Formulas and Calculations for Petroleum Engineering PDF
Preview Formulas and Calculations for Petroleum Engineering
Formulas and Calculations for Petroleum Engineering Formulas and Calculations for Petroleum Engineering Cenk Temizel Tayfun Tuna Mehmet Melih Oskay Luigi A. Saputelli GulfProfessionalPublishingisanimprintofElsevier 50HampshireStreet,5thFloor,Cambridge,MA02139,UnitedStates TheBoulevard,LangfordLane,Kidlington,Oxford,OX51GB,UnitedKingdom ©2019ElsevierInc.Allrightsreserved. Nopartofthispublicationmaybereproducedortransmittedinanyformorbyanymeans,electronicormechanical,includingphotocopying, recording,oranyinformationstorageandretrievalsystem,withoutpermissioninwritingfromthepublisher.Detailsonhowtoseekpermission, furtherinformationaboutthePublisher’spermissionspoliciesandourarrangementswithorganizationssuchastheCopyrightClearanceCenter andtheCopyrightLicensingAgency,canbefoundatourwebsite:www.elsevier.com/permissions. ThisbookandtheindividualcontributionscontainedinitareprotectedundercopyrightbythePublisher(otherthanasmaybenotedherein). Notices Knowledgeandbestpracticeinthisfieldareconstantlychanging.Asnewresearchandexperiencebroadenourunderstanding,changesin researchmethods,professionalpractices,ormedicaltreatmentmaybecomenecessary. Practitionersandresearchersmustalwaysrelyontheirownexperienceandknowledgeinevaluatingandusinganyinformation,methods, compounds,orexperimentsdescribedherein.Inusingsuchinformationormethodstheyshouldbemindfuloftheirownsafetyandthesafety ofothers,includingpartiesforwhomtheyhaveaprofessionalresponsibility. Tothefullestextentofthelaw,neitherthePublishernortheauthors,contributors,oreditors,assumeanyliabilityforanyinjuryand/ordamageto personsorpropertyasamatterofproductsliability,negligenceorotherwise,orfromanyuseoroperationofanymethods,products,instructions, orideascontainedinthematerialherein. LibraryofCongressCataloging-in-PublicationData AcatalogrecordforthisbookisavailablefromtheLibraryofCongress BritishLibraryCataloguing-in-PublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary ISBN:978-0-12-816508-9 ForinformationonallGulfProfessionalpublications visitourwebsiteathttps://www.elsevier.com/books-and-journals Publisher:BrianRomer SeniorAcquisitionEditor:KatieHammon EditorialProjectManager:AliAfzal-Khan ProductionProjectManager:SujathaThirugnanaSambandam CoverDesigner:ChristianBilbow TypesetbySPiGlobal,India Biographies of authors CenkTemizelisareservoirengineerwith15yearsofinternationalexperienceintheindustrywithexpertiseinreservoir simulation,smartfields,heavyoil,optimization,unconventionalsandenhancedoilrecovery.Hewasateaching/research assistantattheUniversityofSouthernCaliforniaandStanfordUniversitybeforejoiningtheindustry.Hewonthe2ndplace atSPEGlobalR&DCompetitionatSPEATCE2014inAmsterdamandthe2ndplaceinTechnicalExcellenceAwardsat 22ndWorldPetroleumCongressin2017inIstanbul.HereceivedtheHalliburtonAwardinInnovationin2012.Heservesas atechnicalreviewerforpetroleumengineeringjournals.Hisinterestsincludereactionkinetics/dynamicsoffluidflowin porousmediaandenhancedoilrecoveryprocesses.Heservedasasessionchairandmemberoforganizingcommitteesfor severalSPEconferences.Hehaspublishedaround100publicationsintheareaofreservoirmanagement,productionopti- mization,enhancedoilrecoveryprocessesandsmartfieldsalongwithUSpatents.HeholdsaBSdegree(Honors)from Middle East Technical University—Ankara (2003) and an MS