Graduate Theses, Dissertations, and Problem Reports
2017
Productivity Index of Horizontal Gas Well Productivity Index of Horizontal Gas Well
Abdullah A. Almuraikhi
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ProductivityIndexofHorizontalGasWell
AbdullahA.Almuraikhi
Thesissubmittedtothe
CollegeofEngineeringandMineralResources
AtWestVirginiaUniversity
Inpartialfulfillmentoftherequirements
forthedegreeof
MasterofScience
In
PetroleumandNaturalGasEngineering
KashyAminian,Ph.D.,Chair
SamAmeri,Prof.
MehrdadZamirian,Ph.D.
DepartmentofPetroleumandNaturalGasEngineering
Morgantown,WestVirginia
2017
Keywords:Productivityindexofgashorizontalwell
Copyright2017AbdullahA.Almuraikhi
ABSTRACTProductivityIndexofHorizontalGasWell
AbdullahA.Almuraikhi
Oneof themostdirect techniquestoevaluategaswellproductioncapacity isbyproductivity
index(PI).Astheapplicationofhorizontalwellshassignificantlyincreasedsince1980s,anumber
ofcorrelationsforpredictingthehorizontalwellPIhavebeendevelopedbymodificationofthe
PIcorrelationsforverticalwells.However,thepredictedPIvaluesbydifferentcorrelationsdiffer
significantly.Furthermore,therearenoavailableguidelinesforproperapplicationofthevarious
correlations. The objective of this research is to determine themost reliable correlation for
horizontalwellproductivityindexinagasreservoirandidentifythekeyparametersthatimpact
PIofhorizontalgaswells.
Inordertoachievetheobjectives,anumerical reservoirmodelwasutilizedtodeterminethe
productivityindexforahorizontalwellinagasreservoir.Aparametricstudywasthenconducted
to investigate the impactofdifferent reservoir/wellparameters including reservoir thickness,
lateral length,horizontalpermeability,andverticalpermeabilityonPI.Theproductivity index
determined by the simulation model was then compared against the values predicted by
different correlations. The results indicate that in all cases the Renard-Dupuy anisotropic
correlation will provide the closest value to the model average PI value. Moreover, Kuchuk
correlationresultedinthehighestvalueforPI,whereasBabu-Odehcorrelationvalueresultedin
thelowestvalueforPIinallcases.
iii
ACKNOWLEDGMENTIwouldliketoexpressmyappreciationtomyacademic/researchadvisorDr.KashyAminianfor
his support and guidance during my graduate program. His support, help and professional
assistancemademecompletedmystudiesandthesis,whichconcludedintheachievementof
M.Sdegree.
SincerelythankstoProfessorSamAmeri,DepartmentChair,forhissupportandguidanceduring
my studies atWestVirginiaUniversity.His support and continuousmotivationwas aperfect
asset.Iappreciatehisenthusiasmtobeonmycommittee.
IwouldliketoextendmysincerethankstoDr.MehrdadZamirianforhissupportandguidance
duringmyresearchandforbeingonthecommittee.
ManythankstotheprofessorsofthePetroleumandNaturalGasEngineeringDepartmentforthe
knowledge they shared with me.I also would like to acknowledge Saudi Aramco for their
financialandconsultationsupportthroughouttheresearch.
Tomy life-time friends,mywife,myson,mydaughter,andmysiblings, I cannot imagine life
withoutthemandIwouldliketothankthemfortheircontinuessupport,loveandeffortthey
havegiventome.TheywillalwaysbemysunshineandIwillalwayslovethemdeepinmyheart.
Finally,deepestgratitudeandlovegoestomyparent,whoarethegreatestparentssomeone
couldeveraskforwhomademethepersonIamtoday.Thisthesisisdedicatedtotheloveofmy
life,myfamily.
iv
TableofContents
ABSTRACT............................................................................................................................................II
ACKNOWLEDGMENT...........................................................................................................................III
LISTOFFIGURES..................................................................................................................................V
LISTOFTABLES....................................................................................................................................V
NOMENCLATURE................................................................................................................................VI
CHAPTER1:INTRODUCTION.................................................................................................................11.1 HORIZONTALWELL..........................................................................................................................11.2 ADVANTAGESOFDRILLINGHORIZONTALWELLS...................................................................................11.3 DISADVANTAGESOFDRILLINGHORIZONTALWELLS...............................................................................11.4 PRODUCTIVITYINDEX.......................................................................................................................2
1.4.1 FlowRegime...........................................................................................................................21.4.1.1 Unsteadystateflow.....................................................................................................................................21.4.1.3 Latetransientflow.......................................................................................................................................31.4.1.4 Pseudosteadystateflow(orSteadystateflow)..........................................................................................3
CHAPTER2:LITERATUREREVIEW.........................................................................................................42.1 PSEUDOPRESSURE..........................................................................................................................62.1 HORIZONTALWELLPRODUCTIVITYINDEXCORRELATIONS.......................................................................7
2.2.1 SteadyStateCorrelations.......................................................................................................72.2.1.1 Borisov’sCorrelation:...................................................................................................................................72.2.1.2 Giger-Reiss-Jourdan’sCorrelation:...............................................................................................................82.2.1.3 Joshi’sCorrelation:.......................................................................................................................................92.2.1.4 Renard-Dupuy’sCorrelation:......................................................................................................................10
2.2.2 PseudoSteadyStateCorrelation:.........................................................................................112.2.2.1 Verticalwell:...............................................................................................................................................112.2.2.2 Babu-Odeh’sCorrelation:...........................................................................................................................112.2.2.3 Kuchuk’sCorrelation:.................................................................................................................................122.2.2.4 Economides’Correlation:...........................................................................................................................13
CHAPTER3:METHODOLOGY..............................................................................................................143.1 BASECASEEXAMPLE.................................................................................................................16
3.2 COMPARISONBETWEENPIOFVERTICALANDHORIZONTALWELL:........................................21CHAPTER4:RESULTSANDDISCUSSION..............................................................................................22
4.1 RESULTS......................................................................................................................................224.1.1 PIvalueswithdifferentHorizontalPermeability..................................................................224.1.2 PIvalueswithdifferentVerticalPermeability.......................................................................234.1.3 PIvalueswithdifferentReservoirThickness.........................................................................234.1.4 PIvalueswithdifferentLateralLength.................................................................................24
4.2 DISCUSSION..................................................................................................................................244.2.1 HorizontalPermeability........................................................................................................254.2.2 VerticalPermeability............................................................................................................274.2.3 ReservoirThickness...............................................................................................................294.2.4 LateralLength.......................................................................................................................31
