Bp Macondo Estimate 1

Exhibit 1 (Part 1 of 2)

Case 2:10-md-02179-CJB-SS Document 10533-2 Filed 06/27/13 Page 1 of 99

CONFIDENTIAL

Inre:OilSpillbytheOilRigDeepwaterHorizoninTheGulfofMexico,onApril20,2010

UNITEDSTATESDISTRICTCOURTEASTERNDISTRICTOFLOUISIANA

MDLNO.2179,SECTIONJJUDGEBARBIER;MAGISTRATEJUDGESHUSHAN

ModellingMacondoAcalculationofthevolumeofoilreleasedduringthe

DeepwaterHorizonincidentPreparedonBehalfofBPExploration&ProductionInc.andAnadarko

Preparedby:MartinJ.Blunt

DepartmentofEarthScienceandEngineeringImperialCollege,LondonSW72AZ,UK

May1st,2013


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TableofContents1. PROFESSIONALBACKGROUND......................................................................................................................4

1.1 SCOPEOFWORK...............................................................................................................................................52. EXECUTIVESUMMARYOFANALYSISANDCONTRASTWITHGOVERNMENTESTIMATES...............................63. THEMATERIALBALANCEMETHODTOCALCULATEOILRELEASED.................................................................9

3.1 INTRODUCTIONTORESERVOIRENGINEERINGBESTPRACTICE......................................................................................93.2 THEMATERIALBALANCEMETHODUSEDBYGOVERNMENTEXPERTSANDME.................................................................93.3 MATERIALBALANCEEQUATION..........................................................................................................................123.4 EACHINPUTINTOMYMATERIALBALANCEEQUATIONWASADOPTED,ATSOMEPOINT,BYAGOVERNMENTEXPERT.............133.5 CONTRASTWITHTHENONMATERIALBALANCEMETHODSUSEDBYGOVERNMENTEXPERTS...........................................133.6 SEQUENCEOFTHEMATERIALBALANCEMETHODTOBEDISCUSSEDHERE.....................................................................15

4. DETERMINATIONOFTHEPARAMETERSUSEDINTHEMATERIALBALANCEEQUATION...............................184.1 FIRSTVARIABLE:CONNECTEDOILVOLUME...........................................................................................................184.2 SECONDVARIABLE:COMPRESSIBILITY..................................................................................................................294.3 THIRDVARIABLE:PRESSUREDROP......................................................................................................................33

5. CONFIRMINGTHECONSISTENCYOFTHECALCULATIONSWITHOTHEREVIDENCE......................................435.1 CROSSCHECKINGSEISMICANDPRESSURETRANSIENTINDICATIONSOFRESERVOIRSIZE,DIMENSIONSANDCONNECTIVITY....435.2 CONSISTENCYWITHFLOWRATEHISTORY..............................................................................................................49

6. RANGEOFCUMULATIVEOILRELEASED.......................................................................................................51APPENDIXA. DATAANALYSISDETAILS.............................................................................................................53

A.1. INTRODUCTIONANDDATASOURCES....................................................................................................................53A.2 FLUIDPROPERTIESANDPETROPHYSICALANALYSIS..................................................................................................54A.3 ROCKPROPERTIES...........................................................................................................................................60A.4 TOTALCOMPRESSIBILITY...................................................................................................................................62A.5 PERMEABILITY................................................................................................................................................63A.6 DATUMDEPTHS,PRESSURESANDTEMPERATURES..................................................................................................69A.7 ANADARKOPETROPHYSICALANALYSIS.................................................................................................................69

APPENDIXB. CONVERSIONFROMCAPPINGSTACKTODOWNHOLEPRESSURES............................................71B.1. REQUIREMENTTOCORRECTTHEDATAANDTHEEQUATIONUSED..............................................................................71B.2 TEMPERATURECHANGESINTHEWELLBORE.........................................................................................................72B.3 ANALYSISOFTEMPERATURECHANGESINTHEWELLBORE........................................................................................75B.4 EFFECTOFANINCORRECTPRESSURECONVERSIONONGOVERNMENTESTIMATESOFOILRELEASED..................................89

APPENDIXC. MATHEMATICALDERIVATIONOFTHEMODELOFTHEPRESSURERESPONSE.............................91C.1 DARCYSLAWANDFLUIDFLOW..........................................................................................................................91C.2 RADIALFLOW.................................................................................................................................................91C.3 LINEARFLOW.................................................................................................................................................95C.4 WELLNOTATTHEENDOFTHECHANNEL............................................................................................................101

APPENDIXD. ADDITIONALPRESSUREANALYSIS............................................................................................104


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D.1. PARAMETERMATCHES,SENSITIVITIESANDMODELCOMPARISONS...........................................................................104D.2. PRESSUREDERIVATIVES..................................................................................................................................111D.3 PRESSUREMATCHFORCHANNELFLOW..............................................................................................................111D.4 HORNERANALYSISANDCAPPINGSTACKPRESSURE...............................................................................................113

APPENDIXE. CONSIDERATIONOFVARIABLEFLOWRATES............................................................................115E.1 SUPERPOSITIONMETHODTOFINDPERMEABILITY.................................................................................................115E.2 EFFECTOFVARIABLEFLOWRATESONTHELINEARFLOWREGIME.............................................................................117E.3 ANALYSISOFSKINANDDOWNHOLEPRESSURE....................................................................................................120

APPENDIXF. CRITIQUEOFGOVERNMENTEXPERTREPORTS.........................................................................125F.1 HOWTHECALCULATIONSWEREPERFORMEDANDWHATPARAMETERSTHEYUSED......................................................125F.2 THEZICKREPORT..........................................................................................................................................126F.3 THEKELKAR&RAGHAVANREPORT...................................................................................................................129F.4 THEPOOLADIDARVISHREPORT.......................................................................................................................132F.5 OVERVIEWOFESTIMATESOFCUMULATIVEOILRELEASED......................................................................................138

APPENDIXG. FURTHERCRITIQUEOFTHEHSIEHANALYSIS............................................................................139G.1 COMPARISONOFPRESSUREDATAANDANALYSIS.................................................................................................139G.2 COMPARISONOFRESERVOIRPROPERTIES...........................................................................................................144

APPENDIXH.CRITIQUEOFPUBLISHEDFLOWRATEESTIMATES........................................................................148H.1 OVERVIEW...................................................................................................................................................148H.2 DETAILSOFSELECTEDPAPERS..........................................................................................................................150

APPENDIXI. NOTEONUNITS........................................................................................................................153APPENDIXJ. NOMENCLATURE......................................................................................................................154APPENDIXK. GLOSSARYOFOILFIELDTERMS.................................................................................................156APPENDIXL. BIOGRAPHYOFMJBLUNT.......................................................................................................158APPENDIXM. MJBLUNTSPUBLICATIONSLIST..........................................................................................159

M.1 JOURNALPAPERS...........................................................................................................................................159M.2 CONFERENCEPROCEEDINGSANDBOOKCHAPTERS...............................................................................................164

APPENDIXN. FACTSANDDATACONSIDEREDINFORMINGMYOPINION......................................................168N.1 USGOVERNMENTANDBPEXPERTREPORTS.......................................................................................................168N.2 CONFIDENTIALREPORTS,DEPOSITIONTRANSCRIPTSANDOTHERMATERIAL...............................................................168N.3 BOOKS,PAPERSANDREPORTSINTHEPUBLICDOMAIN..........................................................................................173N.4 ADDITIONALCONSIDERATIONMATERIALS..........................................................................................................177


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1. Professionalbackground

IamaprofessorofpetroleumengineeringatImperialCollegeLondon.Myspecialityisthestudyofoilflowthroughrocksunderground,afieldknownasreservoirengineering.Ihavetaughtthefluidflowprinciplespresentedinthisreportforover20years.Mystudentshavegoneontoteachandpractisepetroleumengineeringinuniversitiesandoilcompaniesaroundtheworld.Forinstance,Dr.Hughes,atLouisianaStateUniversity,oneoftheleadingreservoirengineerswhoconsultedfortheUSGovernmentsMacondoFlowRateTechnicalGroup,isoneofmyformerPhDstudentsfromStanfordUniversity. Ihavealsotaughtclassesfor industry intheUK,US,China,Brazil, IranandSaudiArabia.Ihavepublishedover200paperswhichhavebeencitedover7,000times.I am a distinguished member of the Society of Petroleum Engineers (SPE). I served as an SPEDistinguished Lecturer in2001. I received theSPECedricFergusonmedal for thebestpaperwrittenundertheageof33,discussinganewmethodforusingcomputerstosimulatehydrocarbonfluidflowthrough reservoirs. I also received the 2011 SPE Lester Uren award for contributions to petroleumengineering technologymade before the age of 45. Iwas given the 2012DarcyAward for lifetimeachievementbytheSocietyofCoreAnalysts.IamtheeditorofthescientificjournalTransportinPorousMedia.IservedasHeadof theDepartmentofEarthScienceandEngineeringat ImperialCollege from20062011.Ihavehelpedfound,andamChiefScientistof,twocompaniesprovidingservicestotheoilindustry.I receivedaPhD inphysics fromCambridgeUniversity in1988. When Igraduated, Iworked for fouryears for BP. I developed new methods to improve the accuracy of reservoir simulators. Thesesimulatorspredictoil recoveryasanaid to reservoirmanagement. For thisworkBPawardedme itsTallowChandlersprize. I then joined the facultyof StanfordUniversity. At Stanfordmy researchonimprovingoilrecoverywasfundedbytheUSGovernmentandaconsortiumofmajoroilcompanies.IleftStanfordtobecomeaprofessoratImperialCollegein1999.I have never testified as an expertwitness before andmy compensation is not dependent on theoutcome.


