Productivity Index of Horizontal Gas Well

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Graduate Theses, Dissertations, and Problem Reports

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

PetroleumandNaturalGasEngineering

KashyAminian,Ph.D.,Chair

SamAmeri,Prof.

MehrdadZamirian,Ph.D.

DepartmentofPetroleumandNaturalGasEngineering

Morgantown,WestVirginia

Keywords:Productivityindexofgashorizontalwell

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.

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.

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

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

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

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.

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.

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.

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.

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

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:

P@ = 2PµCZ

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:

𝐽 = 0.703 ∗ ℎ ∗ 𝐾ℎ ∗ 𝜇𝑔 ∗ 𝑧

𝑇(ln 4𝑟𝑒ℎ𝐿 + 𝐿

ℎ ln( ℎ2𝜋𝑟𝑤))

2.2.1.2 Giger-Reiss-Jourdan’sCorrelation:Thepredictionofproductivityindexofhorizontalgaswelliscorrectedfromthehorizontaloilwell

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

2.2.1.3 Joshi’sCorrelation:Thepredictionofproductivityindexofhorizontalgaswelliscorrectedfromthehorizontaloilwell

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,

𝑎 = 𝐿2 0.5 + 0.25 +

2𝑟𝑒ℎ𝐿

𝑅 = 𝑎 + 𝑎[ + (𝐿2)

𝐿(2)

2.2.1.4 Renard-Dupuy’sCorrelation:Thepredictionofproductivityindexofhorizontalgaswelliscorrectedfromthehorizontaloilwell

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

𝑟e𝑤 = 1 + 𝐵 𝑟𝑤2𝐵

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)

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

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

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 −

2 ∗ 𝑍𝑤ℎ

−12 − ln(sin(

𝜋 ∗ 𝑍𝑤ℎ ))

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.

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

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.

Table3.PIresults

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

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

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

Table6.PIforallcorrelationscomparedwithsimulatoraveragevalue

BestCorrolationwithSimAvg.value

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

PI,SCF/psi2/day/cp

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

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

4.1.2 PIvalueswithdifferentVerticalPermeabilityTable-9displaysthePIresultsfordifferentverticalpermeabilityusingbasecaseparameters.

Table9.PIfordifferentVerticalPermeabilityvalues

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

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

4.1.4 PIvalueswithdifferentLateralLengthTable-11displaysthePIresultsfordifferentlaterallengthsusingbasecaseparameters.

Table11.PIfordifferentLateralLengthvalues

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.

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

ModelAverageValue

Renard-Dupuy Joshi Giger-Reiss-Jourdan Babu-Odeh Economides Kuchuk

PI,SCF/psi^

Figure-4demonstratebettercomparisonofthePIvaluesaftertakingoffEconomidesand

Kuchukcorrelationsthatshowshighvaluescomparingwithothercorrelations.

Figure5.PIfordifferentanisotropicmethodwithKhvalues

ModelAverageValue

PI,SCF/psi^2/day/cp

Kh=0.1md Kh=0.2md Kh=0.3md Kh=0.4md Kh=0.5md

0.0005

0.0015

0.0025

0.0035

ModelAverageValue Renard-Dupuy Joshi Giger-Reiss-Jourdan Babu-Odeh

PI,SCF/psi^

Figure4.PIforanisotropicmethodwithKh=0.1mDvalues

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.

ModelAverageValue Renard-Dupuy Joshi Giger-Reiss-Jourdan Babu-Odeh Kuchuk Economides

PI,SCF/psi^

Figure6.PIvaluesforanisotropicmethodwithKv=0.1mD

0.0005

0.0015

0.0025

0.0035

PI,SCF/psi^

ModelAverageValue

Renard-Dupuy Joshi Giger-Reiss-Jourdan Babu-Odeh Kuchuk Economides

PI,SCF/psi^

Kv=0.01md Kv=0.02md Kv=0.033md

Figure7.PIvaluesforanisotropicmethodwithKv=0.1mD

Figure8.PIforanisotropicmethodwithdifferentKvvalues

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.

ModelAverageValue Renard-Dupuy Joshi Giger-Reiss-Jourdan Babu-Odeh Economides Kuchuk

PI,SCF/psi^

Figure9.PIforanisotropicmethodwithh=10ft.values

0.0002

0.0004

0.0006

0.0008

0.0012

0.0014

PI,SCF/psi^

ModelAverageValue

PI,SCF/psi^

h=10ft h=30ft h=50ft

Figure10.PIforanisotropicmethodwithh=10ft.values

Figure11.PIfordifferentanisotropicmethodwithThicknessvalues

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.

ModelAverageValue

PI,SCF/psi^

Figure12.PIforanisotropicmethodwithLaterallength1000ft.values

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

0.0014

0.0016

0.0018

0.0020

PI,SCF/psi^

ModelAverageValue

PI,SCF/psi^

L=1000ft L=1500ft L=2000ft L=2500ft

Figure13.PIforanisotropicmethodwithLaterallength1000ft.values

Figure14.PIfordifferentanisotropicmethodwithLateralLengthvalues

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.

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.

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.

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

TheuserselectsIMEXsimulator,Fieldunits,Singleporosity,andsimulationstartdateasshown

inFigure-4.

Figure16.Reservoirsimulationsetting

TheuserisabletoviewtheCMGBUILDERbyclicking“OK”asshowninFigure-5.

Figure17.CMGBuilder

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

Theuserdoubleclickson“Rockcompressibility”fromthereservoirsectionandinputsthe

referencepressurefor(CPOR)&(PRPOR)asshowninFigure-8

Figure20.Rockcompressibility

Theuserdoubleclickson“ImwxPVTRegions”frominitialconditionsectionandinputsreservoir

pressure,andgasgravityasshowninFigure-9.

Figure21.ImwxPVTRegions

Theuserclicksonthe“Rocktypes”tabinthemodeltreeviewandrelativepermeabilitytable.

ThentheuserselectsincludecapillarypressureasshowninFigure-10.

Figure22.Rocktype

Figure23.KrVs.Sg

Figure24.KrVs.Sw

Theuserclicksonthe“InitialCondition”tabinthemodeltreeviewandpicksInitialization

Settingthentheuserselects“watergas”fromthe“CalculationMethod”tabasshownin

Figure-13.

Figure25.Initialcondition

Thentheusergoesto“PVTRegionParameters”tabandentersthereferencepressure,reference

depth,andwatergascontactasshowninFigure-14.

Figure26.Initialcondition

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

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

ThisisthetopviewofthereservoirwitheverythingcompletedasshowninFigure-19.

Figure31.Topview

Productivity Index of Horizontal Gas Well

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