Society of Petroleum Engineers

SPE 26182

An Evaluation of Recent "Mechanistic" Models of Multiphase Flowfor Predicting Pressure Drops in Oil and Gas WellsJ.K. Puckne,lI, J.N.E. Mason, and E.G. Vervest, BP ExplorationSPE Members

Copyright 1993, Society of Petroleum En9ineers, Inc.

This paper was prepared for presentation at the Offshore European Conference held in Aberdeen, 7-10 September 1993.

This paper was seillcted for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper,as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The matenal, as presented: does not necessarily reflectany position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are sUbJe~t to pubitcatlon review by EditOrial Co~mlttees of the Societyof Petroleum Engine,ers. Permission to copy is restricted to an abstract of not more than 300 words. illustratIOns may not be copied. The abstract should contam conspicuous acknowledgmentof where and by whom the paper is presented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3838, U.S.A. Telex 163245 SPEUT.

ABSTRACT

The reliable I~alculation of tubing pressure drops in oil and gaswells is important for the most cost effective design of wellcompletions.Noneofthe traditional multiphase flow correlationsworks well across the full range ofconditions encountered in oiland gas fields. Consequently, two of the recently published"mechanistic" models, one by Ansari, the other by Hasan &Kabir, were (~valuated. The performance of these methods wascompared against traditional correlations in three ways:

1) Thepredictedagainstmeasuredpressuredrops werecomparedfor stable flow conditions using 246 data sets collected from8 producing fields, including a gas and gas-condensate field.None of these data were available to the developers ofany ofthe multiphase flow models evaluated.

2) Suitable methods should reliably predict the "lift curveminima". This determines when a well may need to be"kicked off', artificially lifted or recompleted.

3) The multiphase flow model must not contain discontinuitiesor be subject to convergence problems.

No single traditional correlation method gives good results inboth oil and gas wells. In fact, most of the traditional methodswhich workreasonably in oil wells give very poorpredictions forgas wells.

Hasan & Kabir's mechanistic method was generally found to beno better than the traditional correlation methods. However, theAnsari mechanistic model gave consistently reasonableperformance. Although it did not give the most accurate resultsin every field, it gave reasonable results across the complete

References at end of paper

range of fields studied. The Ansari method also gives a reliableprediction of the lift curve minima. Areas in which it needsimprovement were identified.

By comparison the bestof the traditional methods, the Hagedorn& Brown correlation, gave goodresults for stableflow conditionsin oil wells, but itdoes notcorrectly predict the liftcurve minimaA field example shows how thiscan lead to erroneousconclusions.

INTRODUCTION

Background

Flow up the tubing in oil and gas wells is usually multiphase.Calculation of pressure drops in upward multiphase flow is notsimple, due to the slippage of gas past liquid, along with thechanging temperature and pressure conditions. Nevertheless,Petroleum Engineers need to predictpressure drops in oil and gaswells for the following reasons:

I) To construct"liftcurves", which are tablesorplots offlowrateversus bottom hole pressure, used to predict well flowrates.

2) To select the appropriate tubing size. Ifthe tubing diameter istoo large, the well acts as a gas-liquid separator and a flowconduit, and the excessive slippage results in needlessly highbottom hole pressures. However, tubing which is too smallwill cause excessive frictional pressure drops.

3) Todesignartificial liftcompletionssuchaselectricsubmersiblepumps, jet pumps or gas lift

Several multiphase flow correlations are available for predictingtubing pressure drops. The most widely used are the methods of

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2AN EVALUATION OF RECENT "MECHANISTIC" MULTIPHASE FLOW

MODELS FOR PREDICTING PRESSURE DROPS IN OIL AND GAS WELLS SPE26682

Aziz et al),2, Beggs & Brm3, Duns & Ros4, Hagedorn &BrownS and Orkiszewski6. Although each of these gives goodresults undersomeconditions, such as for stableflow in oil wells,none ofthem areaccurate rightacross the rangeofflowrate, GORand water cut conditions found in oil and gas wells.

The mostrecent of the above correlations was published in 1975.Attempts to improve on them have been made recently, in thepublicationofa series of"mechanistic" multiphase flow models."Mechanistic" is a somewhat misleading term, since the earliermethods were, to a degree, based on the mechanisms involved inmultiphase flow. For example the more sophisticated of thetraditional models, such as Duns & Ros, consider the "flowregime" in the tubing,and use differentpressure dropcalculationsaccording to the flow regime. However, the newer methods gomuch further in eliminatingempirical relationships. Inparticular,the boundaries of the different flow regimes are dermed usingmechanistic considerations, following the pioneering work ofTaitel, Dukler and Bamea7.

Models tested

Details of a number of mechanistic models have beenpublished8-14. Two of these models, one by Ansari8 and theother by Hasan & KabirlO,l1,12, are evaluated in this paper.These were chosen because:

I) All the theory and equations used in these models havebeenpublished.

2) The Fortran code for the Ansari method was available fromthe Tulsa University Fluid Flow Project

3) Hasan & Kabir presented the equations for their model in aform which could be readily translated into computer code.