CHAPTER5:CONCLUSION...................................................................................................................33
REFERENCES.......................................................................................................................................34
v
APPENDIX...........................................................................................................................................36
1. CMGMODEL..............................................................................................................................36
ListofFiguresFigure1.ProductivityIndexvs.Time _____________________________________________________________ 18Figure2.showingallvaluesforPIincludingCMG___________________________________________________ 20Figure3.PIforanisotropicmethodwithKh=0.1mDvalues___________________________________________ 25Figure4.PIforanisotropicmethodwithKh=0.1mDvalues___________________________________________ 26Figure5.PIfordifferentanisotropicmethodwithKhvalues ___________________________________________ 26Figure6.PIvaluesforanisotropicmethodwithKv=0.1mD___________________________________________ 27Figure7.PIvaluesforanisotropicmethodwithKv=0.1mD___________________________________________ 28Figure8.PIforanisotropicmethodwithdifferentKvvalues___________________________________________ 28Figure9.PIforanisotropicmethodwithh=10ft.values _____________________________________________ 29Figure10.PIforanisotropicmethodwithh=10ft.values ____________________________________________ 30Figure11.PIfordifferentanisotropicmethodwithThicknessvalues____________________________________ 30Figure12.PIforanisotropicmethodwithLaterallength1000ft.values_________________________________ 31Figure13.PIforanisotropicmethodwithLaterallength1000ft.values_________________________________ 32Figure14.PIfordifferentanisotropicmethodwithLateralLengthvalues________________________________ 32Figure15.CMGlauncher______________________________________________________________________ 36Figure16.Reservoirsimulationsetting ___________________________________________________________ 37Figure17.CMGBuilder________________________________________________________________________ 37Figure18.CMGBuilder________________________________________________________________________ 38Figure19.GeneralPropertySpecification _________________________________________________________ 38Figure20.Rockcompressibility _________________________________________________________________ 39Figure21.ImwxPVTRegions___________________________________________________________________ 39Figure22.Rocktype__________________________________________________________________________ 40Figure23.KrVs.Sg___________________________________________________________________________ 41Figure24.KrVs.Sw___________________________________________________________________________ 41Figure25.Initialcondition _____________________________________________________________________ 42Figure26.Initialcondition _____________________________________________________________________ 43Figure27.Wellevents_________________________________________________________________________ 44Figure28.Wellevents_________________________________________________________________________ 44Figure29.Wellcompletiondata_________________________________________________________________ 45Figure30.Wellcompletiondata_________________________________________________________________ 45Figure31.Topview___________________________________________________________________________ 46
ListofTablesTable1.NOMENCLATURE............................................................................................................................................viTable2.ReservoirandFluid(gas)PropertiesfortheSimulationModel..................................................................15Table3.PIresults.......................................................................................................................................................17Table4.PIforallcorrelationscomparedwithsimulatorhighvalue...........................................................................19Table5.PIforallcorrelationscomparedwithsimulatorlowvalue............................................................................19Table6.PIforallcorrelationscomparedwithsimulatoraveragevalue.....................................................................20Table7.PIforgasverticalwell....................................................................................................................................21Table8.PIfordifferentHorizontalPermeabilityValues.............................................................................................22Table9.PIfordifferentVerticalPermeabilityvalues..................................................................................................23Table10.PIfordifferentReservoirThicknessvalues..................................................................................................23Table11.PIfordifferentLateralLengthvalues..........................................................................................................24
vi
NOMENCLATURE
Table1.NOMENCLATURE
J Productivityindex,SCF/psi2/day/cpK Permeability,mdKh Horizontalpermeability,mdkvVerticalpermeability,mdKx Permeabilityinx-direction,mdKy Permeabilityiny-direction,mdKz Permeabilityinz-direction,mdKave Averagepermeability,mdPi Initialreservoirpressure,psiPwf Flowingbottom-holepressure,psi reh Drainageradius,ft. rw’ Effectivewellboreradius,ft. µg Gasviscosity,cpT Temperature,°FZ Compressibilityfactorh Formationthickness,ft. CH ShapefactorL Horizontalwelllength,ft.Zw Standoff,ordistanceofwellfrommiddleofreservoir,ft. φ Porosity,%A Area,ft2Xo,Zo CoordinatesmeasuringthecenterofwellinverticalplaneDepth,ft.D Depth,ft.a Halfmajoraxisofdrainageellipse,ft.X DimensionlessdrainageconfigurationparameterSR SkineffectPWD DimensionlesspseudosteadystatepressureSm Van Everdingen mechanical skin Xe Extentofdrainageareainx-direction,ft.PD Dimensionless pressure Sx SkineffectSe Eccentricityeffectinverticaldirectionm Pseudopressure,psi2/cp
1
CHAPTER1:INTRODUCTION
1.1 HorizontalWellHorizontalwellisdefinedasawellthathasanaccesstohydrocarbonreservesatwiderangeof
angles.Theinterestinhorizontalwellsinitiatedin1980s.Horizontalwellsaresignificantlymore
productivethanverticalwellssinceitallowsasinglewelltoreachmultiplepointsinthereservoir.
Also,itreducestheriskofpenetratingwateringasoroilexploration.
1.2 AdvantagesofDrillingHorizontalWells
Theadvantagesofdrillinghorizontalwellsare:
1. Toreducewaterandgasconing(encroachment).2. Toincreasedcontactwiththeformation.3. Toincreasehydrocarbonproductionratesinceitisexposedtomoreofthepayzone.4. Toincreaseproductionandlowerrisk.5. Higherprobabilitytoencounternaturalfractureswhichenhancesoverallrecovery.6. Toenabledrillingunderpopulated/protectedareas.7. Tolowerfluidvelocitiesaroundthewellbore.
1.3 DisadvantagesofDrillingHorizontalWells
Thedisadvantagesofdrillinghorizontalwellsare:
1. Higherdrillingandcompletioncosts.2. Higherriskofinterferingwithotherwells.3. Requiresmorecomplicateddrillingandcompletiontechnologiesinespeciallyinthin
zones.4. Holecollapseandcleaningissues.5. Holegeometrywhiledrilling.
2
1.4 ProductivityIndexTheproductivity indexismeasureofpotentialandperformanceofthewell.PIrepresentsthe
ability of a reservoir to deliver the fluid to thewellbore. Therefore, theproductivity index is
definedastheratiooftheflowratetothepressuredrawdownatthemidpointwithaunitof
(bbl/psi/day)asshownbelow:
J = q∆P =
q(p) − p+,)
where,
• J=ProductivityIndex,bbl/psi/day• q=flowrateatstandardconditions,bbl/D• Pr=reservoirpressure,psi• Pwf=flowingwellheadpressure,psi
1.4.1 FlowRegimeDuringthehydrocarbonproductioncycle,theproducingwellgoesthroughthreeflowperiods,flowregimesbasedontheproductiontimeandtheboundaryconditions.Thesethreeperiodsare:
• Unsteadystateflow.• Latetransientflow.• Pseudosteadystateflow(orSteadystateflow).
1.4.1.1 UnsteadystateflowUnsteadystateflowisthestartinglifeofawell.Also,itisknownasaninfiniteactingthatthe
productionof awell hasnot reached to theboundaryof the reservoir. So that the reservoir
boundaries have no effect on thewell performance. During this period the rate of pressure
respecttotimedependsonboththeradiusandthetimeofproductionasshownbelow:
dpdt = f r, t , whereristheradiusandtisthetime.
3
1.4.1.3 Latetransientflow Itisastatebetweentheunsteadystateandthepseudosteadystateregimes.Itoccurswhenthepressure disturbance caused by the production of awell has reached some of the reservoirboundaries.
1.4.1.4 Pseudosteadystateflow(orSteadystateflow)
Pseudosteadystateiswhentheproductionofawellhasreachedallthereservoirboundaries.
Duringthisperiodthepressuredropsatthesameconstantratethroughoutthereservoir.
dpdt = constantrate
Steadystateflowisaspecialcaseofpseudosteadystateflowwhen:
dpdt = 0
In this flow period the production has no impact on the pressure. The reservoir pressure is
sustainedbyeitheranaquifersupportoragascapexpansion.