degree (2005) from University of Southern California (USC), Los Angeles, CA both inpetroleum engineering. TayfunTunaisadatascientistandsoftwaredeveloperwhoholdsaMSandaPhDdegreeincomputersciencefromthe UniversityofHouston.Hisgraduateresearchfocuswasontextmining;applyingmachinelearningtechniquestolecture videosinordertosegmentvideocontentforabetterlearningexperience.HeisacofounderofVideopointsLLC,previously knownasICSVideoProject,aninteractiveeducationalvideoplatformwhichhavebeenusedmorethan50Kusersacross multipleuniversitycampuses.Whilehewasthechiefoperatingofficerandprincipalinvestigator,hisprojectisrewardedby National Science FoundationSmall Business Innovation Research(NSF SBIR) Phase I Grant. In his professional career, he has worked with Halliburton to develop a patented machine learning-based web-based interfacethatpredictschanceofgettingofstuckwhiledrillingforoil.Hehastwopatentsand20researchpaperpublications oneducational technology, social networks, andoil&gasfield. Mehmet Melih Oskay earned his PhD from UT Austin, and he has been in academia and industry as advisors and managerialpositionsfor morethan 30 yearsat several major operators. He has represented operators at JointOperations Committee andJointOperations Tender Committees. HehastaughtatUniversityofTexas—Austin,TX;LouisianaTechUniversity-Ruston,Louisiana;MiddleEastTech- nical University—Ankara, Turkey; andKing Fahd Universityof PetroleumandMinerals, Dhahran, Saudi Arabia. HehasparticipatedinseveralOrganizingCommitteesandSessionChairmanshippositionsatmanySPEOilShowand Technical Conferences. Luigi A.Saputelli is a reservoir engineering senior advisor with over 28 years of experience. He worked in various operators and services companies around the world. He is a founding member of the Society of Petroleum Engineers’ Real-time Optimization Technical Interest Group and the Petroleum Data-driven Analytics technical section. He is the recipient of the 2015 SPE International Production andOperations Award. Hehaspublishedmorethan90industrypapersonappliedtechnologiesrelatedtoreservoirmanagement,real-timeopti- mization,andproductionoperations.HeholdsaBSc.inelectronicengineerfromUniversidadSimonBolivar(1990),witha master in petroleum engineering from Imperial College (1996), and a PhD in chemical engineering from University of Houston (2003). He also serves asmanaging partner for, a petroleum engineeringservicesfirm based inHouston. xxv Foreword FormulasandCalculationsforPetroleumEngineeringunlocksthecapabilityforanypetroleumengineeringindividual, experiencedornot,tosolveproblemsandlocatequickanswers,eliminatingnonproductivetimespentsearchingforthat rightcalculation.Enhancedwithlabdataexperiments,practiceexamples,andacomplimentaryonlinesoftwaretoolbox, thebookpresentsthemostconvenientandpracticalreferenceforalloilandgasphasesofagivenproject.Coveringthefull spectrum,thisreferencegivessingle-pointreferencetoallcriticalmodules,includingdrilling,production,reservoirengi- neering, well testing, well logging, enhanced oil recovery, well completion, fracturing, fluid flow, and even petroleum economics. ptlbx.comprovides access tocalculations ofthese formulas. xxvii Acknowledgement Authors Thisbookisdedicatedtomywife,mylove,Saulewhohassupportedmeunconditionallyinmyendeavorsandhasbeenan inspirationformeinlifewithherlove,care,andunderstandingandtomydaughterAdaAycawhohasbroughtjoyand