Unfortunately, several equations in Hasan & Kabir's paperscontained typographical errors. Through discussions with Prof.A.R. Hasan, ourbest efforts were made to ensure that the methodwas coded as the authors intended.

Criteria for evaluation

The objective of this work was to compare the Ansari and Hasan& Kabir methods against the traditional multiphase flowcorrelations. The following performance measures were used,based on the practical application of these models:

1) When predicted pressure drops are compared withmeasurements made in oil and gas fields, the multiphasemodel should give accurate results across the full range ofproducing conditions.

2) In combination with other information, the method shouldaccurately predict when a well will cease to flow stably. Insome cases, the requirements for "kicking off', addingartificial lift or recompleting with smaller tubing later in thewell's life can be very important

3) The method should not contain any discontinuities whichresult in sudden changes in pressure as a result of smallchanges in flowrate or some other parameter.

4) The model should not be prone to numerical c:onvergenceproblems.

The Ansari and Hasan & Kabir methods were evaluated usingeach of these criteria, as described in the following sections.

COMPARISON OF MEASURED AND PREDICTEDBOTTOM HOLE PRESSURES

In general, the oil flowrate, water cut, GOR and pressure at thewellheadare readily available, along with a well deviation surveyandcompletiondiagram. In addition, abottom hole pressuremustbe obtained to test a multiphase flow correlation. These aremeasured during well tests, usually just prior to a pressure buildup, andalsoduring production logging.Bothsourcesofdata wereused in this study.

246measurementsofbottom hole flowing pressurew.~reobtained,togetherwith the required ancillary data, from 8 producing fields.Virtually all the data were from deviated wells with tubing ofbetween 3 1{2" and 7" and so the findings are particularlyapplicable to North Seawells. Results ofthe evaluation are givenin Tables 1 to 9, which also give a summary of the producingconditionsineach field. Noneofthesemeasurementswas availableduring the development of any of the multiphase modelsconsidered, so their use represents a completely inde]pendent test

Efforts were made to ensure that the data were as accurate aspossible. Inparticular,only stablewellconditions wereevaluated.As noted later, this has implications for the type ofdata obtained.

To predict PVT properties in oilfields, "black oil" correlationswere used. The correlation was chosen to give the most accuratepredictions of known PVT properties, such as the bubble point.To provide additional accuracy, the correlations were often"tuned" toPVTproperties measured in laboratory studies. For thegas and gas condensate fields, PVT data were deJived from acompositional, equation of state, model. The equation of stateused was selected by its accuracy in predicting pvr properties.

In all cases, the multiphase methods were used to calculatebottom hole pressures from wellhead pressures. Although thisgives largererrors than calculations in the reverse direction, mostengineering calculations areactually performed in the downwarddirection because wellhead pressures are more easily measuredthan bottom hole pressures.

The flowing temperatures in the tubing were specified by linearinterpolation between wellhead and bottom hole conditions.More sophisticated methods were not used as past experiencesuggests that it does not materially increase the ac(;uracy of thepressure drops.

Most of the multiphase methods tested were based on Fortrancodes supplied by the Tulsa University Fluid Flow Project Themethods were as originally published, except for Hagedorn &Brown, which was modified as described in Refere~nce 15. The"Aziz"correlationreferred to in theTables is the original model1

110

SPE26682 J.K. PUCKNELL, J.N.E. MASON AND E.G. VERVEST 3

using the same correlation as Duns & Ros in mist flow. The"Aziz, Govie~r & Fogarasi" method is identical except for usingGovier & Fogarasi's equations2 in mist flow.

To evaluate the accuracy of each multiphase flow model, thepercentage error was defined as follows:

% error = .c..ft!::dicted pressure drop - Measured pressure drop) x 100Measured Pressure Drop

Tables 1 to 9 report the mean value and standard deviation of thiserror, and in addition the mean of the absolute values ofthe error.Some of the ,errors are due to the multiphase models, but part ofthe errors will alsobe due to inaccuracy in the measured flowrate,GOR, water cut, bottom hole pressure etc.

Discussion pf the results

The best mulltiphase model results for each field are highlightedin Tables 1 t09. No model gives the best results for all fields. Thevariability in performance can be extreme. For example, Duns &Ros gives good results in oilfield B with absolute errors ofunder3%, however the same method gives an error of 119% in gasfieldA.

The results support the accepted practice of determining whichcorrelation gives the most accurate predictions of bottom holepressure in each field. That method is then used to predict futurefield performance. The disadvantages of this approach are:

1) Field conditions change with time. In particular, water cutsrise, wellhead pressures fall, well rates drop and GOR's mayincrease. The multiphase flow method which gives goodresults illi the early life of a field may give inaccurate resultslater on.

2) Thecritical time to haveaccuratepredictions is when decidingon a field development scheme, before any production wellsare drilled. At this stage, there are very few data to checkwhich multiphase flow method gives the best results.

Therefore, a multiphase flow prediction which works well overa very wide range of conditions is desirable.