4
CHAPTER2:LITERATUREREVIEWProductivityindexrepresentstheproductioncapacityofawell.Productivityindexisdefinedas
the rate of production per unit pressure drawdown. The constant flow rate of awell is also
simulationtoevaluatethelong-termproductivityphenomenaofthewell.Horizontalwellshave
proventobemoreproductivethantheverticalwell.Thisisbecausethehorizontalwellhasan
increaseddrainageareathanaverticalwell.This indicatesthatastimulationverticalwellcan
functionmoreproductivelythananun-stimulationone(Dankwaetal.,2011).
However, horizontal wells have certain disadvantages over the corresponding vertical wells
(Babuetal.,417).Forinstance,thecostofconstructingahorizontalwellexceedsabouttwotimes
the similar vertical well on a reservoir. Therefore, a close analysis should be conducted to
considertheperformanceofhorizontalwellanditsadvantagesoververticalwellsinoilfields.
Thefirststudyisunderpartialcompletionwheretheproductivityindexisinvestigatedbasedon
completion flow rate fromreducedproduction intervalofall the system.This thus inducesa
pressuredecreaseatwellboreareaunderverticalwells.Inordertostudythecompletionflow
rate,variousfactorsarecalculatedsuchaspseudoskin,penetrationratios,reservoirdrainage
systemandshapefactors.Itisnotedthataverticalwellthatispartiallycompleted,itismajorly
controlledbythestrength.However,verticalpermeability,reservoirsize,andthicknessofthe
zoneaffectproductivityindexataminimalrate.
Theinflowperformanceofhorizontalwellscanalsobehypothesizedtoperformcalculationson
its productivity index. However, when devising the formulas, various restrictions and
assumptionswereputinplaceunderthegeometry.Assumptionsweremadethatthelengthof
thewellwaslongerthanthethicknessoftheformationandshorterthanthedimensionsofthe
drainage area. The well is also supposed to be located in the center of the drainage area.
Nevertheless, it is assumed that the cross-sectional area of thewell covers thewholewidth
dimensionofthereservoirlocation.Thisisessentialsoastodeterminetheadditionalpressure
thatdropssincethewellisconsiderednon-fracture.
5
Theinflowperformanceofahorizontalwellisdeemedtobeofasteady-stateofflow.Thesteady
pseudonatureofawellinhorizontalpositionisthedifferencecalculatedbetweentheaverage
pressure of the reservoir and the pressure at the wellbore when it approaches a constant
numerical value. This is also essential when calculating the inflow of the well to determine
productivity index. When this steady-state pressure is kept constant, it enables further
calculationsinvolvingdrawdownpressurewhichisneededtoflowaunitvolumeinthewellper
unittime(Goodeetal.,319).Thestudy,therefore,involvesgenerationofapplicableformulasas
well as their application in bothwellswith a constant-pressure and thosewith the pressure
boundaries.
Subsequent research also includesevaluatingpressure-transient for thehorizontalwells. The
studyincorporatesvariousparametersinbuild-uptestsaswellasdrawdownanalysis.Vertical
wellsdifferfromhorizontalwellsunderpressure-transientbecausehorizontalwellsshowpartial
penetrationphenomenonwhentheyareperforatedallthroughthewell.Nevertheless,sincethe
wellbore volume of horizontal wells has a typically increased capacity than vertical wells, it
enablesagreaterperiodforthestoragevolume in it (Odehetal.,1989).Calculationsarealso
involved incalculatingthedown-holepressureat thewellboreandassisting inexaminingthe
productivityindexofthewell.Theinterpretationusedinthecomputationalsofacedsignificant
challengessince thereexistnumerousboundarieswithunknownseparationdistancesamong
them(Kuchuketal.,974).Also,thelargeanisotropyratioofthewellmadeitdifficulttoformulate
afinalinterpretation.
Anotherresearchtoevaluatetheproductivityofinclinedandhorizontalwellswascarriedoutin
ananisotropicmedium.Thisstudyisessentialbecauseitprovidesformulasthatarerelevantin
determining how the slant and anisotropy of permeability of the well. For the purpose of
determining the effect of inclining the well on pressure, a simulator is used. To design and
recommendthetypeofwelltobedugonareservoir,variousfactorsshouldbeconsideredsuch
aspermeabilityofthearea.Forinstance,alowpermeablereservoirusesthehorizontalwellto
boosttheproductivityindex(Bessonetal.,1990).Theperformancesoftheslantingwellandthe
6
corresponding horizontal well were evaluated using a geometric pseudo skin factor. Under
isotropicreservoirs,drillingahorizontalwellhasproventobemuchmoreadvantageousthanthe
slantingwells.Onthecontrary,underanisotropicreservoirs,thereexistsacriticalpointunder
thelengthofthewellunderwhichslantinghasproventobemoreadvantageousthanhorizontal
well(Joshietal.,729).
Other researchers try toevaluateand formulateequations toworkout the rightproductivity
indexofahorizontalwellfromtheearlierverticalwells.Constructionofsuchwellsalsodepends
on the permeability of the reservoir and numerical geometries (Giger et al., 1997). Various
modelshavebeengeneratedandarguedoverthepastdecadesrangingfromBorisovtoBabu
andOdehmodels.Therefore,toresolvetheissueofemanatingmodelsandargumentationof
suchmodelformulacalculation,obtainingageneralproductivityindexcouldlargelybeofhelp.
The future of petroleum drilling depends on the design and application ofwell-suitedwells.
Horizontalwellshaveproventobethemostefficientdrillingmethodduetoitsabilitytocontact
amuchlargerreservoirarea(Economidesetal.,258).Nevertheless,horizontalwellsdrilledover
the reservoir area come into contact with fractures that assist in draining efficiently. Also,
horizontalwellshavetheabilitytominimizewaterandgasconingbehaviorsforwhichvertical
wells fail todoso.Forthiscase, theemergenceofsoundhorizontaldrillinghasbeenapplied
widelyuptomorethan30wellsacrosstheworld.Forinstance,inColombia,about20wellshave
beenconstructed(Saavedraetal.,2000).However,thehorizontalwellfacesparticularchallenges
suchastheycannotbeappliedinthickreservoirs,expensivetoconstructandanareawithseveral
petroleumzoneswillrequiredrillingofnumeroushorizontalwells.
2.1 PseudoPressurePseudopressureisconsideredtobeapseudopropertyofagassinceitdependsonagasviscosity
andcompressibilityfactors,whicharepropertiesofthegas.Moreover,pseudopressureiswidely
usedformathematicalmodelingofIPRofgaswellsanditgivesanaccuratepressure.Itcanbe
definedas:
7
P@ = 2PµCZ
@
Edp
However,aspreadsheetprogramhasbeendevelopedtoestimatepseudopressurebyentering
certain parameters such as: gas gravity, base pressure, reservoir temperature, and mole
percentagetogettheaccuratepressureofthereservoir.
2.1 HorizontalWellProductivityIndexCorrelationsTherearedifferentcorrelationsavailableforcalculatingtheproductivityindexofhorizontalgas
wells. There are two general categories including Steady-state and pseudo-steady state
correlationswhichwillbepresentedbelow.