happinesstoourlifeandtomyparentsYukselandRasimTemizelandmybrotherEfefortheircontinuoussupportandlove. Cenk Temizel Iam indebted tomywife Suhendanand tomy daughter Ceydafor their unflaggingsupportto finish this book. Mehmet MelihOskay IdedicatethisbooktomyparentsJuliaandEmilio,whoareeternalsymbolsofunconditionalloveandtrueparenthood, fromwhom I learned whatexemplary human values. Luigi A.Saputelli Reviewers My effort that went into the completion of this book is dedicated to my wife Ezgi who assisted me with her love and patience, to Serkan who made me feel lucky to have an honest brother like him, and also to my beloved parents Fusun andKayaCanbazwhogavetheirtruelovewithoutanyexpectationsandsupportedmewithpatienceinanycircumstances. Celal Hakan Canbaz IwouldliketoexpressmydeepestloveandrespecttoespeciallymybelovedparentsandwifeElifwhoalwayshassup- portedandinspiredmetocontributetothisbookandmyself-improvementintermsofbothprofessionalandpersonalways during allmy life. Yildiray Palabiyik xxix Chapter 1 Reservoir engineering formulas and calculations Chapter Outline 1.1 APIgravity 3 1.31 Effectivewellboreradiusofahorizontalwell—van 1.2 Averagepermeabilityforlinearflow—Layeredbeds 3 derVlisetal.method 16 1.3 Averagepermeabilityforlinearflow—Seriesbeds 4 1.32 Effectivewellboreradiusofawellinpresenceof 1.4 Averagepermeabilityforparallel-layeredsystems 4 uniform-fluxfractures 16 1.5 Averagepermeabilityinradialsystems 4 1.33 Effectivewellboreradiustocalculateslantwell 1.6 Averagetemperatureofagascolumn 5 productivity—vanderVlisetal. 16 1.7 Calculationoffractionalflowcurve 5 1.34 Estimationofaveragereservoirpressure—MDH 1.8 Capillarynumber 6 method 17 1.9 Capillarypressure 6 1.35 Formationtemperatureforagivengradient 17 1.10 Characteristictimeforlineardiffusioninreservoirs 6 1.36 Fractionofthetotalsolutiongasretainedinthe 1.11 Coleplot 7 reservoirasfreegas 17 1.12 Communicationbetweencompartmentsintightgas 1.37 Fractionalgasrecoverybelowthecritical reservoirs 7 desorptionpressureincoalbedmethanereservoirs 18 1.13 Communicationfactorinacompartmentintightgas 1.38 Freegasinplace 18 reservoirs 7 1.39 Gasadsorbedincoalbedmethanereservoirs 19 1.14 Compressibilitydriveingasreservoirs 8 1.40 Gasbubbleradius 19 1.15 Correctionfactor—Hammerlindl 8 1.41 Gascapratio 19 1.16 Criticalrateforhorizontalwellsinedge-waterdrive 1.42 Gascapshrinkage 20 reservoirs 8 1.43 Gasdriveindexingasreservoirs 20 1.17 Crossflowindex 9 1.44 Gasexpansionfactor 20 1.18 Cumulativeeffectivecompressibility—Fetkovich 10 1.45 Gasexpansiontermingasreservoirs 21 1.19 Cumulativegasproduction—Tarner’smethod 10 1.46 Gasflowrateintothewellbore 21 1.20 Cumulativeoilproduction—Undersaturatedoil 1.47 Gasflowunderlaminarviscousconditions 22 reservoirs 11 1.48 Gasformationvolumefactor 22 1.21 Deliverabilityequationforshallowgasreservoirs 11 1.49 Gashydratedissociationpressure 22 1.22 Dimensionlesspressure—KamalandBrigham 11 1.50 Gasmaterialbalanceequation 23 1.23 Dimensionlessradiusofradialflow—Constant-rate 1.51 Gasproducedbygasexpansion 23 production 12 1.52 Gassaturation—Water-drivegasreservoirs 24 1.24 Dimensionlesstime—MyhillandStegemeier’smethod 12 1.53 Gassolubilityincoalbedmethanereservoirs 24 1.25 Dimensionlesstimeforinterferencetestingin 1.54 Geertsma’smodelforporosity/transit-time homogeneousreservoirs—Earlougher 13 relationship 25 1.26 Dimensionlessverticalwellcriticalrate 1.55 Geothermalgradient 