The 246 data sets were split into oil and gas wells, as shown onTable 1. This was done because many methods gave reasonableresults in oil wells but gave very poor results in gas wells. For theoil wells tested, Orkiszewski gives the lowest average error.However, as Figure 1 shows, Hagedorn and Brown performsbetter as it has a low absolute error and the lowest standarddeviation. For these gas wells, the Gray method outperforms allother approaches, as shown on Figure 2. Gray's method16 is acorrelation designed for gas wells. For these oil wells, the Ansarimethod would be second choice after Hagedorn and Brown, andpossibly also the second choice for the gas wells. Hasan &Kabir's performance in these oil wells is no better than thetraditional c:orrelations, but in the gas wells tested it is moreaccurate than most of the older methods.

111

The averages in Table 1 include both good and bad results. Thestatistics can be misleading since it is usually more important tobe sure that the error is within certain limits than to use a methodwhich may give some very good and some quite poor results. Toclarify this, the models were ranked according to the % ofresultswithin certain error limits. Table 10 and Figure 3 show thisranking, which indicates that three methods Ansari, Duns & Rosand Aziz, Govier & Fogarasi, give good results (within +/- 6%)in the majority of oil wells (62%). For the gas wells, plotted onFigure 4, both the Ansari and Gray methods give the best results.The percentage of good predictions (within 6%) was only 35%.The accuracy ofgas well predictions is generally poorer, becausethe pressure drops are much lower. The actual psi error in thebottom hole pressure is somewhat smaller than these resultsimply.

The only method that gave reasonable results in both oil and gaswells is the Ansari method.

Table 11 analyses the errors according to the water cut in the datasets. The performance of multiphase flow predictions does notdecrease in any significant way as water cut rises. This is despitethe fact that none of the methods accounts for slippage betweenoil and water, and emulsion formation is ignored

Gas oil ratio has a more profound effect on accuracy. In general,all methods show a decrease in accuracy above 1000scf/stb. Thismay be because at lower GOR's, much of the well is in singlephase flow and provided thatPVTproperties arecorrect,pressuredrops in singlephase flow shouldbepredictedwith goodaccuracy.

Neither mechanistic model showed any loss of accuracy whencompared with other methods at a particular water cut or gas oilratio.

Predicting when a well dies

Tables 1 to 9 and Figures 1 and 2 show that the Hagedorn &Brown method gives very good results in many cases, which isconsistent with its widespread use. However, as shown on Figure5, the minimum in the Hagedorn & Brown lift curve (at least inthe larger tubing sizes considered here) occurs at a much lowerflowrate than predicted by other widely used methods. Theoriginal Hagedorn & Brown correlation only has a minimumbecause it has been modified to use the Griffith correlation inbubble flow l5.

The minimum in a lift curve occurs when the reduction inhydrostatic head caused by reduced slippage balances with theincrease in frictional pressure drop. The location ofthe minimumdetermines when a well will cease production. The assumptionthat a well will not flow at rates below the lift curve minimum isa valid "rule of thumb", but is only occasionally accurate.

Figure 6 shows a well in stable flow. The stable flowrate occurswhere the lift curve intersects the inflow performance curve. Inthe Figure 6 example, the bottom hole flowing pressure is abovethe bubble point pressure, so the inflow performance curve is

4AN EVALUATION OF RECENT "MECHANISTIC" MULTIPHASE FLOW

MODELS FOR PREDICTING PRESSURE DROPS IN OIL AND GAS WELLS SPE26682

DISCONTINUITIES AND CONVERGENCE PROBLEMS

Hagedorn & Brown Ansari

This result is more qualitative than quantitative, but it does showa reason why a mechanistic method such as Ansari ils preferred.

Well XprovidesararecomparisonbetweenAnsariandHagedornand Brown for flowrates around the minimum. Both methodsgave goodresults in the fIeld whenpredictingpressuresmeasuredat higher rates.

23030.51

1079630

1900

13590.29

115960

Gas lift at 2.2 MMscfldPredicted bottom hole pressure (psia)Predicted flowrate increase (bpd)

Actualflowrate increase (bpd)

An ideal multiphase flow model would predict pressures whichchanged smoothly when some other variable, such as flowrate,was changed. In reality, sudden changes in pressures are oftenpredicted across flow regime boundaries or where the modelchanges from one set of equations to another. For example,Orkiszewski provided a set of equations for continuous oil flowand another set when water was the continuous phase. Thechange from one set of equations to another is commonly fIxedat a water cut of between 50% and 70%. This causes a pressurediscontinuity in larger tubing sizes.Discontinuities and other irregular behaviour are undesirablesince:

NaturalflowPredicted bottom hole pressure (psia)Productivity index estimated (bpd/psi)

Well X was reluctant to flow and a decision onwhether to installgas lift was required. A test rate of640 bpd was obtained, whichis low for the4 1/2" tubingcompletion. Basedon the flowrate andwellheadpressure, thebottomholeflowing pressurewaspredicted,and from this the productivity index. Using this productivityindex, the effect of gas lift was predicted. As shown below,Ansari predicted a much larger increase in production rate thanHagedorn & Brown, but even this was less than what the wellactually produced. A larger increase was predicted by Ansaribecause it correctly predicted that prior to gas lift, the well wasflowing at less than the lift curve minimum, as shown on Figure12.