2.2.1 SteadyStateCorrelationsTherearefourmajorsteadystatecorrelationstopredicttheproductivityindexofgashorizontal
wells.Thesemethodsare:
1. Borisov’smethod.
2. Giger-Reiss-Jourdanmethod.
3. Joshi’smethod.
4. Rendard-Dupuymethod.
2.2.1.1 Borisov’sCorrelation:Thepredictionofproductivityindexofhorizontalgaswelliscorrectedfromthehorizontaloilwell
equationbythecompressibilityandviscositydifferencebetweenoil(slightlycompressible)and
gas(compressible).Thus,theequationwillbe:
8
𝐽 = 0.703 ∗ ℎ ∗ 𝐾ℎ ∗ 𝜇𝑔 ∗ 𝑧
𝑇(ln 4𝑟𝑒ℎ𝐿 + 𝐿
ℎ ln( ℎ2𝜋𝑟𝑤))
2.2.1.2 Giger-Reiss-Jourdan’sCorrelation:Thepredictionofproductivityindexofhorizontalgaswelliscorrectedfromthehorizontaloilwell
equationbythecompressibilityandviscositydifferencebetweenoil(slightlycompressible)and
gas(compressible).Thus,theequationwillbe:
Isotropicreservoir:
𝐽 = 0.703 ∗ 𝐿 ∗ 𝐾ℎ ∗ 𝜇𝑔 ∗ 𝑧
𝑇( 𝐿ℎ ln 𝑋 + ln( ℎ2𝑟𝑤))
An-isotropicreservoir:
𝐽 = 0.703 ∗ 𝐾ℎ ∗ 𝜇𝑔 ∗ 𝑧
𝑇( 1ℎ ln 𝑋 + (𝐵[
𝐿 )ln( ℎ2𝑟𝑤))
Where,
𝑋 = 1 + 1 + ( 𝐿
2𝑟𝑒ℎ)[
𝐿(2𝑟𝑒ℎ)
𝐵 = 𝐾ℎ𝐾𝑣
9
2.2.1.3 Joshi’sCorrelation:Thepredictionofproductivityindexofhorizontalgaswelliscorrectedfromthehorizontaloilwell
equationbythecompressibilityandviscositydifferencebetweenoil(slightlycompressible)and
gas(compressible).Thus,theequationwillbe:
Isotropicreservoir:
𝐽 = 0.703 ∗ ℎ ∗ 𝐾ℎ ∗ 𝜇𝑔 ∗ 𝑧
𝑇(ln 𝑅 + (ℎ𝐿 )ln(ℎ2𝑟𝑤))
Anisotropicreservoir:
𝐽 = 0.703 ∗ ℎ ∗ 𝐾ℎ ∗ 𝜇𝑔 ∗ 𝑧
𝑇(ln 𝑅 + (𝐵[ℎ𝐿 )ln( ℎ
2𝑟𝑤))
Where,
𝐵 = 𝐾ℎ𝐾𝑣
𝑎 = 𝐿2 0.5 + 0.25 +
2𝑟𝑒ℎ𝐿
`E.a
𝑅 = 𝑎 + 𝑎[ + (𝐿2)
[
𝐿(2)
10
2.2.1.4 Renard-Dupuy’sCorrelation:Thepredictionofproductivityindexofhorizontalgaswelliscorrectedfromthehorizontaloilwell
equationbythecompressibilityandviscositydifferencebetweenoil(slightlycompressible)and
gas(compressible).Thus,theequationwillbe:
Isotropicreservoir:
𝐽 = 0.703 ∗ ℎ ∗ 𝐾ℎ ∗ 𝜇𝑔 ∗ 𝑧
𝑇(coshbc 2𝑎𝐿 +(ℎ𝐿 )ln(
ℎ2𝜋𝑟𝑤))
An-isotropicreservoir:
𝐽 = 0.703 ∗ ℎ ∗ 𝐾ℎ ∗ 𝜇𝑔 ∗ 𝑧
𝑇(coshbc 2𝑎𝐿 +(𝐵ℎ𝐿 )ln( ℎ
2𝜋𝑟′𝑤))
Where,
𝑎 = 𝐿2 0.5 + 0.25 +
2𝑟𝑒ℎ𝐿
`E.a
𝐵 = 𝐾ℎ𝐾𝑣
𝑟e𝑤 = 1 + 𝐵 𝑟𝑤2𝐵
11
2.2.2 PseudoSteadyStateCorrelation:There are four major pseudo steady state equations to measure the productivity index of
horizontalgaswells.Forcomparisonpurposes,allofthesehorizontalmodelsarecomparedto
productivityindexthatbeencalculatedfromasimulatormodel(CMG).Thesemethodsare:
1. Verticalwell.
2. Babu-Odehmethod.
3. Kuchukmethod.
4. Economidesmethod.
2.2.2.1 Verticalwell:Thepredictionof theproductivity indexofverticalgaswells iscorrected fromtheverticaloilwells’equationtoaccountforthecompressibilityandviscositydifferencesbetweenoil(slightlycompressible)andgas(compressible).Thus,theequationwillbe:
𝐽 = 0.703 ∗ 𝑘 ∗ ℎ ∗ 𝜇𝑔 ∗ 𝑧
𝑇 ln 𝑟𝑒𝑟𝑤 − 0.75 + 𝑠
2.2.2.2 Babu-Odeh’sCorrelation:TheobjectiveofthismethodistoprovideaneasywaytocalculatePIofagashorizontalwell. Theproductivityindexofhorizontalgaswelliscorrectedfromthehorizontaloilwellequationby
the compressibility and viscosity difference between oil (slightly compressible) and gas
(compressible).Thus,theequationwillbe:
𝐽 = 0.703 ∗ 𝑏 ∗ 𝐾𝑥𝐾𝑧 ∗ 𝜇𝑔 ∗ 𝑧
𝑇 (ln(𝐶𝐻 ∗ 𝐴c[ ∗ 𝑟𝑤) − 0.75 + 𝑆𝑅)
12
Where:SRisafunctionthatdependsstronglyonthewelllengthL.SR=0whenL=b(thefully
penetratingcase).
𝑙𝑛 𝐶𝐻 = 6.28 ∗𝑎ℎ
𝐾𝑧𝐾𝑥 ∗
13 −
𝑋𝑜𝑎 +
𝑋𝑜𝑎
[
− ln 𝑠𝑖𝑛180𝑧𝑜ℎ − 0.5 ln((
𝑎ℎ)
𝐾𝑧𝐾𝑥)
− 1.088xoandzoarecoordinatesthatmeasurethecenterofthewell intheverticalplane, (a) is the
dimensionofthedrainagearea.
2.2.2.3 Kuchuk’sCorrelation:The productivity equation suggested by Kuchuk used an approximate infinite conductivity
solution.Theproductivityindexofhorizontalgaswell iscorrectedfromthehorizontaloilwell
equationbythecompressibilityandviscositydifferencebetweenoil(slightlycompressible)and
gas(compressible).Thus,theequationwillbe:
𝐽 = 0.703 ∗ 𝐾𝐻 ∗ ℎ ∗ 𝜇𝑔 ∗ 𝑧
𝑇(𝑃𝑤𝐷 + 𝑆𝑀∗)
𝐾w = 𝐾𝑥 ∗ 𝐾𝑦
𝑃𝑤𝐷 =ℎ
2𝐿 12𝐾𝑥𝐾𝑧 (ln
8ℎ𝜋 ∗ 𝑟e𝑤cot(
𝜋 ∗ 𝑍𝑤2ℎ )) +
𝑍𝑤 − ℎ
𝐿 12𝐾𝑥𝐾𝑧)
𝑆𝑚 = 2𝜋 ∗ 𝐿 12 𝐾𝑦 ∗ 𝐾𝑧
𝜇 ∗ 𝑞 ∗ ∆𝑃𝑠
13
𝑆𝑀∗ = ℎ
2𝐿 12𝐾𝑥𝐾𝑧 ∗ 𝑆𝑚
Sincetheskiniszero,bothSmandSm*shouldbenegligible.