25 correlations—Hoyland,Papatzacos, 1.56 HagenPoiseuilleequation 26 andSkjaeveland 13 1.57 HagoortandHoogstragasflowintightreservoirs 26 1.27 Dimensionlesswellborestoragecoefficientof 1.58 Hammerlindlmethodforgasinplace 26 radialflow—Constant-rateproduction 13 1.59 High-pressureregiongasflowrate 27 1.28 Effectivecompressibilityinundersaturatedoil 1.60 Horizontalwellbreakthroughtime—Withgascap reservoirs—Hawkins 14 orbottomwater 27 1.29 Effectivewellboreradiusofahorizontal 1.61 Horizontalwellcriticalratecorrelation—Chaperon 28 well—Method1—Anisotropicreservoirs 14 1.62 Horizontalwellcriticalratecorrelations—Efros 28 1.30 Effectivewellboreradiusofahorizontal 1.63 Horizontalwellcriticalratecorrelations—Giger well—Method1—Isotropicreservoirs 15 andKarcher 29 FormulasandCalculationsforPetroleumEngineering.https://doi.org/10.1016/B978-0-12-816508-9.00001-9 ©2019ElsevierInc.Allrightsreserved. 1 2 Formulasandcalculationsforpetroleumengineering 1.64 Horizontalwellcriticalratecorrelations—Joshi 1.108 Porositydetermination—IESandFDClogs 47 methodforgasconing 29 1.109 Producedgas-oilratio 47 1.65 Hydrocarbonporevolumeoccupiedbyevolved 1.110 Productivityindexforagaswell 48 solutiongas 30 1.111 Pseudo-steadystateproductivityofhorizontal 1.66 Hydrocarbonporevolumeoccupiedbygascap 30 wells—Method1 48 1.67 Hydrocarbonporevolumeoccupiedbyremainingoil 31 1.112 Pseudo-steadystateproductivityofhorizontal 1.68 Hydrostaticpressure 31 wells—Method2 49 1.69 Incrementalcumulativeoilproductionin 1.113 Pseudo-steadystateproductivityofhorizontal undersaturatedreservoirs 31 wells—Method3 50 1.70 Ineffectiveporosity 32 1.114 Pseudo-steadystateradialflowequation 50 1.71 Initialgascap 32 1.115 Relativepermeability—Coreyexponents 51 1.72 Initialgasinplaceforwater-drivegasreservoirs 32 1.116 Remaininggasinplaceincoalbedmethane 1.73 Injectivityindex 33 reservoirs 51 1.74 Instantaneousgas-oilratio 33 1.117 Roachplotforabnormallypressuredgasreservoirs 52 1.75 Interporosityflowcoefficient 34 1.118 Rockexpansionterminabnormallypressuredgas 1.76 Interstitialvelocity 34 reservoirs 52 1.77 Isothermalcompressibilityofoil—Vasquez-Beggs 1.119 Shapefactor—Earlougher 52 correlation—p>pb 34 1.120 Solutiongasoilratio—Beggs-Standing 1.78 Isothermalcompressibilityofoil—villena-Lanzi correlation—p<pb 53 correlation—p<pb 35 1.121 Solutiongasoilratio—Standing’scorrelation 53 1.79 Isothermalcompressibilityofwater—Osifcorrelation 35 1.122 Solutiongaswaterratio 54 1.80 Kernsmethodforgasflowinafracture 35 1.123 Somertonmethodforformationpermeabilityin 1.81 Klinkenberggaseffect 36 coalbedmethanereservoirs 54 1.82 Kozenyequation 36 1.124 Specificgravityofgashydrateformingcomponents 54 1.83 Kozeny-Carmanrelationship 36 1.125 Timetoreachthesemi-steadystateforagaswell 1.84 LeverettJ-function 37 inacircularorsquaredrainagearea 55 1.85 Line-sourcesolutionfordamagedorstimulated 1.126 Timetotheendofinfinite-actingperiodforawell wells 37 inacircularreservoir 55 1.86 Low-pressureregiongasflowratefornon-circular 1.127 TorcasoandWyllie’scorrelationforrelative drainagearea 38 permeabilityratioprediction 55 1.87 Materialbalanceforcumulativewater 1.128 Totalcompressibility 56 influx—HavlenaandOdeh 38 1.129 Totalporevolumecompressibility 56 1.88 Maximumheightofoilcolumnincaprock 39 1.130 Transmissibilitybetweencompartments 57 1.89 ModifiedColeplot 39 1.131 Transmissibilityofacompartment 57 1.90 