Field example

However, more confIdence can be placed in mechanistic modelsthan in empirical correlations such as Hagedorn & Brown. Aconsideration of theory, rather than analysis of test data, guidedthe workers who constructed the Ansari method. For this reason,ifitgives good results where test data is available, it is reasonableto assume that the theory is sound and that it will give reliableresults at low fluid velocities where there is no measured data.Correlations derived empirically are only reliable within therange of data on which they are based.

1) As shown on Figure 7, high productivity index wells will notflow in this region, so no measuredpressures can be obtained.

2) Where wells do flow at rates below the minimum, flow isoften unstable. The use of bottom hole pressure recordings,such as those shown in Figure 9, cannot be used to check thepressures predicted by multiphase flow correlations.

Although the location ofthe liftcurve minimum and thepressuresat lower rates can be very important, comparisons ofactual andpredicted pressure drops in this region are rarely possible for tworeasons:

1) A well with a high productivity index, as shown in Figure 7,will cease to flow at a flowrate just below the lift curveminimum.

2) Figure 8 shows a well with moderate productivity indexwhich will flow at rates below the lift curve minimum. If thereservoir pressure is greater than the hydrostatic pressure ofthe liquid column plus the wellhead pressure, some flow willalways occur but may not be stable. Figure 9 shows a fIeldexample ofbottom hole flowing pressures recorded in such awell. Since the lift curve and PI line intersect at a shallowangle, a stable flowrate cannot be maintained.

3) If the reservoir pressure is very high and the productivityindex is very low, as shown in Figure 10, the angle ofintersection is much larger and stable flow will occur.

4) Figure 11 shows a well that flows at the point of intersectionto the right of the lift curve minimum. However, some meansof"kicking the well off' may be required, such as gas liftingwith coiledtubing. Theintersection to the leftofthe minimumis 'metastable', and will not allow stable flow.

As reservoir pressure falls or the water cut rises, four situationscan arise:

accurately described by a straight line fIxed by the reservoirpressure and the formation's productivity index.

The location of the lift curve minimum predicted by Ansari (andindeed Hasan & Kabir) compares favourably with Duns & Ros,as shown on Figure 5. The Orkiszewski method predicts theminimum to occur at a slightly lower rate. Hagedorn & Brownis considered to be very unreliable at lower flow rates, yet goodat higher rates.

1) They often have no physical basis.2) They can cause convergence problems when thlt: lift curves

are used in a reservoir simulator.3) They can give incorrectconclusions whencomparingdifferent

development or completion options, which involve similarbottom hole flowing pressures.

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SPE26682 J.K. PUCKNELL, J.N.E. MASON AND E.G. VERVEST 5

Figure 13 shows a case in which Hasan & Kabir predicted adouble minimum, which is considered improbable. Ansatiperformedsomewhatbetteralthough,asFigure 14 shows, smoothliftcurves are notalways obtained. In general Ansari performs aswell as many of the traditional methods in producing "smooth"lift curves, Illevertheless, there is scope for improvement.

To calculate the pressure drop in multiphase flow, variousequations arl~ solved iteratively and in some cases, convergenceon the correct answer is not achieved. When testing against thedataset used to construct Tables 1 to 9, no convergence problemswere encountered with either of the mechanistic models tested.Some datasets for thegas condensate wells were omittedbecausemost of the models failed to converge. The problems arosebecause the equation of state model predicted that pure gaschanged to pure condensate in the supercritical region, in anerratic manl1ler across small pressure variations.

When examininglargerdatasets, convergenceproblems occurredwith the Ansari method. These appeared no more common thansimilar problems with many of the traditional methods such astheOrkiszewski, Duns & Ros.and Aziz methods. However, workis needed to eliminate them all together. Few problems of thisnature occurred with the Hasan & Kabir model.

FURTHER STUDY OF THE ANSARI METHOD

As the AnsaJi method appeared to hold most promise, additionalinvestigations were performed.

Therewas a GOncern that the theory used within the Ansari modelwas unsouml when applied to deviated weIls. Oilfield F wasselectedfor special examination as multiphaseconditions existeddown to the bottom of the wells in this field due to the highGOR's. Contrary to expectations, Table 7 shows that the Ansarimethod actually gave better results in the high angle wells.

To establish the conditions at which Ansari performed poorly,only data sets giving more than +/-6% error were considered.Smaller errors could easily be due to measurement errors inflowrate, PVT properties, et:e.

Clear trends were difficult to find. An increasing error with anincrease in GOR was observed,but the same trend is seen in othermethods, as shown in Table 12. Some semblanceofa pattern wasfound by plotting liquid velocity against gas velocity. As shownbyFigure 15, Ansari appears to predictpressuredrops lower thanactual (negative errors) at the lower liquid and gas velocities atthe bottom I(:ft of the graph. This is also the region most prone topressure drop predictions of over 20% more than measured.

CONCLUSIONS AND RECOMMENDATIONS

1) Despite the development of new mechanistic models, nosingle method gives accurate predictions of bottom holeflowing pressures in all fields.