2.2.2.4 Economides’Correlation:
Economides suggestedamethodologyof calculatingwellperformanceofarbitrarilyoriented,
singleormultiplewellconfigurations,basedonevaluatedanalyticalsolutions.Thisapproachis
general,readilyreproducewell-knownanalyticalsolutions,andcanbeusedfortransient,mixed,
and no flow boundary conditions. However, the productivity index of horizontal gas well iscorrectedfromthehorizontaloilwellequationbythecompressibilityandviscositydifference
betweenoil(slightlycompressible)andgas(compressible).Thus,theequationwillbe:
𝐽 = 0.703 ∗ 𝐾𝑎𝑣𝑒 ∗ 𝑋𝑒 ∗ 𝜇 ∗ 𝑧
𝑇(𝑃𝐷 + 𝑋𝑒2𝜋𝐿 𝑆)
Where,
𝑃𝐷 = 𝑋𝑒𝐶𝐻4𝜋ℎ +
𝑋𝑒2𝜋𝐿 𝑆𝑥
𝑆𝑥 = ln(ℎ
2𝜋𝑟𝑤) −ℎ6𝐿 + 𝑆𝑒
𝑆𝑒 = ℎ𝐿
2 ∗ 𝑍𝑤ℎ −
12
2 ∗ 𝑍𝑤ℎ
[
−12 − ln(sin(
𝜋 ∗ 𝑍𝑤ℎ ))
14
CHAPTER3:METHODOLOGYTheobjectiveofthisresearch istoevaluatedifferentproductivity indexcorrelationsforagas
horizontal well using different reservoir/well parameters. To achieve this goal, the following
stepswereconsidered:
1. Anumericalreservoirsimulator(CMG)wasutilizedtobuildagasreservoirmodelwith
onehorizontalwell.Thereservoirpropertiesusedindevelopingthesimulationmodelare
listedinTable2.
2. Afterrunningsimulatorandtakingtheresults(gasrate&reservoirpressure),thepressure
can be corrected to pseudopressure (Pp). Subsequently, the productivity index was
calculated.
3. The calculated PI was compared to estimate values from both steady state and
pseudosteadystatecorrelationstoevaluatewhichcorrelationprovidesthemostreliable
results.
4. ThePIforverticalwellwascalculatedusingpseudosteadystatecorrelationtocompareit
withthehorizontalPIinordertoillustratetheadvantageofhorizontalwell.
Thefollowingexampleillustratesthemethodologyindetailforthebasecase.
15
Table2.ReservoirandFluid(gas)PropertiesfortheSimulationModel
Parameters BaseCase RangeFormationthickness(h),ft. 30 10-50Horizontalpermeability(kh),md. 0.1 0.1-0.5GasViscosity(u),cp. 0.019 0.019Depth(d),ft. 6000 6000-7000Lengthofhorizontalwell(L),ft. 2000 1000-2500Wellboreradius(rw),ft. 0.5 0.5VerticalPermeability(kv),md. 0.01 0.01-0.5Temperature(T),oF. 120 120Reservoirradius(re),ft. 2000 2000-4000Skinfactor(s). 0 0InitialReservoirpressure(P),psi. 3000 3000Flowingbottom-holepressure(pwf),psi. 500 500DrainageArea(a×b),ft2. 2000-4000 2000-4000Centerofthewellintheverticalplane(Zo),ft. mid-point mid-pointPorosity. 10 10Swi. 0.25 0.25RockCompressibility. 3.003E-3 3.003E-3
16
3.1 BASECASEEXAMPLEThe simulation run results (time, flow rate, pressure...) for a constant flowing bottomhole
pressurewereimportedtoanexcelsheet.Then,thereservoirpressuresvalueswereconverted
topseudopressure(Pp)byusinganavailablePseudoExcelSheet.Theproductivityindexwasthen
calculatedforoverafour-yearperiodofproductionasshownintheTable3.Subsequently,aplot
wascreatedtoobtainthehigh, low,andtheaveragevaluesofPI forahorizontalgaswellas
shownintheFigure1.Finally,PIvalueswereestimatedfrombothsteadystateandpseudosteady
statecorrelationsusingthesamereservoirparametersasthoseusedinthesimulationmodel
andsummarizedinTables4,5and6.Figure2comparesthePIvaluesfromthesimulationand
variouscorrelations.
Thisprocesseswererepeatedusingdifferentparameterstocomeupwiththebestcorrelation
thatmatchesthemodel.
17
Table3.PIresults
18
Figure1.ProductivityIndexvs.Time
0.00000
0.00200
0.00400
0.00600
0.00800
0.01000
0.01200
0 200 400 600 800 1000 1200 1400 1600
PI,SCF/psi2/day/cp
Time(days)
HighValueAverage Value
LowValue
19
Table4.PIforallcorrelationscomparedwithsimulatorhighvalue
BestCorrelationwithSimhighvalue
Correlation LateralLength,ft. PI,SCF/psi2/day/cp
SimusingPp:HighValue 2000 0.00360Borisov 2000 0.00304
Renard-DupuyIsotropic 2000 0.00300JoshiIsotropic 2000 0.00299
Renard-DupuyAn-Isotropic 2000 0.00281Giger-Reiss-JourdanIsotropic 2000 0.00280
JoshiAn-Isotropic 2000 0.00217Giger-Reiss-JourdanAn-Isotropic 2000 0.00207
Babu-Odeh 2000 0.00181Economides 2000 0.01136Kuchuk 2000 0.01420
Table5.PIforallcorrelationscomparedwithsimulatorlowvalue
BestCorrelationwithSimLowvalue
Correlation LateralLength,ft. PI,SCF/psi2/day/cp
SimusingPp:LowValue 2000 0.00261
Giger-Reiss-JourdanIsotropic 2000 0.00280Renard-DupuyAn-Isotropic 2000 0.00281
JoshiIsotropic 2000 0.00299Renard-DupuyIsotropic 2000 0.00300
Borisov 2000 0.00304JoshiAn-Isotropic 2000 0.00217
Giger-Reiss-JourdanAn-Isotropic 2000 0.00207Babu-Odeh 2000 0.00181Kuchuk 2000 0.01420
Economides 2000 0.01136
20
Table6.PIforallcorrelationscomparedwithsimulatoraveragevalue
BestCorrolationwithSimAvg.value
Correlation LateralLength,ft. PI,SCF/psi2/day/cp
SimusingPp:Avg.Value 2000 0.003105Borisov 2000 0.003045
Renard-DupuyIsotropic 2000 0.002999JoshiIsotropic 2000 0.002990
Renard-DupuyAn-Isotropic 2000 0.002807Giger-Reiss-JourdanIsotropic 2000 0.002802
JoshiAn-Isotropic 2000 0.002170Giger-Reiss-JourdanAn-Isotropic 2000 0.002070
Babu-Odeh 2000 0.001813Economides 2000 0.011356Kuchuk 2000 0.014196
Figure2.showingallvaluesforPIincludingCMG
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
PI,SCF/psi2/day/cp
21
3.2 ComparisonbetweenPIofverticalandhorizontalwell:ThePIvalueoftheverticalwellisillustratedinTable7(5.22071E-06),whichissignificantlylowerthan the PI average value calculated from the model as shown in table 6 (3.105E-03). ThiscomparisonwasperformedtoindicatethatthePIvalueforhorizontalwellismuchhigherthanthevertical.