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1.1 ScopeofWorkIhavecalculatedtheamountofoilspiltduringtheDeepwaterHorizonincidentusingthemethodsofmyfield, reservoir engineering. I have drawn on thework of other BP experts, including the pressuretransient analysis of Professor Alain Gringarten; the rockcompressibility results of Professor RobertZimmerman; thepressuredatageneratedbyProfessorMartinTrusler; the fluidsanalysisofProfessorCurtisWhitson;andtheseismicinterpretationofProfessorCarlosTorresVerdin.Myanalysisusesawellestablishedmethodfrommyfieldcalledmaterialbalance.MyImperialCollegeLondoncolleagueProfessorGringartenissubmittingareportestimatingcumulativeflowusingdifferenttechniquesfromhisfieldofexpertise,pressuretransientanalysis.Imakeuseofsomeoftheresultsofhisstudy,whileheusestheresultsofsomeofmyanalysis. Eventhoughthereareafewsteps inourrespectivecalculationsthatusethesameprinciplesand interimmethodologies,ourdeterminationsofcumulative floware independentand involvedistinctapproaches. Forexample,ProfessorGringartendoesnotdirectlyusethemainprincipleinmyapproach,materialbalance.AndIdonotusethemethodthatProfessorGringartenpioneered,calleddeconvolution.


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2. ExecutivesummaryofanalysisandcontrastwithGovernmentestimates

I calculate that the volume of oil released from theMacondo reservoirwas 3.26million stock tankbarrels(MMstb).Ihaveusedconservativeassumptionstoavoidunderstatementofthevolume.Ifindarangeofoilreleasedbetween2.9and3.7MMstb.This is the total volume of all the oil that left the reservoir, including any oil burnt or collected,convertedtoavolumeatsurface(stocktank)conditionsof60oFand1atmospherepressure.MycalculationusesthesamereservoirengineeringprincipleemployedbytheGovernmentsreservoirengineeringexpertsDrs.Kelkar&Raghavan,namelymaterialbalance.In material balance, three quantities the oil volume connected to the well, compressibility andpressuredepletionaremultipliedtogethertocalculatecumulativeoilflow.Compressibilitydetermineshowmuchoil is released from the rockas thepressuredrops. Themaindifference betweenmy estimate and those of Dr. Kelkar & Raghavan and another US GovernmentexpertDr.Hsieh, is that theydouble the compressibility from the valuemeasuredonMacondo rocksamplesatanindependentservicelaboratory.ThisisaswitchfromtheapproachthatDr.KelkarusedwhenhefirstevaluatedMacondooilflowfortheUSFlowRateTechnicalGroupin2010,wherehetookameasuredvalueforrockcompressibility,asIdointhisreport.Dr.Kelkar&Raghavansexpertreportacknowledgesthat iftheyusethesamerockcompressibilityas Ido,theyobtainroughlymyvalueforcumulative flow.1 Similarly,when Dr. Hsieh input into hismodel themeasured compressibility, heobtainedanestimateofcumulativeflowinmyrange.2NeitherDr.KelkarnorDr.Hsiehhaveprovidedascientificjustificationfortheirdecisiontodoubletherockcompressibilityfromthemeasuredvalues.WewillseethatthishasbeenarepeatedproblemintheworkoftheGovernmentexperts.Inordertoobtaintheirestimatesof5MMstboilreleased,theyhadtomakeassumptionsthatdisagreesignificantlywithdirectmeasurementsof theMacondo rockand fluidproperties. TheGovernment investigatorseachdisregardedvitalpiecesofexperimentalevidencewithoutjustification;notalloftheirerrorswereidentical,yettheyarrivedatthesamefinalanswer.Thereisachoice:eitheraccepttheircalculationof5MMstb,despitethelackofanyscientificexplanationofwhythemeasurementsarewrong;orperformacalculationconsistentwiththedataandarriveatalowervalue.Ihavechosenthelatterapproach.Nevertheless, there isan implicit consensusonmanyof the inputs intoa calculationofoil released,whichhighlightstheremainingdisagreements. Thetablebelow isolatesthemost importantbiases intheGovernment calculations, juxtaposesmy approach, and shows thenet effectof eachdifference:1SeeKelkar&Raghavanexpertreport[KR],page45.(BracketedinformationreferstothetableofsourcesinAppendixN,whichcontainsafulldescriptionofthereferenceddocuments.)2SeeDr.Hsiehsdeposition[42],page267,line5(Q.Andifyouinputarockcompressibilityof6microsips,yourmodelyieldedacumulativeflowestimateof3.4millionbarrels?A.That'scorrect);page269,line3(A.Ibelievethatitwillgiveanumbersimilar,closeto2.9millionbarrels);Exhibit8635,pages73and74.


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TherearethreeotheroverarchingproblemsintheGovernmentexpertreports.1. Government experts assumed an unchanging outflow path, predetermining a total flow

estimateof5MMstb. TheexpertswhodidnotusethematerialbalancemethodDr.Hsieh,Dr.GriffithsandDr.PooladiDarvish tookanestimateof the final flow ratebefore shutin,approximately50,000stbperday,andassumedthattheflowrateduringthepreceding86dayswasevenhigher.Ofcourse,simplemathematicsdictatesthattheoutcomeofacumulativeflowcalculationbasedon thisassumptionwillexceed4.5MMstb. They justified thisapproachbyassuming that therewereno impedimentstooil flow in thewellbore,blowoutpreventerortubingthatmighthavecausedflowtobelowerinthoseprecedingdays.Theydidnotprovethisassumption; indeed, theyhardlydiscussed it. Bycontrast, thematerialbalancemethodusedhereisnottiedtoanassumptionabouthistoricalflowrates(seeSection3.5).

2. Government experts assumed the reservoir oilwas completely connected to theMacondowell, omitting to analyze geological features that the Governments nonlitigation expertconsultant said would limit connectivity. None of the Government experts analyzed theevidence from theMacondogeologyand seismicanalysis that indicates that theoil reservoirwas not completely connected to the well. This is a change from prior expert analysiscommissionedby theGovernment. Dr.Hsiehwas toldby theGovernments consultantProf.Fleming from theUniversityofTexas that the geologicalevidencepointed to a significantprobability of poor connectivity in the Macondo reservoir.4 The Government estimatesthereforehavean implicitupwardbias from ignoringevidence thatsomeof theoilwas likelycompartmentalizedandhencecutofffromflowingtothewell(seeSection4.1).

3. Government experts overestimated flow by overstating the pressure depletion in thereservoir.Theyusedanimproperconversionfromthepressuremeasurementsatthecappingstacktothepressureinferredinthereservoir.Theydidnotaccountforpressureincreasesastheoiltrapped inthewellborecooled. TheestimatesofoilflowbyDrs.Kelkar&Raghavan,HsiehandPooladiDarvishoverstatedthereservoirpressuredepletionthatdrovetheflow.Alloftheseexpertsusedthepressuremeasurementstakenfromthecappingstackmountedabovethe blowout preventer, as do I. Thesewere used to deduce the bottomhole or reservoirpressure. But between the capping stack and the reservoir was a column of trapped oilthousandsoffeettall.Sothereservoirpressurewashigherthanatthecappingstackithadacolumnofoilsittingabove it. Thishead isafunctionofthedensityofthetrappedoil. Thedensityrosefollowingtheshutin.Theoilwashotasitflowedfromthereservoirtotheocean.Whenflowstopped,theoilcooleddown,graduallybecomingheavier.TheGovernmentexpertsbasedtheircalculationonmeasurementsofcappingstackpressureincreasingslowlyovertime,butthereservoirpressurewasrisingfasterthantheysuggest:therewasanextrafactortheweightofoilthatwasalsoincreasing.Aswewillseebelow,noneoftheGovernmentexpertspresentedananalysisaccountingforthischangingoildensity. Byassumingtheoilwashotterand lighter than itactuallywas, indeedunfeasiblyhot, theyendupoverestimatingpressuredepletion,andhencetheoilflow(seeSection4.3).