2) Traditional methods ofpredicting pressure drops, such as theDuns & Ros method, which give good results in oil wells cangive very poor results in gas wells. The new mechanisticmodels are different in that they give reasonable results inboth oil and gas wells.

3) Overall the Ansari mechanistic method gives the best resultsof all the methods evaluated, both new and old. 62% of thepressure drops in oil wells were predicted with errors oflessthan +/-6%. In gas wells, 68% of the pressure drops werecalculated to within +/-15%. These conclusions were derivedfrom deviated wells with larger tubing sizes, typical ofNorthSea wells.

4) To predict when a well will "die" or flow in an unstablefashion, the minimum in the lift curve must be accuratelypredicted. This is difficult as stablebottom hole pressures arerarely measured at rates below the minimum. Nevertheless,the Ansari method appears to predict the correct minimumpoint location. Hagedorn & Brown, one of the traditionalmethods, should therefore only be used with great caution asit gives good results under stable flowing conditions, butwrongly predicts the location of this minimum.

5) Ansari and Hasan & Kabir behave no better than many of thetraditional methods in predicting erroneous discontinuities.

6) Reliable convergence is desirable in any multiphase flowmodel. Ansari performed only as well as theexistingmethods,but Hasan & Kabir performed rather better.

7) The Ansari model shows promise, but further development isneeded. Large errors were found at some conditions, inparticular when both liquid and gas velocities were in themoderate to low range. Use of a larger dataset and theinvestigationoferrorasa function ofanumberofdimensionlessgroups may be useful. Additional work is also needed toensure "smooth" lift curves and to minimize convergenceproblems.

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6AN EVALUATION OF RECENT "MECHANISTIC" MULTIPHASE FLOW

MODELS FOR PREDICTING PRESSURE DROPS IN OIL AND GAS WELLS SPE26682

ACKNOWLEDGEMENTS

The study presented here is the culmination of a great deal ofworkbypastandpresentemployees ofBP, including: S. Cooper,G. Elliot, C. Selmer, N. Whitehead, G. Makin, P. Bainbridge, P.Newberry, C. Elliot, A. Geddes, P. Jenkins, R. Zamarripa, G.Stewart, R. Lee, and I. Mackley.

REFERENCES

1) Aziz, K., Govier, G.W. & Fogarasi, M.:''Pressure drop inwells producing oil and gas", J. Can.Pet.Tech. (July-Sept1972). 38-48.

2) Govier, G.W. & Fogarasi, M.: "Pressure drop in wellsproducing gas and condensate", J.Can.Pel.Tech. (Oct-Dec1975),28-41.

3) Beggs. H.D. & Brill, J.P.: "A study of two-phase flow ininclined pipes", JPT (May 1973),607-617.

4) Duns, H. & Ros. N.CJ.: "Vertical flow of gas and liquidmixtures in wells". Proc. of the Sixth World PetroleumCongress, Vol 10 (1963), Section 2, Paper 22. PD6. 451-465.

5) Hagedorn, A.R. & Brown, K.E.:"Experimentai study ofpressure gradients occurring during continuous two-phaseflow in small diameter vertical conduits", JPT (April 1965).475-484.

6) Orkiszewski, J.:"Predicting two-phase pressure drops invertical pipe", JPT (June 1967),829-838.

7) Taitel, Y., Dukler. A.E. & Bamea, D.:''Modeling flowpattern transitions for steady upward gas-liquid flow invertical tubes", AIChE J.(1980) 26, 345-354.

8) Ansari. A.M. Sylvester,N.D. Shoham.O. & Brill,J.P.:"Acomprehensive mechanistic model for upward two-phaseflow in wellbores", paper SPE 20630 presented at the 1990SPE Conference. New Orleans. September 23-26.

9) de A.Barbuto, F.A. & Filho. E.C.: "Performance ofmechanistic modelsappliedtomultiphaseflow in theCamposBasin's Wells", Multiphase Flow - Proceedings of the 4thInternational Conference, Ed. C.P.Fairhurst. Nice, 1989.363-380.

10) Hasan,A.R. & Kabir.C.S.:"A study of multiphase flowbehaviourin verticaloilwells: Part1-Theoretical treatment".paper SPE 15138 presented at the 56th California RegionalSPE Meeting. Oakland. April 2-4, 1986.

11) Hasan,A.R. & Kabir,C.S.:"Predicting multiphase flowbehaviour in a deviated well", paper SPE 15449 presentedat the 1986 SPE Conference, New Orleans, October 5-8.

12) Hasan,A.R. & Kabir,C.S.:"Performance of two-phase gaslliquid flow model in vertical wells", Journal of PetroleumScience and Engineering, (1990) 4, 273-289.

13) O1;on, P.M, Ferschneider, G. & Chwetzoff, A.:"A newmultiphase flow model predicts pressure and temperatureprofiles in wells", paper SPE 16535 presented at OffshoreEurope 1987, Aberdeen, September 8-11.

14) Stoisits, R.F.:"Mechanistic model for multi-phase flowpressure loss calculation in wells", Multiphase Flow -Proceedings of the 4th International Confc,rence, Ed.C.P.Fairhurst, Nice, 1989.