Table7.PIforgasverticalwell
VerticalwellBaseCcase
Parameters PI,SCF/psi^2/day/cph,ft. 30Kh,md 0.1zfactor 0.8284
Temperature,F 120specificGravity 0.6Viscosity,cp 0.01925
Re,ft. 1595.8Rw,ft. 0.5S 0J 5.22071E-06
22
CHAPTER4:RESULTSANDDISCUSSION
4.1 ResultsAfter conducting multiple simulation runs for different reservoir scenarios (Horizontal
permeability,Verticalpermeability,reservoirthicknessandlaterallength),theproductivityindex
valueswerecalculatedafterconvertingthereservoirpressuretoapseudopressureoverafour-
yearperiodofproduction.Then,aproductivityindexplotsweregeneratedtoobtainthehigh,
lowandaveragevaluesfromthestabilizedzoneasshowninFigure1.Moreover,thePIvalues
fromboththesteadystateandpseudosteadystatecorrelationswerecalculatedusingthesame
reservoir parameters as those used in the simulation model, and were compared with the
averagePIvalues thatwereobtained fromthesimulator.Finally, thecorrelationvalueswere
arrangedperthenearestvalueofthesimulator.
4.1.1 PIvalueswithdifferentHorizontalPermeabilityTable-8displaysthePIresultsfordifferenthorizontalpermeabilityusingbasecaseparameters.
Table8.PIfordifferentHorizontalPermeabilityValues
CorrelationPI,SCF/psi^2/day/cp
Kh=0.1md Kh=0.2md Kh=0.3md Kh=0.4md Kh=0.5md
ModelAverageValue 0.003105 0.00691 0.01036 0.013815 0.017265Borisov 0.003045 0.006089 0.009134 0.012178 0.015223
Renard-DupuyIsotropic 0.002999 0.005997 0.008996 0.011994 0.014993JoshiIsotropic 0.002990 0.005979 0.008969 0.011959 0.014948
Renard-DupuyAn-Isotropic 0.002807 0.005615 0.008422 0.011229 0.014036Giger-Reiss-JourdanIsotropic 0.002802 0.005604 0.008406 0.011208 0.014010
JoshiAn-Isotropic 0.002170 0.004341 0.006511 0.008681 0.010852Giger-Reiss-JourdanAn-Isotropic 0.002070 0.004139 0.006209 0.008279 0.010348
Babu-Odeh 0.001813 0.003627 0.005440 0.007254 0.009067Economides 0.011356 0.022713 0.034069 0.045425 0.056781Kuchuk 0.014196 0.028392 0.042588 0.056784 0.070980
23
4.1.2 PIvalueswithdifferentVerticalPermeabilityTable-9displaysthePIresultsfordifferentverticalpermeabilityusingbasecaseparameters.
Table9.PIfordifferentVerticalPermeabilityvalues
CorrelationPI,SCF/psi^2/day/cp
Kv=0.01md Kv=0.02md Kv=0.033mdModelAverageValue 0.003105 0.00327 0.0033
Renard-DupuyIsotropic 0.002999 0.002999 0.002999
JoshiIsotropic 0.002990 0.002990 0.002990
Renard-DupuyAn-Isotropic 0.002807 0.002885 0.002929
Giger-Reiss-JourdanIsotropic 0.002802 0.002802 0.002802
JoshiAn-Isotropic 0.002170 0.002560 0.002755
Giger-Reiss-JourdanAn-Isotropic 0.002070 0.002421 0.002598
Babu-Odeh 0.001813 0.001866 0.001894
Kuchuk 0.014196 0.020353 0.011163
Economides 0.016154 0.020382 0.026565
4.1.3 PIvalueswithdifferentReservoirThicknessTable-10displaysthePIresultsfordifferentreservoirthicknessusingbasecaseparameters.
Table10.PIfordifferentReservoirThicknessvalues
CorrelationPI,SCF/psi^2/day/cp
h=30ft h=10ft h=50ftModelAverageValue 0.003105 0.00117 0.0045
Borisov 0.003045 0.001039 0.004507Renard-DupuyIsotropic 0.002999 0.001031 0.004261
JoshiIsotropic 0.002990 0.001030 0.004798Renard-DupuyAn-Isotropic 0.002807 0.001017 0.004821Giger-Reiss-JourdanIsotropic 0.002802 0.000963 0.004928
JoshiAn-Isotropic 0.002170 0.000947 0.003371Giger-Reiss-JourdanAn-Isotropic 0.002070 0.000890 0.002828
Babu-Odeh 0.001813 0.000522 0.002724Economides 0.011356 0.003903 0.011356Kuchuk 0.014196 0.009248 0.014196
24
4.1.4 PIvalueswithdifferentLateralLengthTable-11displaysthePIresultsfordifferentlaterallengthsusingbasecaseparameters.
Table11.PIfordifferentLateralLengthvalues
CorrelationPI,SCF/psi^2/day/cp
L=1000ft L=1500ft L=2000ft L=2500ftModelAverageValue 0.00173 0.00242 0.003105 0.00409
Borisov 0.00172 0.00243 0.003045 0.00377Renard-DupuyIsotropic 0.00184 0.00240 0.002999 0.00369
JoshiIsotropic 0.00186 0.00240 0.002990 0.00367Giger-Reiss-JourdanIsotropic 0.00187 0.00232 0.002807 0.00345Renard-DupuyAn-Isotropic 0.00189 0.00224 0.002802 0.00329
JoshiAn-Isotropic 0.00127 0.00171 0.002170 0.00268Giger-Reiss-JourdanAn-Isotropic 0.00125 0.00167 0.002070 0.00247
Babu-Odeh 0.00122 0.00149 0.001813 0.00219Economides 0.00638 0.00820 0.011356 0.01449Kuchuk 0.00716 0.01068 0.014196 0.01771
4.2 DiscussionInitially,correlationsforisotropicreservoirswereincludedincalculationofthePIforbothsteady
stateandpseudosteadystate,toinvestigateiftherewasanysignificantdifferencesbetweenthe
outcomesoftheisotropicandanisotropiccorrelationsasshownontheresultsection.Sincethe
reservoirmodel was built based on an anisotropic reservoir, the isotropic correlations were
excluded to have more accurate comparison. Furthermore, the best correlation will be
determined after evaluating the different scenarios which include different horizontal
permeability,verticalpermeability,reservoirthicknessandlaterallengths.
25
4.2.1 HorizontalPermeabilityPIvaluesobtainedfromdifferentcorrelationsusinghorizontalpermeabilityrangefrom0.1to0.5
md,alongwiththeaveragePIvaluesobtainedfromthemodel.Figure-3&4demonstratesthe
model average PI value and the PI values from the other correlations using a horizontal
permeabilityof0.1md.ThemodelaveragePIvaluewas0.003105,anditisclearthatRenard-
DupuyAnisotropic correlationPI is the closest value to themodel averagePI value. Figure-5
showsacomparisonbetweenPIvaluesfromthedifferentAnisotropiccorrelationsandmodel
average value, using horizontal permeability values from 0.1 to 0.5 md. Renard-Dupuy
correlationPIvalueremainedtobethenearestvaluetothemodelaveragePIvalue.