4SeeExhibit8624(presentationtotheUSGS)[64],slide7.


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3. ThematerialbalancemethodtocalculateoilreleasedThisSectionexplainsthemethodologyusedinmyanalysis,knownasmaterialbalance,whichalsowasusedbytheGovernmentexpertsDrs.Kelkar&Raghavan.FlowfromtheMacondowellinvolvedtwodistinctphysicalsystems.Oneconsistedofthewellboreandequipmentthroughwhichhydrocarbonsflowedupwardand intotheocean.Beforeenteringthewellbore,thehydrocarbonshadtoflowthroughtherockinwhichtheyhadbeenstored.Thissecondsystemiscalledthereservoir.Iwillfirstprovideabriefoverviewofreservoirengineeringasitpertainstothiscase,thenintroducetheparticularmethodologyusedinmyanalysis.3.1 IntroductiontoreservoirengineeringbestpracticeOne hundred years ago at Imperial College London,where I teach, Vincent Illing began pioneeringmethods for appraising petroleum reservoirs. Reservoir engineering has evolved evermoremoderntoolstopredictthebehaviourofhydrocarbonfields,harnessingthepowerofhighspeedcomputing.Ihave helped develop some of these tools, and have founded two startup companies to pursueinnovative approaches to predict fluid flow. But the results from any model, no matter howsophisticated, are only valid if the inputted data are sound. Therefore, best practice requires thereservoirengineertocheckthemodelagainstmeasurementsandanalysisfromotherdisciplines,suchasgeology.TheGovernmentexpertshave (1)repeatedly inputteddatacontradictedby laboratorymeasurementsandthen(2)omittedtheimportantprocessofgeologicalverification.Thustheyhave:overlookedthelikelihood that the reservoirwasnot fullyconnected to thewell (seeSection4.1); ignored laboratorymeasurements of rock compressibility (Dr.Hsieh andDrs. Kelkar& Raghavan, see Section 4.2); andneglected the changing temperature of the oil in the wellbore column, thereby overstating thepressuredepletion(allGovernmentexperts,seeSection4.3).3.2 ThematerialbalancemethodusedbyGovernmentexpertsandmeThe most basic principle in reservoir engineering, and the cornerstone of this report, is materialbalance.5AstheGovernmentexpertreportbyDrs.Kelkar&Raghavanstates,materialbalance[is]astandardpetroleumengineeringcalculationbasedontheprincipleofconservationofmass.6Becauseconservationofmassisauniversallawofphysics,materialbalancecalculationscanbeusedtoanalyzetheworkoftheotherGovernmentexpertsaswell,sincetheirsoftwarepackages(iftheyarevalid)arewrittentoconservemass. Thisiswhy,forexample,GovernmentexpertDr.Hsiehcalculatedthesame

5See,forinstance,thestandardtextbookbyDake(1978).6Kelkar&Raghavanreport[KR],page23.


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3.3 MaterialbalanceequationThematerialbalanceequationfortheoilreleased,Np,canbewrittenasfollows:

(3.1)

3.3.1 Oil connected to the well. The oil volume contained by the Macondo reservoir, N, can becalculatedfromananalysisoftheseismicsurveyperformedbeforethewellwasdrilledthatfindstheoverallextentof the field. EachoftheGovernmentexpertsused thismethod,asdo I. Inpetroleumengineering it is common to refer to the stock tankoil initially inplace,or STOIIP. This is the totalamountofoilinthewholefield.Inapropermaterialbalanceanalysis,however,itisnotSTOIIPthatweneed,butthevolumeofoilthatwasconnectedtothewell.AswediscusslaterinSections4.1and5,itisunlikelythatthisonewellwasconnectedtoallthesandstonechannelsinMacondo:theNweuseinthe equation can be less than the STOIIP determined from the seismic survey. The value of N isinformedbytheseismicsurvey,thegeologyofthefieldandtheanalysisofthepressuredata.3.3.2Compressibility.Thisisthecombinedcompressibilityoftherock,waterandoilintheporespace.10Itmeasures the fractional change involumeperunitdecrease inpressure. Technically, this is calledcompressibility,eventhough inourcasethefluidsareexpanding. Ananalogywouldbetheair inabicycletyre.Ifyoureleasethepressure,theairexpandsandflowsoutofthevalve.Morecompressiblefluidsexpandmoreasthepressureisdropped,pushingoutmoreoil.Inthereservoir,thefluidpressuredropsandthefluids(oilandwater)expand,pushingoiloutthroughtherockporesand intothewell.The rock also gets compressed like squeezing a sponge to releasewater and this adds to theproduction.Unlikespongesorair,thecompressibilityoftherockandfluidsweconsiderismuchlower,sothechangeinvolumeisrelativelysmaller.3.3.3Pressuredrop.Thethirdand finalquantity inthematerialbalanceequation isp, thepressuredropinthereservoir.Thisisthedifferencebetweentheinitialreservoirpressureandthefinalpressure:p=pipf.Thefinalpressureistheaveragepressureinthereservoirattheendofthespillafterthewellhasbeenclosed: it isthepressure inthewellatreservoirdepthonlyafteravery longtime,oncethepressure everywhere in the reservoir equalizes, which takes time, since it involves communicationthroughtinyrockpores,ratherthantheopenspaceofabicycletyre.Thus,wecannotsimplyderivethisnumberbyusingthepressureinthewellwhenthecappingstackwasshutandthespillended,norevenwhen thewellwas cemented in almost threeweeks later: thepressures at these earlier times varyacrossthereservoirandwillbelowestatthewell.Ittakesalongtimeforthepressuresthroughoutthereservoirtoevenout,sothefinalequilibriumpressureisalwaysgreaterthanthatmeasuredatthewellsoonaftertheflowceases.10SeeAppendixA.4fortheprecisederivationthecompressibility,c,definedsoastoobeymaterialbalanceexactly.TheequationsmorenormallyemployedEqs.(A.6)and(A.7)areexactlyequivalenttoEq.(3.1).

Oilreleased PressuredropfromcappingstackpressureanalysisOilvolumeconnectedto

thewellfromseismicsurveys,geologyandpressureanlaysis

Compressibilityofrockandfluidsfromfluidandcoremeasurements


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This constraint explains how Dr. PooladiDarvish, who considered 25 quite different scenarios, canapparentlymatchthepressuredatawithonlyanarrowrangeofcumulativereleasenumbersatornear5MMstb;whenherelaxedtheassumptionofaconstantoutflow,hewasabletofindlowervalues.14Hissuperficially impressive array of seemingly diverse simulations essentially answers the question: If Iassumeacumulativeflowofaround5MMstb,whataretheconsistentreservoirproperties?AsIshowinSection4and inAppendixF.4, thereservoirpropertiesthathe inputtomakehismodelmatchthepressure data lie outside themeasured values, precluding the ability to validate his assumption ofconstantoutflow.Thisisakeyflawinthisapproach:sinceitisnotpossibletoknowtheoutflowwithanycertaintyduringtheearlierpartofthespill,theseassumptionsare,atbest,somewhatspeculative,andinanyevent,donottrulyamounttoanindependentassessmentofcumulativeflow.3.5.2Evidence foran increasing flowratecausedbyerosionofobstacles inthe flowpath. There ispersuasiveevidencethattheoutflowconfigurationdid,infact,changeovertime.Forexample,Phase1expertDr.Emilsenconcludesthatatthetimeoftheblowout,theoilflowed intothewellboreoverarestricted intervalofthereservoir,perhapsbecauseofresidualcementblockingthe flow. Thiswouldleadtoanadditionalpressuredropbetweenthereservoirandthewellbore,causingaslowerflowrateattheoutsetoftheincident,ratherthanthehigherrateassumedbytheGovernmentexperts. Attheendoftheincident,justbeforethewellwascemented,theinjectivitytestshowednegligibleresistance:themeasuredpressureincreaseoninjectionwasanorderofmagnitudelessthaniftheseimpedimentswerestillpresent.15Outflow impediments inoilwells are common:petroleumengineers are accustomed toplanning forhuge losses in pressure (thedriving force of flow rate) from such restrictions. However, petroleumengineersgenerallyconsiderthemtobefixedovertime,unlessparticulareffortsaremadetoincreasetheflowfromthewell(byinjectingacid,fracturingormakingnewperforationsthroughthecasing).ThisperhapsexplainswhyDr.Hsiehneglectedthiseffectcompletely,whileDr.PooladiDarvishconsideredonlyaconstantadditionalflowresistance.Unlike a normal well, the Macondo oil flow was unplanned and uncontrolled: the flow resistancebetween the reservoir and thewellboremost likely decreased over time, as the oil forced itswaythroughmoreoftheformation,perhapsthrougherosionofthecement,andasabrasivematerialsintheoil(suchassandorcementfragments)erodedbarrierstoflow,either intheblowoutpreventeror intheequipmentcloggingthebottomofthehole.Itislikelythatinitiallytherewasaverylargepressurelossdownhole,givingalowinitialflowrate,whichthenroseovertimeastherestrictionseroded,evenifwe ignore changes in the surface equipment. It is very difficult tomake a reliable estimate themagnitude or duration of this effect, making any calculation of cumulative flow that depends onassumptionsabouthistoricalflowratesparticularlyintheearlyperiodofthespillhighlyunreliable.Governmentestimates thatassumeaway thisproblem (Drs.Hsieh,PooladiDarvish,andGriffiths)arethereforeunreliable.Thisconfirmswhyitissoimportanttohaveanindependentanalysisthatassessesthecumulativeflowdirectly,suchasthematerialbalancemethodusedhere.Indeed,thisisaccepted14SeePooladiDarvishreport[PD],page26.15SeeFinalEmilsenreport[27]andAppendixE.3forfurtherdiscussionandquantitativeanalysis.