15) Brown. K.E.:"The Technology of Artificial Lift" Volume1.1977.

16) API Manual 14BM for "API 14B. Subsurface, controlledsubsurface safety valve sizing computer program". SecondEdition. January 1978.

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SPE26682 J.K. PUCKNELL, IN.E. MASON AND E.G. VERVEST 7

IAmJil IADLIUCOMPARISONS OF ACfUA1. AND PREPIClIDJ RFSU! IS FOR on FIElJ) B

BOTIOM HOLE PRESSURENumba' of points: 74

R08llits for all (212) 011 wells: ~i1ratio: 700scfJbblOil/c:ondalsale gravity: 0.83

Method Average Average SlaDdud Gugravity: 0.92DepIbs (vertiCIl): 10000ftFzror Absolute Deviation Wellhead pressures: 400 to 2687 psia(%) Error(%) Tubing size: 7"

Wal.a'cul: 0-1.7%OIkiszewski 0.13 11.87 19.42 FIowrate I'8I1llO: 2900 - 37000 bpd Qiquid)k:iz -8.63 14.01 18.38k:iz. Govier and Fogussi 2.13 8.10 13.27 No._lIftBe:88s & Brill 11.67 13.47 18.19Duns&Ros 2.10 8.63 14.15 Mdhod Average Avenge StsndudHllgedorn & Brown -4.02 7.60 U2 Error Absolute DeviationHa,san & Kabir -3.70 13.64 20.38 (%) Error (%)Aa,sari 251 7.62 11.76 OI~ 0.99 3.85 4.98

AzIz -7.40 8.61 9.08R.,.ults for all (34) gas aDd aas condensate wells: AzIz, Govi.. and Foguasi -us 3.00 3.72

Bqgs & Brill 3.33 4.91 5.56Mllthod Average Average SlaDdud Duns & Ros -0.39 :U2 3.50

Fzror Absolute Deviation Hagedorn & Brown -4.83 5.6S 4.63(%) Error(9O) Hasan & Kabir -3.20 6.76 8.71

Ansari 1.87 3.91 4.64OIldszewski 342.96 323.43 225.93A2iz 52.33 54.25 45.99 ~A2iz. Govier and Fogussi 30.92 41.02 56.27

RESULTS FOR OILFIELD CBe88s&Brill 30.21 31.13 18.32D1Jns& Ros 101.46 10358 84.21 Number of points: 8Hagedorn & Brown 15.32 20.65 20.48 Gas...i1 ratio: 360 scflbblHasan & Kabir -19.12 20.02 14.71 OiVcondensate gravity: 0.84An,sari 14.85 17.68 23.68 Gas gravity: 1.29Guy 3.84 11.22 14.02 Depths (vertiCIl): 5200ft

Wellhead pressures: 162 to 309 psiaTubing size: 27/8"-41/2"Wal.a'cu!: 0-1.8,325

TABLE 2 Flowrate l'8I1lle: 500 - 6200 bpd Qiquid)

RESULTS FOR OIT.FIEI D A No lI"sllft

Ntmber of datasets: 47 ~ethod Avenge Average StandardGIS-oil ratio: 3OOscf/bb1 Error Absolute Deviation

OiVcondensate gravity: 0.84 ('I Error ('IGIS gravity: 1.04 Orkiszewski 0.35 9.92 1295Depths (vertical): 7000ft Aziz 4.00 10.63 13.52Wlillhead p_sures: 9410310 psia Aziz, Govier and Fogarasi 5.17 9.57 1242Tubing size: 4.5" - 7" Beggs&BriU 6.23 9.26 11.87W'llerCUt: 0-73% Duns&Ros 4.45 9.00 12.20Flowrate :range: 3800 - 19400 bpd (liquid) Hagedorn & Brown G.l4 9.84 12.41

Hasan&Kabir 11.19 1234 10.53N.'gullft Ansari 7.36 10.32 11.85

M,:thod Average Average StandardError Absolute Deviation I.AB.lJil(%) Error(9O)

RFSULTS FOR OII.FlEID POJldszewski 2.34 4.12 5.15A2iz -220 6.09 7.14 Number of points: 5A2iz. Govier and Fogarasi 2.40 3.84 4.79 Gas...i1ratio: 650 scfJbblBeggs & Brill 659 6.82 4.36 OiVcondensste gravity: 0.82Duns&Ros 1.80 3.61 4.70 Gas gravity: 0.96Hagedorn & Brown -242 4.22 5.76 Depths (vertical): 11800 ftHasan & Kabir 5.51 5.87 5.52 Wellhead pressures: 441 to 810 psia

Ansari 2.05 3.92 4.96 Tubing size:7"

Watereu!: o. 0.6, 20'1>

Ga.llnFlowrate range: 6840 - 18500 bpd (liquid)

Muhod Average Average StandardNo pollft

Error Absolute Deviation Method Average Avenge Standard(%) Error (%) Error Absolute Deviation