Figure3.PIforanisotropicmethodwithKh=0.1mDvalues
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
ModelAverageValue
Renard-Dupuy Joshi Giger-Reiss-Jourdan Babu-Odeh Economides Kuchuk
PI,SCF/psi^
2/da
y/cp
26
Figure-4demonstratebettercomparisonofthePIvaluesaftertakingoffEconomidesand
Kuchukcorrelationsthatshowshighvaluescomparingwithothercorrelations.
Figure5.PIfordifferentanisotropicmethodwithKhvalues
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
ModelAverageValue
Renard-Dupuy Joshi Giger-Reiss-Jourdan Babu-Odeh Economides Kuchuk
PI,SCF/psi^2/day/cp
Kh=0.1md Kh=0.2md Kh=0.3md Kh=0.4md Kh=0.5md
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
ModelAverageValue Renard-Dupuy Joshi Giger-Reiss-Jourdan Babu-Odeh
PI,SCF/psi^
2/da
y/cp
Figure4.PIforanisotropicmethodwithKh=0.1mDvalues
27
4.2.2 VerticalPermeability
PI values obtained fromdifferent correlations using vertical permeability range from0.01 to
0.033md,alongwiththeaveragePIvaluesobtainedfromthemodel.Figure-6&7demonstrates
the model average PI value and the PI values from the other correlations using a vertical
permeabilityof0.01md.ThemodelaveragePIvaluewas0.003105,anditisclearthatRenard-
DupuyAnisotropic correlationPI is the closest value to themodel averagePI value. Figure-8
showsacomparisonbetweenPIvaluesfromthedifferentAn-isotropiccorrelationsandmodel
average value, using vertical permeability values from 0.01 to 0.033 md. Renard-Dupuy
correlationPIvalueremainedtobethenearestvaluetothemodelaveragePIvalue.
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
ModelAverageValue Renard-Dupuy Joshi Giger-Reiss-Jourdan Babu-Odeh Kuchuk Economides
PI,SCF/psi^
2/da
y/cp
Figure6.PIvaluesforanisotropicmethodwithKv=0.1mD
28
Figure-7demonstratebettercomparisonofthePIvaluesaftertakingoffEconomidesand
Kuchukcorrelationsthatshowshighvaluescomparingwithothercorrelations.
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
ModelAverageValue Renard-Dupuy Joshi Giger-Reiss-Jourdan Babu-Odeh
PI,SCF/psi^
2/da
y/cp
0
0.005
0.01
0.015
0.02
0.025
0.03
ModelAverageValue
Renard-Dupuy Joshi Giger-Reiss-Jourdan Babu-Odeh Kuchuk Economides
PI,SCF/psi^
2/da
y/cp
Kv=0.01md Kv=0.02md Kv=0.033md
Figure7.PIvaluesforanisotropicmethodwithKv=0.1mD
Figure8.PIforanisotropicmethodwithdifferentKvvalues
29
4.2.3 ReservoirThicknessPIvaluesobtainedfromdifferentcorrelationsusingreservoirthicknessrangefrom10to50ft.,
alongwiththeaveragePIvaluesobtainedfromthemodel.Figure-9&10demonstratesthemodel
averagePIvalueandthePIvaluesfromtheothercorrelationsusingareservoirthicknessof10
ft. The model average PI value was 0.00117, and It’s clear that Renard-Dupuy An-isotropic
correlationPIistheclosestvaluetothemodelaveragePIvalue.Figure-11showsacomparison
betweenPIvaluesfromthedifferentAn-isotropiccorrelationsandmodelaveragevalue,using
reservoirthicknessvaluesfrom10to50ft.Renard-DupuycorrelationPIvalueremainedtobe
thenearestvaluetothemodelaveragePIvalue.
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
ModelAverageValue Renard-Dupuy Joshi Giger-Reiss-Jourdan Babu-Odeh Economides Kuchuk
PI,SCF/psi^
2/da
y/cp
Figure9.PIforanisotropicmethodwithh=10ft.values
30
Figure-10demonstratebettercomparisonofthePIvaluesaftertakingoffEconomidesand
Kuchukcorrelationsthatshowshighvaluescomparingwithothercorrelations.
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
ModelAverageValue Renard-Dupuy Joshi Giger-Reiss-Jourdan Babu-Odeh
PI,SCF/psi^
2/da
y/cp
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
ModelAverageValue
Renard-Dupuy Joshi Giger-Reiss-Jourdan Babu-Odeh Economides Kuchuk
PI,SCF/psi^
2/da
y/cp
h=10ft h=30ft h=50ft
Figure10.PIforanisotropicmethodwithh=10ft.values
Figure11.PIfordifferentanisotropicmethodwithThicknessvalues
31
4.2.4 LateralLengthPIvaluesobtainedfromdifferentcorrelationsusinglaterallengthrangefrom1000to2500ft.,
alongwith theaveragePIvaluesobtained fromthemodel.Figure-12&13demonstrates the
modelaveragePIvalueandthePIvaluesfromtheothercorrelationsusinga lateral lengthof
1000ft.ThemodelaveragePIvaluewas0.00173,andIt’sclearthatRenard-DupuyAn-isotropic
correlationPIistheclosestvaluetothemodelaveragePIvalue.Figure-14showsacomparison
betweenPIvaluesfromthedifferentAn-isotropiccorrelationsandmodelaveragevalue,using
laterallengthvaluesfrom1000to2500ft.Renard-DupuycorrelationPIvalueremainedtobethe
nearestvaluetothemodelaveragePIvalue.
0.000
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
ModelAverageValue
Renard-Dupuy Joshi Giger-Reiss-Jourdan Babu-Odeh Economides Kuchuk
PI,SCF/psi^
2/da
y/cp
Figure12.PIforanisotropicmethodwithLaterallength1000ft.values
32
Figure-13demonstratebettercomparisonofthePIvaluesaftertakingoffEconomidesand
Kuchukcorrelationsthatshowshighvaluescomparingwithothercorrelations.
0.0000
0.0002
0.0004
0.0006
0.0008
0.0010
0.0012
0.0014
0.0016
0.0018
0.0020
ModelAverageValue Renard-Dupuy Joshi Giger-Reiss-Jourdan Babu-Odeh
PI,SCF/psi^
2/da
y/cp
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
0.018
0.020
ModelAverageValue
Renard-Dupuy Joshi Giger-Reiss-Jourdan Babu-Odeh Economides Kuchuk
PI,SCF/psi^
2/da
y/cp
L=1000ft L=1500ft L=2000ft L=2500ft
Figure13.PIforanisotropicmethodwithLaterallength1000ft.values
Figure14.PIfordifferentanisotropicmethodwithLateralLengthvalues
33
CHAPTER5:CONCLUSIONThe main purpose of this research is to evaluate and compare the productivity index of a
horizontalwellinagasreservoirusingareservoirmodelanddifferentsteadystateandpseudo-
steadystatecorrelations.Toachievethisobjective,anumericalreservoirsimulator(CMG)was
usedtoconstructthereservoirmodelanddeterminePIforanumbercases(differentvaluesof
horizontalpermeability,verticalpermeability,reservoirthickness,andlaterallength).Later,the
averagemodelPIvaluewascomparedwiththepredictedvaluesbythevariouscorrelations.The
followingconclusionswerereacheduponcompletionofthisstudy:
1. Renard-Dupuy’sanisotropiccorrelationconsistentlyprovidedtheclosestagreementwith
themodelaveragePIvalueinallcasesinvestigated.
