 5-Construct Ap across grsvel pack.

*

BHP

A: RATESK)SSIBLE

Fig. 6-Evaluation of various shot densities. Fig. 7Grsvel pack solution by including 3Pcompletion in IPR curve.

.87

Pr = 4000 PslDEPTH = 11,000K=1OQMD

1 I 1 i I I I20 40 60 80 100 120 140

RATE, MMCFD

Fig. 8lPR curve for gas well-gravel packanalysie.

.

4 -

m3 -

& AP

&

~2 -

bn. DEPTH = 11,000zm Pwtl = 1200Psl

1 - AP

i Io 10 20 30 40 50 60 70

RATE, MMCFD

Fig. 1OAP avaiiabla from sandface to tubingintake.

4 1/2 TUBiNG

\

TPwh = 1200 Psl ~

s

RATE, MMCFD

Fig. 12-CompMon effacta inciuded with iPR.gravel packed Woii.

8-DEPTH = 11,000Wh = 1200 PSI

6 - ,

G5&&;4 -kz

2 -

oo~10 20 30 40 50 60 70

RATE, MMCFD

Fig. 9Evacuation of tubing sizes.

4 -

DEPTH = 11,000

g3 -Pwh = 1200 Psl

gx

:2 -8n

%1 -

00 10 20 30 40 50 60 70

RATE. MMCFD

Fig. 1lAp acroea gravei pack at 4, 8, 12, and16 SPFa.

t

DEPTH = 11,000

I00 10 20 30 40 50 60 70

RATE, MMCFD

Fig. 12-Effect of woiihead praaeure-gravei.Packed WOfi.

88

,

bl

3.0-

2.5 -

- 2.0 -if

~; 1.5 -

:,0 -

.5 -

DEPTH = SOIWpr. ~M = 140 Psl

I 1 1 I I I \ Io looo2000m#om ~

RATE, am

Fig. 14-IPR and tubiq CL$WOS for $wfomted oilWM.

3.Or

- \.

DEPTH =SODO2.5 TUBINGI.D. = 2.992-

Fr.3500Psl3? 2.0 -:

%

.5 -\

RATE, BID

Fig. lB-prodUCtti vs. VadOllSf)erbreted COfll-ptettolls.

2.5s-

2.0 -

E

&-1 .5-

s

i%1.0 -

.5 -

\

DEPTH = 10,OW

+9 P.-u%%30 B/MMCFD CDND.5 WMMCFD WATER

I I I I to 50

I100 150 2W 250

RATE,McFD

F@. 18-Tubi~ dismeter effeofs-~k gsswell.

3.0

h

DEPTH - BOW2.5 R=3500PsITUBINQ I.D. = 2.9s2

E %

1 1, \ I ,\lo 1000 2000 313J13 41J@J 5000 6000

RATE, BID

Fig. 15Trsnsfer the Ap curve-perforated oilWetl.

~r w400

~ . TUBINQ I.D. = 2.441 Pwh = BOPSIR = 2100 Psi

200

q&-L+-_ , 1 I \ 1w

I1200

RATE. BID

Fig. 17-Wellhesd nodsl plot-flowline sizelffeote.

DEPTH = 7000TUBNQ I.D. = 1.925-R=2400PSI

/

fjll28%!q[II

RATE, MCFD

Fig. lg-f%dloted vs. observed otlwell per-fownsnoe.