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by Drs. Kelkar & Raghavan who, while they estimated a final flow rate, used material balance tocomputethecumulativerelease.3.5.3Analogy that illustrates theadvantageof thematerialbalancemethodover theGovernmentmethodofassumingaconstantoutflowconfigurationandextrapolatingbackwardfromafinalflowrate.Imaginethatoneeveningapoliceofficerarrestsathiefwhoisemergingfromaholethroughthesideofabuildingthatconnectstoabankvault. Thethiefisarrestedandfoundtobecarryingaround$53,000.Thepolicelookatclosedcircuittelevisionpicturesandnoticethatthisholehasbeenpresentfor86days. Then theyguess that thedaily takewashigherattheoutset,perhapsbecause thethiefinitiallyselectedstacksofhigherdenominations,sotheyassumeanaveragedailylossof,say,$58,000.The newspaper headlines say $5 million taken in bank heist. Through a wellmeaning series ofunverifiedassumptions,thiswouldexaggerate,ifnottheamountstolen,thenthedegreeofunderlyinguncertainty.Aswehavediscussed,thisisakintotheerroneousassumptionsandextrapolationsmadebysomeGovernmentinvestigators.Now, imagine further that thebank is insured for this loss, so they contact their insurerswith theseestimatesandaskfor$5millionincompensation.Wouldtheinsurerspay?No,theywouldaskthebanktocheck their recordsandsayhowmuchwas in thebankvaultbefore theholewasmade,and thenreturn to the vault, count themoney and report thedifference. Thismay bemoreor less than $5million,butavoidsthesomewhatdifficultandproblematicanalysisofexactlyhowmuchwasstolenoneachofthe86days.Material balance is the petroleum engineering equivalent to counting the money in the vault. Itaccountsfortheoilvolumeinthereservoirbeforeandafterthespill,toprovideadirectcalculationofthetotalvolumeofoilreleased.Itdoesnotrelyonanassessmentofflowrateatanygiventime.3.6 SequenceofthematerialbalancemethodtobediscussedhereFigure3.3 isaflowchartthatsummarizestheapproachIwillfollow.Iwilldeterminethevalueforthethreeparametersinthematerialbalanceequationvolumeofoil,compressibilityandpressuredropbasedonmeasureddataorpreincidentanalysissupplementedbyindependentexpertassessment.I find an effective compressibility of around 21 microsips, including the 6 microsips for rockcompressibility,basedon independent laboratorymeasurements. Ifindthepressuredroptobe1,367psi. Ifwemultiply the compressibilityby thepressuredrop,weobtain the fractionof theoil in thereservoirreleased:thisis0.029or2.9%. Ideducethattheconnectedoilvolumeislikelytobearound112MMstb.Thenthevolumeofoilreleasedis112MMstbmultipliedby0.029,giving3.26MMstb.16Iwillalsocalculatearangeofcumulativeflow,from2.9to3.7MMstb,definedbytherange invaluesassignedtothematerialbalanceequationvariables. Therangeforthosevariables isderivedfromthevariation of laboratory measurements of fluid and rock properties (see Appendix A). Thus, mycumulativeflowcalculation isbasedonexperimentalmeasurements,butmyquotedrange isalsotieddirectlytothevariabilityofmeasurements.Inotherwords,myapproachisdatabased.16SeeSection4foractualnumbersused;forthisintroductionIamusingaveragesofmymidrangecalculations.


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Mycalculationsarealsoconservative. Wherethedataaresusceptibleto interpretation, Itakevaluesthatwould leadtothehighestestimateofoilreleased. Foroilvolume,Ihaveassumedaconnectivityconsistentwith the highest plausible assessment of permeability (the ability for fluids to flow) (seeSection4.1).Forcompressibility,Iallowthehighestmeasuredvaluefromonerocksample,eventhoughitappearsinconsistentwithmyreviewoftheliterature(seeSection4.2).Forpressuredrop,Iignoretheeffectsofcoolingfromtheoceanthatwouldmaketheoildenser,leadingtoalargerpressuredrop(seeAppendixB).IntheSectionsthatfollow,andintheAppendices,Iwillcarefullyassesseveryinput,reviewingthedirectmeasurementsandplacingtheminthecontextofthescientificliterature.Ialsotakeinformationfromindependent expertswho have looked at different aspects of this problem: pressure analysis, fluidproperties,pressurereadingsandrockmechanics.Ialsolookformutualconsistencybetweendifferentassessments of reservoir properties. This follows best practice: a conscientious reservoir engineercombines insights from experimentalmeasurements, geophysical surveys (the seismic) and geology.Finally,IwillcontrasttheapproachtoeachvariableusedbytheGovernmentexperts,highlightingwheretheyhavedepartedfrommeasureddata.


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4. Determinationoftheparametersusedinthematerialbalanceequation

This Section has three parts, each discussing one of the three properties in the material balanceequation,whichwhenmultipliedtogethergivethetotaloilreleased:theoilvolume;thecompressibilityoffluidsandrock;andthepressuredrop. TheGovernmentcounterparttothisdiscussion infound inthereportofDrs.Kelkar&Raghavan,whoapplymaterialbalanceintheirSectionIII,atpages2328.4.1 Firstvariable:connectedoilvolumeEachoftheGovernmentexpertswhohavestudiedtheMacondoreservoirhasusedthesamenumberasIdoforconnectedoilvolumearound110MMstbaseithertheirsolevalue,analternativebasecase,orasoneendof their rangeof inputvalues. Dr.Hsiehemployed thisvalueexclusively;Dr.PooladiDarvishadopteditforwhathetermedhisanalyticalcase;whileDrs.Kelkar&Raghavanuseditastheirlowendestimate.17Drs.Kelkar&RaghavanandDr.PooladiDarvishusedahighervalueof137MMstbfortheirhighendandsimulationbasecases,respectively. Theirstartingpointthoughwasthesameasmine:theyacceptedBPspredrillseismicanalysisofthevolumeofreservoirrock.Wepartwaysintwosubsequentstepsinthecalculation. Firstly,theyassumedthatalltheoilcontained inthereservoirwasconnectedtotheMacondowell,asIdiscussimmediatelybelow.Secondly,theyoverestimatedthetranslationtosurfaceoilvolumes,usingaconversionfactordifferentfromthatmeasureddirectlyonMacondooilsamples.IwilldiscussthisissueinSection4.1.8.4.1.1GeologicalcomplexityisignoredintheGovernmentassumptionof100%oilconnectivity.NoneoftheGovernmentreportsconsideredthereservoirgeology.Theyassumedwithoutdiscussionthatalltheoilinthefieldisconnectedtothewell.TheUSGeologicalSurvey(USGS)didconsiderthegeologyofMacondoinaninternalpresentationcoauthoredbyProf.FlemingsfromtheUniversityofTexas,whoconcluded:Itisgeologicallyreasonablethatthereislimitedchannelconnectivity,18yetDr.HsiehfromtheUSGSdidnotmentionconnectivityinhispublishedanalysis.Connectivity directly affects the calculation of the amount ofoil released,which under thematerialbalanceequationisproportionaltothevolumeofoilcontactedbythewell;ifthereservoirhaslimitedconnectivity, then less oil flows. The connectivity is controlled by the structure of the sandstonechannelscomprisingthereservoir,sosomediscussionofthegeologyisinorder.4.1.2 Geological history and resulting complexity of reservoir structure. For 50 million years theMississippi River and its tributaries have been transporting sediment from the erosion of theNorthAmericanmountainrangesgrainbygraindowntotheMississippidelta.17Sources:IGS642000215(Dr.Hsiehs10/13/2010Predecisionaldraftreport,Tables1and2)[11];Drs.Kelkar&Raghavan[KR],page28,Tables9and10;Dr.PooladiDarvish[PD],AppendixII,slide31mentionsOOIP=109MMSTB.18SeeExhibit8624(Geologicalevidenceforanelongate,heterogeneousreservoir)[64],slide6.