2. KuchukcorrelationresultedinthehighestcalculatedvalueforPI.
3. Babu-OdehcorrelationresultedinthelowestcalculatedvalueforPI.
FutureworkmayincludeevaluationofthePIforahydraulicallyfracturedhorizontalgaswellwithusingthereservoirmodelandtoattemptdevelopingacorrelationforPI.
34
REFERENCES
1. Dankwa, Ohenewaa Kakra. Effects of Partial Completion on Productivity Index. Diss.AfricanUniversityofScienceandTechnology,2011.
2. Babu, D. K., and Aziz S. Odeh. "Productivity of a HorizontalWell (includes associatedpapers20306,20307,20394,20403,20799,21307,21610,21611,21623,21624,25295,25408,26262,26281,31025,and31035)."SPEReservoirEngineering4.04(1989):417-421.
3. Goode,P.A.,andF.J.Kuchuk."Inflowperformanceofhorizontalwells."SPEReservoirEngineering6.03(1991):319-323.
4. Kuchuk, Fikri J., et al. "Pressure-transient analysis for horizontal wells." Journal ofPetroleumTechnology42.08(1990):974-1.
5. Besson, J. "Performance of slanted and horizontal wells on an anisotropic medium."EuropeanPetroleumConference.SocietyofPetroleumEngineers,1990.
6. Joshi,S.D."Augmentationofwellproductivitywithslantandhorizontalwells(includesassociatedpapers24547and25308)." Journal of PetroleumTechnology40.06 (1988):729-739.
7. Giger, F. M. "Low-permeability reservoirs development using horizontal wells." LowPermeabilityReservoirsSymposium.SocietyofPetroleumEngineers,1987.
8. Saavedra,N.F.,andS.D.Joshi."ApplicationofhorizontalwelltechnologyinColombia."SPE/CIMInternationalConferenceonHorizontalWellTechnology.SocietyofPetroleumEngineers,2000.
9. Odeh, Aziz S., and D. K. Babu. "Transient flow behavior of horizontal wells, pressuredrawdown,andbuildupanalysis."SPECaliforniaRegionalMeeting.SocietyofPetroleumEngineers,1989.
10. Economides, M. J., C. W. Brand, and T. P. Frick. "Well configurations in anisotropicreservoirs."SPEFormationEvaluation11.04(1996):257-262.
11. Saavedra,N.F.,&Joshi,S.D.(2000,January1).ApplicationofHorizontalWellTechnology
inColombia.SocietyofPetroleumEngineers.doi:10.2118/65477-MS.
12. Escobar, F. H., Saavedra, N. F., Aranda, R. F., & Herrera, J. F. (2004, January 1). AnImproved Correlation to Estimate Productivity Index in Horizontal Wells. Society ofPetroleumEngineers.doi:10.2118/88540-MS.
35
13. Suk Kyoon, C., Ouyang, L.-B., & Huang,W. S. B. (2008, January 1). A Comprehensive
Comparative Study on Analytical PI/IPR Correlations. Society of Petroleum Engineers.doi:10.2118/116580-MS.
14. Dankwa, O. K., & Igbokoyi, A. O. (2012, January 1). Effects of Partial Completion on
ProductivityIndex.SocietyofPetroleumEngineers.doi:10.2118/163030-MS.
15. Alarifi,S.,AlNuaim,S.,&Abdulraheem,A.(2015,March8).ProductivityIndexPredictionfor Oil Horizontal Wells Using Different Artificial Intelligence Techniques. Society ofPetroleumEngineers.doi:10.2118/172729-MS.
36
APPENDIX
1. CMGModelCMG(computerModelingGroup)isoneofthelargestprovidersofreservoirsimulationsoftware
in the world which was originated in 1978. In this research, CMG-IMEXmodel was used to
evaluate the correlation for horizontal well productivity index in a gas reservoir. Themodel
startedbyclickingontheBuildericonontheCMGtechnologieslauncherasshowninFigure-3.
Figure15.CMGlauncher
37
TheuserselectsIMEXsimulator,Fieldunits,Singleporosity,andsimulationstartdateasshown
inFigure-4.
Figure16.Reservoirsimulationsetting
TheuserisabletoviewtheCMGBUILDERbyclicking“OK”asshowninFigure-5.
Figure17.CMGBuilder
38
Theuserclicksonthe“Reservoir”tabinthemodeltreeviewandselects“Creategrid”andthen
“Cartesian”. Theuser inputs thenumberof grid blocks in the I-direction, J- direction, andK-
directionasshowninFigure-6.
Figure18.CMGBuilder
Theuserselectsthe“SpecifyProperty”tabandinputthevaluesincludinggridtop,gridthickness,
porosity,matrixpermeability(I,J,andK-directions).“GeneralPropertySpecification”screenis
showninFigure-7.
Figure19.GeneralPropertySpecification
39
Theuserdoubleclickson“Rockcompressibility”fromthereservoirsectionandinputsthe
referencepressurefor(CPOR)&(PRPOR)asshowninFigure-8
Figure20.Rockcompressibility
Theuserdoubleclickson“ImwxPVTRegions”frominitialconditionsectionandinputsreservoir
pressure,andgasgravityasshowninFigure-9.
Figure21.ImwxPVTRegions
40
Theuserclicksonthe“Rocktypes”tabinthemodeltreeviewandrelativepermeabilitytable.
ThentheuserselectsincludecapillarypressureasshowninFigure-10.
Figure22.Rocktype
41
Figure23.KrVs.Sg
Figure24.KrVs.Sw
42
Theuserclicksonthe“InitialCondition”tabinthemodeltreeviewandpicksInitialization
Settingthentheuserselects“watergas”fromthe“CalculationMethod”tabasshownin
Figure-13.
Figure25.Initialcondition
43
Thentheusergoesto“PVTRegionParameters”tabandentersthereferencepressure,reference
depth,andwatergascontactasshowninFigure-14.
Figure26.Initialcondition
44
Theuserclicksonthe“Wells&Recurrent”tabinthemodeltreeviewandcreatesnewwellby
rightclickingonWellsandselectNew.Thiswillallowtheusertocreateanewwellandtheuser
givesaname“Horizontal”andselectstypeas“Producer”inFigure-15.
Figure27.Wellevents
Theuserclickson“Constraints”tabandcheckstheboxforConstraintdefinition.Inaddition,the
userselectsnew(intheConstraintcolumnofthetable),selectsOPERATE.Thentheuserselects
BHPbottomholepressure,MIN,toanypressureasshowninFigure-16.
Figure28.Wellevents
45
The user double clicks on “PERF” and selects the general tab and fills out the information
includingdirection,andradiusofthewellboreasshowninFigure-17.
Figure29.Wellcompletiondata
Theuserselectstheperforationtabandtoaddperforationwiththemouse,theuserpresses
buttonandpickstheblocksforperforationsasshowninFigure-18.
Figure30.Wellcompletiondata
46
ThisisthetopviewofthereservoirwitheverythingcompletedasshowninFigure-19.
Figure31.Topview