('I Error (%)Orldszewski 8.68 8.68 3.69Aziz 250 3.52 3.06 Orkiszewski 3.20 6.18 8.18Aziz. Govier and Fogarasi 1.10 1.20 1.80 Aziz -2.37 6.67 7.78Beggs & Brill 6.92 6.92 2.30 Aziz, Govier and Fogarasi -0.02 6.09 7.08DuIl8&Ros 1.78 1.78 1.28 Beggs & Brill 3.52 6.22 8.36

Ha;~edorn & Brown 0.18 0.95 1.26 Duns & Ros 0.51 6.58 7.82H"l8l1&Kabir 5.50 5.50 3.81 Hagedorn & Brown -4.83 8.33 9.54An,ari 2.20 2.20 0.89 Hasan & Kabir -0.50 5.95 7.07

Ansori 244 6.85 9.34

115

8AN EVALUATION OF RECENT "MECHANISTIC" MULTIPHASE FLOW

MODELS FOR PREDICTING PRESSURE DROPS IN OIL AND GAS WELLS SPE26682

RESULTS FOR OILFIElD E RESULTS FOR GAS FIELD A

Number of points:Gas-oil ratio:OiVcondensate gravity:Gas gravity:Depths (vertical):Wellhead pressures:Tubing size:Watereu!:FIowrate range:

19280 to 5300 scflbbl0.93 to 0.900.716000 ft105 to 1245 psia3.5"o260 - 3600 bpd (liquid)

Number of points:Condensate-gas ratio:Water-gas ratio:OiVcondensate gravity:Gas gravity:Depths (vertical):Wellhead pressures:Tubing size:Watercul:FIowrate range:

29\.5 bbVMMscf0.3 bbVMMscf0.750.606800-9300 ft863 - 1941 psia4" and 4.5"0-73%4.07 - 40.7 MMscfld

Nogaslln

Method

OrkiszewskiAzizAziz. Govier and FogarasiBeggs & BrillDuns & RosHagedorn & BrownHasan & KabirAnsari

AverageError(%)

-33.4-35.0

9.0518.7-9.84-1.89

-24.2-2.45

Average StandardAbsolute DeviationError(%)

35.2 28.941.4 29.423.0 27.128.2 27521.6 23.814.4 16.942.5 42.223.4 28.8

Method

OrkiszewskiAzizAziz. Govier and FogarasiBeggs & BrillDuns&RosHagedorn & BrownHasan & KabirAnsariGray

AverageError(%)

377.862336.9327

119.316.9

-20.717.34.66

Average StandardAbsolute DeviationError(%)

377.8 207.662.3 42.346.8 58.933.7 18.3

119.3 78.722.6 21.521.5 15.019.6 24.912.1 14.8

RESill.IS FOR OILFIELD FRESIn.IS FOR GAS CONDENSATE FIELD E,

Number of datasets: 59Gas-oil ratio: 600 to 27000 scflbbl (produced GOR)OiVcondensate gravity: 0.90Gas gravity: 0.80Depths (vertical): 8900 ftWellhead pressures: 200 to 2400 psiaTubing size: 3.5" - 7"Watereut: 0 - 97%FIowrate range: 200 - 12900 bpd (liquid)Gas 11ft wells Included

Number of points:Condensate-gas ratio:OiVcondensate gravity:Gas gravity:Depths (vertical):Wellhead pressures:Tubing size:Watereu!:FIowrate range:

592 to 194 bbVMMscf0.70.611400ft1213 to 4320 psia3.5"0%3.8 to 17.50 MMscf/d

Orkiszewski 6.11 8.03 1/i.43Aziz -5.25 7.75 7.53Aziz. Govier and Fogarasi -3.64 7.23 7.98Beggs & Brill 15.91 16.50 11.12Duns & Ros 1.75 15.71 17.79Hagedorn & Brown 6.05 9.51 10.02Hasan & Kabir -9.72 11.51 9.46Ansari 1.97 7.5g 11.70Gray -0.95 5.98 11.02

Lower deviation wells

Method Average Average StandardError Absolute Deviation(%) Error(%)

Orkiszewski 15.66 23.59 24.41Aziz -14.67 23.19 23.0Aziz. Govier and Fogarasi 0.10 13.55 16.66Beggs&BriU 28.98 28.98 18.28Duns&Ros 8.69 17.89 2\.4Hagedorn & Brown -5.67 10.27 10.38Hasan & Kabir -14.16 20.62 20.60Ansari 4.65 11.55 14.46

High angle wells (nollncluded in previous lable)

Method AverageError(%)

Average StandardAbsolute DeviationElTOr(%)

Method Average Average StandardError Absolute Deviation(%) Error (%)

OrkiszewskiAzizAziz. Govier and FogarasiBeggs &BriUDuns&RosHagedorn & BrownHasan & KabirAnsari

-11.442.95

11.2717.08

9.86-6.147.034.43

14.251206128419.01128511.1918.526.74

11.0816.0418.593\.8416.521\.5024.15

8.08

High angle wells have deviations below kick off depth ofbetween 47 and 57 degrees.