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Someof these sedimentsbecame theMacondo field,which lies40milesoff the shoreof Louisiana,approximately130milesSEofNewOrleans,beneaththeGulfofMexicoseeFigure4.1. Thewaterdepthisalmost5,000ftandtheoilreservoiritselfliesafurther13,000ftundertheseabed.

Figure4.1. ThelocationoftheMacondofieldundertheGulfofMexico intheMississippiCanyonarea. Thefield isbelowdeepwater,justoffthecontinentalshelf.19TheMacondo reservoir is formedof sanddeposited in theMiddleMiocene age around13millionyears ago.20 The sandwas deposited in underwater flows called turbidites. These flows follow avariablepathoverthecourseofgeologictime,forming long,sinuouschannelsthatcanaccumulate indifferent geometricpatterns like those shown in Figure4.2. The reservoirwas formedof severalofthesechannelswith impermeablemud inbetween. TheyweredepositedwithinaNWtoSEtrendingfairway severalmileswide. Over time, huge volumes of further sediment have been laid down,crushing the sand at very high pressures and temperatures, fusing the grains together and formingsandstone. Sandstone is porous, and if the pores are sufficiently connected, oil can flow into andthrough them.Themud sediments thatweredeposited inbetween the sandstone channelsbecameshaleuponburialovergeologictime.Shaleislargelyimpermeabletotheflowofoil.

19BPHZN2179MDL00059145(BPShallowHazardspresentation,[29].20BPHZN2179MDL03290054(BPPostWellSubsurfaceTechnicalMemorandum)[6],page3;BPHZN2179MDL05181294(MacondoReview,slide24)[36].


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4. TheMacondowell likely contacted threeof these complexes: these are the three layersencounteredwhendrilling thewell shown in Figure4.5 as the red,orange and yellowstrandsofclay.

5. TheoilvolumecontactedbytheMacondowellrepresentsthemajorityofthetotalvolumeofthefield,butnotallofit.Theoilinsomeofthechannelscannotflowtothewell.Thesearethe lilaccolouredchannels inthepicture. This isconsistentwithBPs interpretationseeFigure4.4wherethechannelcomplextotheleftisnotconnectedtothewell.

6. There couldbeother sourcesof compartmentalization, suchas faults,and there is someindicationintheseismicdatathatfaultscuttheMacondochannels.28

4.1.4 Evidence for limited connectivity in channelled reservoirs. Theoriginaldevelopmentplan forMacondoproposeddrillingthreewellstoproducethefield.29Threewellsasopposedtoonewouldlead tohigherproduction rates,butalsohas theadvantageofensuring that thevastmajorityof thereservoirvolumewouldindeedbeconnectedtoatleastoneofthesewells.ToquotefromBPspredrillassessment30Estimate80%ofprospectresourcerecoverablefromwellsonMC252.Whatthismeansisthatevenwiththreewellsandaproductiontimeofseveralyears,BPconsideredthatonly80%ofthefield would be drained. BP stated that a single well will confirm 63% of the predicted resourcevolume.31 BP considered In the event of a compartmentalized reservoir, additional wells may berequiredtoadequatelydrainthereservoir.32IntheopinionofBPgeophysicistDr.RitchieIthinkitisaveryunlikely case thatonewellwoulddrain the fullyconnectedvolume.33Healso states.. the fullyconnectedvolume Ibelieve isunrealistic.34BPsgeologicalreviewstates:35Floodingalongtheaxisofthe channelmay result ingoodcommunication. Floodingacross thechannel..with the risk thatpermeabilitybarrierspreventpressuresupportattheproducer.BasedonBPsanalysisbeforetheaccidentandthe interpretationoftheirgeologists,theGovernmentexperts assumption that thewell drained the entire fieldwill overstateN in thematerial balanceequation. It is very likely that not all the oilbearing sandstone channels inMacondo intersect orotherwiseconductflowacrosstheshalebarriersthatseparatethem.Published petroleum reservoir literature also recognizes that the connectivity of turbidite channelreservoirs is a problem in field development:36 operators have encountered severely impairedreservoirs..attributedinlargeparttoreservoircompartmentalization.37Dr.Kelkarisacoauthoronapaper 38 that states, in reference to deepwater fields, some of these reservoirs are highly28ForinstancetheredlineintheBPseismic(upperpartofthefigure).29BPHZN2179MDL06566208(BPPreDrillReview)[31],slide24.30Id.,slide24[31];BPHZN2179MDL02107723(BPTechnicalAssuranceMemorandum,Section3,row11)[10].31BPHZN2179MDL02107723(BPsTechnicalAssuranceMemorandum,[10])Section3,row11.32Id.,.33SeeBryanRitchieDeposition[46],page322,line21.34Id.,page324,line17[46];seealsoId.,page325,line13[46]35BPHZN2179MDL06604338(BPspresentationofreservoirgeology,slide2)[39].36See,forinstance,Abreuetal.(2003),RagagninandMoraes(2008),andAlpaketal.(2010).37Alpaketal.(2010).38Liuetal.(2008).


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compartmentalized. Limited connectivity has hampered production in channelled turbidites in theSchiehallionfieldWestofShetlands,theBitternFieldintheNorthSea,andtheRamPowellfieldintheGulfofMexico.394.1.5Governmentexpertsdeducesmallerreservoirareaswithoutreducingconnectedvolume.LaterinthisreportwewilldiscusshowboththeGovernmentexpertsandIusemeasurementsofthepressurebuildupafterwell shutin todeduce the size and shapeof theMacondo reservoir (see Section4.3).Everyexpertfoundthattheconnectedreservoirhasasmallerarea(andwidth)thandeterminedfromBPs seismic analysis in Figure 4.5.40BP likewise used pressure analysis after choke closure and alsopresentedamodelwithasmallerarea.41ThissuggeststhatthewellknowngeologicalphenomenonofcompartmentalizationofturbiditesystemshasindeedlimitedtheconnectivityofthegreaterMacondoreservoir shown by BPs seismic analysis. Yet the Government experts omit the next step ofproportionatelyreducingtheirconnectedvolumeofinitialoil.Theprimaryjobofareservoirengineer,Drs.Kelkar&Raghavan tellus,is toobtainaproduction forecast . . .afteraddressing threeprimaryquestions: . . . (3)howmuchof theavailablequantityof fluidmaybeproduced.42Yet theydidnotassesswhatpercentageoftheMacondofieldcouldbeproducedbythesingleMacondowell.Findingasmallerareafromapressureanalysisdoesnotaloneprovepoorconnectivity:thegeologyhastobeconsideredcarefullytodetermineifitisplausiblethatthewholefieldcandraintothewellinthetimes indicated by the pressure analysis: I suggest that this is not possible for the BP seismicinterpretation(seeSection5).Itisunreasonabletosuggestthatoillocatedfarbeyondtheboundariesdetectedbythepressureanalysiscanresidewithintheseconfines.4.1.6Mymethodforassessingconnectivityandconnectedoilvolume.IusetheareaIcomputefromthepressure analysis. I take the largestplausiblepermeability value,which gives the largest area. Iassumethattheoiloutsidethisareaisnotconnectedtothewell,butthatthereservoirthicknessisonly10 ft in these regions: the purple areas shown in Figure 4.5. 10 ft is the limit of the seismicinterpretation,43so this is a lower bound on the disconnected volume, or an upper bound onconnectivity.Thisisthemostoptimisticassessmentofconnectivitythatisconsistentwiththepressureanalysis,theseismicinterpretationandcalculationsofpermeability.ThedetailsaregiveninSection5:dependentonthefluidandrockpropertiesassumed,theconnectivityis8790%.FromFigure4.5,thisisevidently a very generous interpretation, placing the vastmajority of the oil in the yellow, red andorange channelswhilemaking the lilac channels very thin in comparison. This approachwill give aplausibleupperboundonoilreleased.

39Govanetal.(2006),Alpaketal.(2010),Alpaketal.(2013).40IGS64200215(Hsiehsdraftreport,page12,Table2(1,958acres:22,270ftlengthtimes3,830ftwidth)[11];PooladiDarvishreport[PD],AppendixV,slides4and5(between1,686and2,228acres,usingthequotedwidthsandlengths);BPsmidrangeareais4,482acres.BPHZN2179MDL05173765(BPgrossrockvolumeassessment)[30].41SeeDr.Levitansdeposition[56],page141,lines14and15(2,185acres).42SeeKelkar&Raghavanreport,[KR],page31.43SeeBPHZN2179MDL05173765(BPsgrossrockvolumeassessment)[30],slide1,mostlikelycase:10ftcutofffootprint(noisebackground).