ModifiedKozeny-carmanrelationship 39 1.132 Transmissivity 57 1.91 Normalizedsaturation 40 1.133 Trappedgasvolumeinwater-invadedzones 58 1.92 Oilbubbleradiusofthedrainageareaofeachwell 1.134 Two-phaseformationvolumefactor 58 representedbyacircle 40 1.135 Undergroundfluidwithdrawal—HavlenaandOdeh 59 1.93 Oildensity—Standing’scorrelation 41 1.136 Verticalwellcriticalratecorrelations—Craft 1.94 Oilformationvolumefactor—Standing’scorrelation 41 andHawkinsmethod 59 1.95 Oilformationvolumefactor—Beggs-standing 1.137 Verticalwellcriticalratecorrelations—Hoyland, correlation—p<pb 41 Papatzacos,andSkjaeveland—Isotropicreservoirs 60 1.41 Oilformationvolumefactor—Beggs-standing 1.138 Verticalwellcriticalratecorrelations—Meyer, correlation—p>pb 42 Gardner,andPirson—Simultaneousgasandwater 1.42 Oilinplaceforundersaturatedoilreservoirs coning 60 withoutfluidinjection 42 1.139 Verticalwellcriticalratecorrelations—Meyer, 1.98 Oilinplaceinsaturatedoilreservoirs 43 Gardner,andPirson—Waterconing 61 1.99 Oillostinmigration 43 1.140 Verticalwellcriticalratecorrelations—Meyer, 1.100 Oilsaturationatanydepletionstatebelowthe Gardner,andPirson—Gasconing 61 bubblepointpressure 44 1.141 Viscosibility 62 1.101 Originalgasinplace 44 1.142 ViscosityofcrudeoilthroughAPI 62 1.102 Paynemethodforintercompartmentalflowin 1.143 Viscosityofdeadoil—Standing’scorrelation 62 tightgasreservoirs 44 1.144 Viscosityofdead-oil—Egbogahcorrelation—p<pb 63 1.103 Performancecoefficientforshallowgasreservoirs 45 1.145 Viscosityofliveoil—Beggs/Robinsoncorrelation 63 1.104 Poisson’sratio 45 1.146 Viscosityofoil—Vasquez/Beggscorrelation—p>pb 63 1.105 Porethroatsorting 46 1.147 Viscosityofwateratatmosphericpressure—McCain 1.106 Porevolumeoccupiedbyinjectionofgasandwater 46 correlation 64 1.107 Porevolumethroughsquaredmethodintightgas 1.148 Viscosityofwateratreservoirpressure—McCain reservoirs 46 correlation 64 Reservoirengineeringformulasandcalculations Chapter 1 3 1.149 Volumeofgasadsorbedincoalbedmethanereservoirs 64 1.156 Water-driverecovery 68 1.150 Volumetricheatcapacityofareservoir 65 1.157 Waterexpansiontermingasreservoirs 68 1.151 Waterbreakthroughcorrelationinvertical 1.158 Waterformationvolumefactor—McCaincorrelation 68 wells—BournazelandJeanson 65 1.159 Waterinflux—Potaquifermodel 69 1.152 Waterbreakthroughcorrelationsinvertical 1.160 WaterinfluxconstantforthevanEverdingen wells—SobocinskiandCornelius 66 andHurstunsteady-statemodel 69 1.153 Watercontentofsourgas 66 1.161 Watertwo-phaseformationvolumefactor 70 1.154 Watercut—Stiles 67 1.162 Waxmanandsmitsmodel—Cleansands 70 1.155 Water-driveindexforgasreservoirs 67 1.163 Welgeextension—Fractionalflow 70 1.1 API gravity Input(s) SGo: SpecificGravity of Oil Phase (fraction) Output(s) API: API Gravity (dimensionless) Formula(s) 141:5 API¼ (cid:2)131:5 SG o Notes: SG ¼ roil at 60F. o rwater Reference:Wikipedia.org. 1.2 Average permeability for linear flow—Layered beds Input(s) k : Permeabilityfor Layer 1 (mD) 1 k : Permeabilityfor Layer 2 (mD) 2 k : Permeabilityfor Layer 3 (mD) 3 A : Area ofLayer 1 (ft2) 1 A : Area ofLayer 2 (ft2) 2 A : Area ofLayer 3 (ft2) 3 Output(s) kavg: Average Permeability inLinearSystems when there is no crossflow between layers (mD) Formula(s) k (cid:3)A +k (cid:3)A +k (cid:3)A k ¼ 1 1 2 2 3 3 avg A +A +A 1 2 3 Reference:Ahmed,T. (2006). ReservoirEngineering Handbook.Elsevier, Page: 238.
The list of books you might like