116

SPE26682 J.K. PUCKNELL, J.N.E. MASON AND E.G. VERVEST 9

RANKING OF MULTIPHASE H.QW PREDICTIONMEJJ{ODS

SUMMARY OF PRESSURE DROP PREDICIJONSAS A FUNCTION OF GOR

011 wells

Method Good Fair Poor

Orkiszewski 48 27 25Aziz 39 26 35JWz. Govier & Fogarasi 62 21 17Beggs & Brill 44 29 27Duns&Ros 62 19 19Ha8edorn & Ilrown 49 36 15Hasan & Kabir 43 28 29Ansari 62 22 16

C;.sweUs

Method Good Fair Poor

Orkiszewski 0 9 91Aziz 3 15 82Aziz, Govier & Fogarasi 21 35 44Beggs & Brill 12 9 79Duns&Ros 0 9 91Hagedorn & Brown 9 32 59Hasan & Kabir 9 26 65Ansari 35 33 33Gray 33 35 33

The above scores show the percentage of predictions for each..ethod which fall within the following three bands:

Hand Range of absolute errors

Good less than 6%Fair 610 15%Poor over 15%

Average % Jl'zrorAverage ab,,,lute % errorStandard de,iation

Azjz

orkiszeWSkiiiiiiiiiiic:!:::

Beggs & Brill

Duns & Ros

AnsariHasan & Kabir

Average % ErrorAverage abl!lute % errorStandard deviation

Hagedorn & Brown

Low GOR (4000 scflbbl) 011 wellsORK AZJZ AZJWAF B&B D&R H&B H&K Ansari

Average % Error 6.49 -17.88 5.48 33.22 6.76 -2.58 -28.45 1.88Averageabl!lute % error 40.45 23.14 19.53 39.22 29.01 U.34 28.45 19.31Standard deviation 46.79 25.80 26.61 34.81 33.48 14.26 22.64 24.52

Medium GOR (I00050%) 011 wellsORK AZJZ AZJWAF B&B D&R H&B H&K Ansari13.23 -14.19 -3.97 10.30 -3.74 -6.59 -8.34 -0A613.23 16.87 7.81 10.30 7.20 7.09 16.95 4.7110.00 17.80 9.94 5.64 9.16 6.96 19.75 6.16

Note:

o 50 100 150 200 250 300 350Fig. 2 Comparison or predicted and measured pressures for all gas wells

117

10AN EVALUATION OF RECENT "MECHANISTIC" MULTIPHASE FLOW

MODELS FOR PREDICTING PRESSURE DROPS IN OIL AND GAS WELLS SPE26682

7060

~Plune

/

Choke chang.1ll to 116.0"

40302010

Bottomhoi.

flowingpr...ur.

FlowreteFlg. 7 A well with a large Productivity Index this wl1il cease production

("die") at a Dowrate slightly less than the 11ft curve minimum

FlowraleFlg.6 Well Dowlng In stable fashion

AUltcurve

Flowrat.Flg.8 Well with a moderate Productivity Index this well will Dow In an

unstable fashion at rates lower than the 11ft curve minimum375Ot::====:::::;-.==::::;--------------,

Bottomhole

flowingpressure

Bottomhole

flowingpressure

3500

3250

J... 3000iI 2750...

.. 2500.5

10 ! 2250t...

2000

J 17501500

12500

-0-- Ansari--- Hagedom & Brown-- Orkiszewski.......

SPE 26682 J.K. PUCKNELL, J.N.E. MASON AND E.G. VERVEST 11

5

30

120

25

4

100

20

8060

Flowrate, Mstblday

Flg.14.

- Orkiszewski--- Ansari

10 15

40

Flg. 13 Oilfield E Lift Curve

~'\, .... -_ ...."... ----

' ..........

5

20

0A less Ihan -10%

-1010-6%A 0

o 61010%

~ A 101020% 201040%

0 A 00 D over4O%OA o A

A~ OAi D'-A 0 A~~ 0 A AIt ... A ... Ao

o

2000

1800

i 1800i 1400I... 1200r] 1000i 800

J 800400200

00

3000

2900

2800..

1 2700rf..

II 2600!A-D>c 25001co 2400jE0 2300~ID

2200

2100

20000

14

12

u 10~=~ 8~

1.5 ~ 63!..

:! 42

___ No gas lift

---.-- Gas liftPI line

1.00.5

Flowrete, Mstbldeyo

2000

4000 1----:-::-:-::------;::========~Klckoll problemsindicated

FlowreteFlg. 10 Well with a small Productivity Index but a high reservoir

pressure

I~/ureexerted by full column of liquid in Ihe lubing

I ~eservoir pressure

Predicted f10wralew~h gas lift

Fli:.12 Effect of gas 11ft on well X as predicted by Ansari

o-J---........--.,......--.....---.------.r----f

..

1 3000!..

IA-g'

~.5!o~Ei 1000 i .._"""""_--tI,.....-.......~...--t~-~~,~1

FlowreteFlg. 11 Wt!1I will flow stably at rates higher than the 11ft curve minimum

but may need to be "kicked off"

Bottomhole

flowingpressure

Bottomhole

flowingpressure

Gas velocity, ftIsec

Flg. 15 Error of Ansari pressure drop prediction as a Function of liquidand gas velocities

119

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