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IcontrastmyapproachwiththatoftheotherGovernment investigators inTable4.1below. Iallowalarger connectedarea than all theotherexperts,but this is still smaller than inferredbyBP in theirseismicinterpretation(4,482acres).Inbrief,theGovernmentinvestigatorssqueezedtoomuchoilintotheirmodelsofthereservoir.4.1.7 Oil volume underground. Table 4.1 also shows the total oil volume in the reservoir. Havingcalculatedtheextentoftherockcontainingoil,weneedtodeterminehowmuchoilisinthisrock.Thisisdoneusing logsofdownholemeasurementsofporosity(thefractionoftherockthat isvoidspace)andsaturation(thefractionofthevoidspacethatcontainsoiltherestcontainswater). IfollowthesameapproachhereasDr.Kelkar&Raghavanandfindvirtuallyidenticalnumbers;Dr.PooladiDarvishandDr.Hsiehalsousedvaluesthatcorrespondtomine.Sincethereisnodisagreementonthispartofthe analysis either in termsof themethodor the conclusions and since it is standard in anyoilindustryassessment,IleavethedetailstoAppendixA.2.Bearinmind,however,thatwhileweagreeontranslatingreservoirrockvolumetoreservoiroilvolume,thesimilarnumbersmasktheissuediscussedin the preceding sections: the Government numbers do not account for the geological evidence ofincompleteconnectivity.

ExpertReservoirareafrompressureanalysis

(acres)Connectivity

Reservoirvolume(MMreservoir

barrels)Surfacevolume(MMstb)

Myanalysis44 1,9312,590 8790% 258 109114(112midrange)

Drs.Kelkar&Raghavan45 Notstated

Assumedtobe100% 293

110137(124midrange)

Dr.Hsieh46 1,958 Assumedtobe100% 259 110Dr.PooladiDarvish47 2,167

Assumedtobe100% 296 137

Table4.1.AreasandoilvolumesconnectedtothewellproposedbymeandtheGovernmentexperts.

4.1.8Conversionofoilvolume to surface conditions. Our focusnow switches from the rock to thefluidscontainedwithin them. Macondooilsampleswerecollectedusingdownhole toolsbefore theaccident. Three laboratories Schlumberger, Intertek (Westport Labs) and Core Labs (Pencor)4844Ishowthefullrangeofconnectedareasandconnectivity,themidrangedeterminationofreservoirvolumeandtherangeofsurfacevolumesusingthemidrangerockcompressibility.SeeSection5andAppendixD.1.6forfurtherdetails.45FromKelkar&Raghavanreport[KR],page27.Alsoconsiders110MMstb,([KR],page28)sothemidrangeoilvolumeis124MMstbquotedinthesummarytableinSection2andTable4.1.46ValuescomputedfromvaluesinDr.Hsiehsdraftreport[11],Tables1and2.47Dr.PooladiDarvishbasecase[PD],valuesfromAppendixIV,slide10.SurfacevolumesfoundusingBoi=2.15306inhissimulationinputfiles.48Ihavetakendatadirectlyfromtheirreports:BPHZN2179MDL04440732(Intertekfluidpropertyreport)[18],BPHZN2179MDL00063016(CoreLabsfluidpropertyreport)[19];BPHZN2179MDL00063084(CoreLabsfluidpropertyreportwithcoverpage)[20];BPHZN2179MDL01608973(SchlumbergerFluidAnalysisonMacondosamples)[34];BPHZN2179MDL01872218(CoreLabsfluidpropertiesreport)[35];seeAppendixA.1forfurtherdetails.


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Macondowasanexceptionallylightoilwhichshranksignificantlywhentakentothesurface.AsaresulttheshrinkagecoefficientBoplaysamajorroleinthecalculationofoilreleased.4.1.10 Twodifferentmethods to convert to surface volumes. Twoapproachesareused in theoilindustry to convert from oil volume in the reservoir to oil volume at surface conditions. A higheramountofproducedoil iscalculatedusing theconversion factorproducedby theGovernments fluidexpert Dr. Zick. He used a method known as multistage separation. This is what is used by oilcompanies tomaximize volume during normal, planned production. When oil companies normallyproduce oil, they separate the oil and exsolved gas through a deliberatelyengineered series ofseparators at a successionofdecreasing temperatures andpressures. Thismultistage separation isdesignedtoproduceasmuch(valuable)oil,andaslittle(lessvaluable)gasaspossible.ThevalueofBodependsontheexactsequenceofseparations.ItwillbethelowestpossibleBo,inordertoproducethehighestpossiblesurfacevolume.Dr.ZicktriestoconstructthehighvolumeseparationprocessthatheassertsBPwasplanningtouseifitproducedoilfromMacondoforsale.Butofcourse,theMacondooilwas not produced in such a fashion. It flowed through various openings at different depths,temperaturesandpressuresover86days.BPsfluidsexpertDr.Whitsontriestoreconstructwhattheactualmultistageseparationwouldhavebeenduringtheincident,andderivesahighernumberforBo,whichyieldsatranslationtofewerbarrelsatsurfaceconditions. Healsoconcludes,asdo I,thatthecomplexityofthisanalysiscanbeavoidedbyusingtheother industrymethodforconversiontostocktankconditions,knownasasinglestageseparation.Thisoccurswhentheoilandgasremainincontactastheyarebroughttosurfaceconditions.Dr.WhitsonfindsthatthenumberforBousingthisdefinitionisclosethevaluederivedfromtheappropriatemultistageprocess.Thus,IwillusethevaluesofBofromthesinglestageseparationinmycalculations.50ThemeasuredvalueofBoforthesinglestageseparationusedinmycalculationsrangesfrom2.3to2.4depending on the reservoir pressure.51Government expertDr.Hsieh used a value similar tomine:2.35.52 Dr. PooladiDarvish and Drs. Kelkar & Raghavan used a significantly lower number ofapproximately 2.1.53Dr. PooladiDarvish, however, said that he used a singlestagemethod for theconversion,54sohisnumbershouldbeclosertomine.554.1.11Connectedoilvolume:109114MMstb.Table4.2showsmydeterminationsofinitialoilinplace:there are three values, derived from the values of Bomeasured by the three different laboratories.Thus,aswillbethecaseforeachinputvariable,Ibasetherangeonthemeasureddata.Iarriveatanumberaround110MMstbwhichhasbeenagreedasplausiblebyalltheGovernmentinvestigators.56However,wearrivetherebydifferentmethods.TheGovernmentexpertsomittedthe50SeeAppendixF.2andAppendixA.2.51SeeTableA.4.52Dr.Hsiehsdraftreport[11],Table1.53Dr.PooladiDarvishvalueof2.15306forinitialformationvolumefactorforhisbasecasesimulationmodeltakenfromhiscomputerinputfiles;Drs.Kelkar&Raghavanused2.14([KR]page27).54SeePooladiDarvishreport[PD],AppendixII,slide45.55SeeAppendixF.2,TableF.1andTableA.4.56AllbutoneofDr.PooladiDarvishsgoodmatchsimulationmodelsoverstatetheoilvolumeAppendixF.4.


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stepofevaluatingthegeologyandselectingandjustifyinganestimateofconnectivitytothewellofthevarious sandstonechannels comprising theMacondo field. Thus, theirvalue foroilvolume implicitlyassumedaconnectivityof100%.Furthermore,theconversionfromreservoirtosurfaceconditionsusedvalues thatwerenot justifiedbydirectmeasurements.Thus, theiranalysiswas incompleteand theircalculationswerebiasedtooverstatetheoilreleased.

HighcaseIntertek

MiddlecaseSchlumberger

LowcaseCoreLabs

AveragevalueConnectedoilvolume 114MMstb 112MMstb 109MMstb 112MMstbTable4.2.Connectedoilvolumeusingthethreesetsoffluidproperties.57

57Thisassumesthemidrangerockcompressibility;seeSection5forfurtherdiscussion.


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Dr.PooladiDarvishsanalyticalmodelusedanoilcompressibilityof28microsips,twicethemeasuredvalue.58Thisisthemaincontributortohisoverstatementofoilproduced.Furthermore,hissimulationmodelstookanothervaluewhichisalsooutsidethemeasuredrange.59Whilehepresentedreasonablevalues in his report, the numbers used in quantitative calculations depart significantly from themeasurements,aproblemthatwewillseeagaininhistreatmentofpressure.604.2.3Watercompressibility:3microsips.Waterismuchlesscompressiblethatthereservoiroil.TherearenodirectmeasurementsofthecompressibilityofthereservoirbrinesatMacondoconditions.Sincethewatersaturation is low,differentplausiblevaluesofwatercompressibilitymakeanegligible (lessthan0.3%)differenceincalculatedoilreleased.Itakeanupperboundvaluebasedonmyreadingoftheliterature:3microsips.61TheGovernmentexpertsusedasimilarvalueaswell.4.2.4 Pore volume compressibility: 4.3 8.6 microsips. This is themain source of the departurebetweenmyestimateofcumulativeproductionand thoseofGovernmentexpertsDr.HsiehandDrs.Kelkar&Raghavan(seethesummarytableinSection2).Rock properties were measured on core samples by Weatherford laboratories. These cores wereextractedfromthewellduringdrilling.Thesemeasurementsprovidetheonlydirectassessmentofthecompressibility and permeability. 62 Neither Dr. Hsieh nor Drs. Kelkar & Raghavan used thesemeasurementsorprovidedascientificexplanationfordisregardingthem.Before drilling, BP predicted thatMacondo rock compressibilitywould be 5 6microsips, based onpropertycorrelationsfromotherfields intheGulfofMexico.63AcomprehensivereviewofproductionintheGulfofMexico,coauthoredbyDr.Kelkar,consideredarangeof110microsips,withamidrangevalue of 3microsips for fields of similar geological age toMacondo.64Once experimental datawereavailable,avalueof6microsipswastakenforBPsreservoirmodelling.65ThisvaluewasalsousedbyDr.PooladiDarvish.66Dr.Kelkar,whenworkingfortheMacondoFlowRateTechnicalGroupin2010,usedabasecasevalueof5.61microsips.67So,themidrangevalueIwilluse,basedonthemeasurements,isalsoaround6microsips.

58Avalueof28.5microsips;PooladiDarvishreport[PD],AppendixII,slides30and31.5915.3microsips,seeAppendixF.4.6.60SeeSection4.3andAppendixB.4.ValuesinPooladiDarvishreport[PD],AppendixIII,slides8and9.61Osif(1988).62Therawdatafromthemeasurementsofporevolumecompressibilityaregiveninspreadsheetform;BPHZN2179MDL02394185(Weatherfordporevolumecompressibility)[24].Asummaryofthemeasurementsisalsoprovided;BPHZN2179MDL02393883(Weatherfordsummaryofporevolumecompressibility)[26].TheresultsofpermeabilitymeasurementsarereportedinBPHZN2179MDL02394182(Weatherfordpermeabilitymeasurements)[23].63SeeFigureA.1takenfromBPHZN2179MDL06566208(BPPreDrillReview,slide17)[31].64SeeLiuetal.(2008),Table2.65See,forinstance,PinkyVinsonsdeposition[47],page300,line15.AlsoDr.Merrilldeposition[54],page214:2123.66PooladiDarvishreport[PD],AppendixIII,slide8.67SeeDonMaclaysdeposition[62],page393,line9topage394,line1.


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therawdata.Iwilldefertohissuperiorexpertise,notingthatusinghisvaluesleadstohigherestimatesofoilreleased.72Iwillconsidervaluesthatcoverthefullrangeofthemeasurements.Published literature regardingGulf ofMexico fields also supports the reliability of theWeatherfordmeasurements.73 For instance, a comprehensive review of compressibility measurements in theliterature is provided byNewman (1973). Hismeasurements for consolidated sandstones of similarporositytothatencounteredinMacondo indicatevaluesofaround3.5microsipsor lower. However,he states: The salient conclusion is that to evaluate rock compressibility for a given reservoir it isnecessarytomeasurecompressibilityinthelaboratory.FollowingNewmansadvice, Iwillusethemeasuredcompressibilities inmycalculations,eventhoughtheyappearattheupperendoflikelyvaluesbasedontheotherevidenceIhavepresented.4.2.5 Effective compressibility for input into thematerial balance equation: 18.7 24.5microsips.Table4.4reportsthevaluesofeffectivecompressibilitythatIwilluseinthematerialbalanceequation.74I have combined the values of oil, water and rock compressibility together in a way that exactlyreproducesthevolumechangeasthereservoirpressuredeclines.Thereareninevalues:threesetsoffluidmeasurementstimesthreerockcompressibilities:thehigh,middleandlowcases.Thiscoversthefullrangeofthemeasurements.

Effectivecompressibility,c(microsips)Fluidproperties

HighcaseCoreLabs

MiddlecaseSchlumberger

LowcaseIntertek

Averagevalue(midcase)

Highcaserockcompressibility 24.48 23.64 23.45 Midcaserockcompressibility 22.01 21.16 20.97 21.38Lowcaserockcompressibility 19.76 18.91 18.72 Table4.4.Valuesofeffectivecompressibilitythatwillbeusedtocomputeoilreleasedinthematerialbalanceequation.

72SeeAppendixA.2forfurtherdiscussion.73FormoredetailseeAppendixA.3.74SeeAppendixA.4foradiscussionofcompressibilitydefinitions.


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4.3 Thirdvariable:pressuredropThethirdparameterinthematerialbalanceequationisthepressuredropinthereservoircausedbytheoutflow of oil. My analysis here departs from that of the Government experts in two significantrespects: theconversion fromcappingstack todownholepressure;and theextrapolationto findthefinalreservoirpressure.4.3.1Conversion from capping stack todownholepressure. Weneed toknow thepressure in thereservoir.However,therewasnopressuregaugethereduringandaftertheincident.Thepressuredatawasmeasuredonagauge inthecappingstack. Thiswasseparatedfromthereservoirbyacolumnoftrappedoilthousandsoffeettall.Duringthebuildupperiod(whenthewellwasclosed)therewasnoflow,andthedownholepressurewasthecappingstackpressureplustheweightoffluidfromthecappingstacktothereservoir:this iscalled the head. I have performed this conversion for the three sets ofmeasured fluid data.75TheGovernmentexpertshaveallperformedthistranslationincorrectly. Itisthebiggestsourceoferrorintheirderivationofthepressurechangeinputintothematerialbalanceequation.Here isthepartofthatanalysisthattheGovernmentexpertsgotwrong. Duringthespill,hotoilrosethroughthewell,heatingthecasing,cementandsurroundingrock fromthereservoirtotheseabed.Whenflowceased,therock,andtheoilinthewellbore,cooleddownagain.Colderfluidsaredenser,andso thepressuredifferencebetween thecappingstackand the reservoir increasedover time. Toaccountforthischangingheadproperlyrequiresananalysisofheattransportconservationofenergyinthewellboreandthesurroundingrock.ThisispresentedinAppendixB.Thecappingstackpressureincreasedslowly,veryslowlyindeedbythebeginningofAugust.ThismisledtheGovernmentexperts:fromthegradualriseofthecappingstackpressuretheymistakenlyconcludedthatthereservoirwashighlypermeable.Morepermeablereservoirsallowoiltoflowmoreeasily,andhencebuildup lesspressure. However,evenwhenthecappingstackpressurewas flat, the reservoirpressure continued to rise: this cooling oilwas pressing downmore andmore. The rising reservoirpressurewasmasked by the apparent flattening of pressure readings at the capping stack. If theGovernmentexpertshadaccountedfortheextrapressureriseduetocooling,theywouldhavededucedalowerpermeabilityandflowrate,aswediscussbelow.4.3.2Thepoorconversionofthecappingstackpressures istheprincipalproblemwiththepressureanalysis of the Government investigators. In Appendix B.4 I quantify the effect of using a poorconversion fromcappingstack to reservoiron thepressuredropandoil released in theGovernmentreports.76 Here Iwill provide an overview to highlight its importance to their overestimates of oilproduced.

75ThedetailsarepresentedinAppendixB.76FurtherdetailsofmycritiquearealsoprovidedinAppendicesFandG.


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Tofindthefinalreservoirpressure(andhencethepressuredepletion)therearetwosteps:convertingthecappingstackpressuretodownholevalues,andthenpredictingtheadditionalincreaseinpressureafterthewellwascementedin.Ifocusonthisfirststephere,beforemovingtothesecond.TheGovernmentexpertsassumedthattherewasafixedpressuredifferencebetweenthecappingstackandthereservoirofbetween3,100and3,200psi.77Myvalueschangewithpressureandtemperature.They are typically 150 psi higher: this discrepancy alone has a 10% (0.5 MMstb) impact on theGovernmentsestimatedoilreleased. However,Dr.Hsiehconsideredaconversionclosetomine,butneverusedit,78whileDr.PooladiDarvishcalculatedawiderangeofvaluesyetinexplicablychoseavaluebelowthemallforhisbasecasesimulationmodel.79Thecriticalpartofthecalculation istoassessthecoolingrateoftheoiltrappedbetweenthecappingstackgaugeand thereservoiratthebottomof thehole. IshowthattheoilbecamecoolerthantheGovernmentexpertspresumed,hence the reservoirpressurewashigher than they realized, and thedepletionlower.Mycalculationserronthesideofhighertemperature,hencelowerreservoirpressureandmoreoilproduced:Icalculatethatthetemperatureoftheoilneartheseabedcoolsfromclosetoreservoirtemperaturestoaround95oFatthetimeofcementingthewell:thisisstillmuchwarmerthanthe surrounding ocean and sediment, which is at 40oF.80 What temperature did the Governmentinvestigatorsassume? Ihaveextractedthetemperaturethatwouldgivethepressureconversiontheyused(usingdataforoildensity).81ThetemperaturevaluesIcalculateareimplausible:closetoorabovethemaximum recorded flowing temperatureof221oF,82and, forDrs.PooladiDarvishandGriffiths, inexcessofthereservoirtemperatureitself(243oF).TheGovernment investigatorsmadetheoilunfeasiblyhot;they impliedthatoilsitting inthecappingstack,surroundedbycoldsteelanddeepoceanfor19days,wouldremainashotas,orhotterthan,thedeepreservoir.Thisis impossible.Technically,theGovernmentcalculationsdisobeyedthesecond lawofthermodynamics:hotthingscooldown.Thispressureconversionerrorcausedlargeerrors inthesimulationworkofDr.HsiehandDr.PooladiDarvish:notonlydiditleadtoanoverstatementofpressuredropthatdrivestheflow,butalsoofthepermeability, the connectednessof the rockpores thatalsodirectlygoverns the flow rate,discussedlaterinthisSection.Thecorrectpressureheadconversionwouldhaveledtheseinvestigatorstohalvetheirestimatesofoilreleased.Iwillnowdiscussthesecondstep inthepressureanalysis:extrapolatingto latetimestofindthefinalreservoirpressure,andhencethepressuredroptoinputintothematerialbalanceequation.77Thesourcesandprecisevaluesare:Drs.Kelkar&Raghavan[KR],page19(3,220psi);Dr.Hsieh,(pressureanalysis)(3,199psi)[44];Dr.PooladiDarvish[PD],AppendixIII,slide23,basecasemodelassumingawellheadtemperatureof220oF(3,137psi);Dr.Griffiths,[SKG],AppendixF,page39(calculatedstaticheadof3190psi).78Exhibit8617;indigitalformatasIGS770000026(Dr.Hsiehsspreadsheet),firsttab,cellH2(3,350psi).79SeePooladiDarvishreport[PD],AppendixIII,slide23(range3,3183,148psi).80AppendixB.3.81AppendixB.1.82Reddyetal.(2012).


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4.3.3 Pressure analysis to determine reservoir size and pressure decline. In standard oilfieldoperations,asocalledpressure transientorwelltest isoftenperformed. Thepressure inthewell ismeasuredasa functionof timewhile thewell is flowing,declining inwhat is called thedrawdown.Afterthewellisshutin,thepressureincreasesinwhatiscalledthebuildup.During a drawdown or buildup, pressure changes radiate outward from thewellbore, like awavemovingthroughthereservoir. Thissocalledpressuretransientcanbethoughtofasripples inapondmovingout in circlesuntil they encounter somebarrier to flow (such as the riverbank). Just as thereactionofripplestotheriverbankcanbeseenwiththeeye,theencounterofthepressurewaveswithreservoirboundariescanbedetectedinchangesintheslopeofthepressureresponse.ThisisshowninFigures4.8and4.9below;wewill reviewhow Ideduce theMacondo reservoirboundaries from thepressuretransientinthefollowingsections.Wewill alsouse thepressuremeasurements todetermine the final variable in thematerialbalanceequation,reservoirpressuredepletion.TheMacondothewellproducedforalmost86days.Thenthewellwasclosed.Thepressureatthecappingstackwasmeasuredbeforethewellwasclosed,andfor19daysafterwards.Thatpressurewasstillincreasingwhenthewellwascementedin,soweneedtouseproper methods of extrapolation to determine the final average reservoir pressure and hence thedepletionfromtheinitialpressuretoobtainourthirdmaterialbalancevariable.ThiswillbeanalyzedinSections4.3.611.4.3.4 Radial flow period to determine permeability. Government experts Drs. Hsieh and PooladiDarvisharriveatenormouslyoverstatedflowestimatesbecausetheirmodelsdoublethecorrectvalueforpermeability.Permeabilityisarockpropertythatmeasureshoweasilytheoilcanmovethroughthetiny, tortuouspathwaysconnecting theporesbetween thegrainsofsand,shownpreviously inFigure3.1.Highervaluesforpermeabilitygivehigherflowrates.Permeabilityiscontrolledbythesizeofthepores(largerporesallowmoreflow)andbyhowwelltheyareconnectedtogether.TheGovernmentexpertsallassumedapermeabilityofover500mD.83Thatismorethantwicethemostlikelyvalue,andproportionately inflates theGovernmentestimatesof flow. Tounderstandhow theGovernment experts made this mistake, and to determine an appropriate value for permeabilityourselves,weneedto introducethemethodsfor interpretingthepressurechangesthatoccurwhenareservoirstopsproducingandbuildsuppressure.Torepresentthepressureresponse,wetreatthereservoirasabox,shownschematicallyinFigure4.8,as has every other investigator who has studied Macondo. This box contains all the oilbearingsandstoneconnectedtothewell.Ifwereturntotheanalogyoftheripplesinthepond,thepressuresignalmovesoutincircles(radially)before it encounters a boundary (the edges of the reservoir channel or channel complex). This isdepicted inFigure4.9. Permeability isdeducedfrom identifyingthe initialradialflowperiod. WewillplottheMacondoradialflowpressuretransienttocalculatethepermeabilityinSection4.3.8.83SeeSection4.3.8.AppendixCdiscussespermeabilityinmoremathematicaldetail.


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theradialflowanalysisasdescribed intheprevioussection,wewillbeabletodeducethesizeoftheconnectedreservoirfromthetimesatwhichthepressuretransienthitstheboundaries.Fromthegeologicalinterpretationofthefielditisreasonabletoconsiderthatthereservoiriscomposedofoneormorechannelcomplexes,whichforsimplicityIwillrefertoaschannelsfromnowon.Oncetheperiodofradialflowends,ouranalysisshiftstothemovementofpressurealongthechannelthisisonedimensionalorlinearflow.Wecandetectthetimeswhenthepressurewavehitsthetwoendsofthechannel,andcalculatethelengthofthechannels.Fromthewidthandthelengthwecandeterminetheareaofthereservoirconnectedtothewell:theareaoftheboxinFigure4.8.Iemploya rectangular flowmodel tostudy radial flowand the transition to flow inachannel,andalinearflowmodelforthelatetimebehaviourtodeterminethetimestoreachtheendsofthereservoirandthepressuredrop.Wenowhavetheprinciplesforanalyzingthepressuredataasafunctionoftime.Wewillshowhowitprovidesuswithfourimportantpiecesofinformation:(1)thefinalreservoirpressure,usedtocalculatepressure depletion, a direct input into the material balance equation; (2) permeability, the criticaldeterminantofflowrate,fromtherateofpressurebuildup intheradialflowperiod;(3)thetimeforthepressureresponsetohitthesidesofthechannel,whichwillbeusedtomeasurereservoirwidthandcheckconnectivity;and(4)thetimesforthepressureresponsetoreachthetwoendsofthechannel,whichwillbeusedtohelpassessoriginaloilvolumeandexcludethepossibilityofaquifersupporttotheproductionofoil.4.3.6Pressureprediction.Westartwithaplotofthebuildupofpressureasafunctionofthetimeafterthecappingstackwasshut in. Ihaveplottedthispressureresponse inFigure4.10 togetherwiththepredictions of my analytical rectangular and linear flow models.85 I obtain a close match to themeasuredpressure,demonstratingthatmymodelisanaccuratedepictionofthebehaviourbyreservoirengineeringstandards:86thisisshownbytheredandblacklinesinFigure4.10.Butthere isamorepowerfulmethodologyforplottingandanalyzingthepressurebuildup. Itfocuseson the trend, or slope of the data. Analyzing the changes in slope provides insight into thecharacteristicsof the reservoir. Matching the slope changeswith amodel is an extra litmus testofmodelvalidity.4.3.7 Pressure derivative methodology and its importance. A revolution in the ability to interpretpressure tests and thereby determine reservoir properties occurred in the 1980s,87when reservoirengineersbegantofocusontheplotofthechange inpressureasafunctionoftime. Usingthisplot,characteristicshapesappear in theslope, fromwhichanengineercandeterminethestructureofthereservoirandthepermeability. LikeaphysicianwithachestXRay,areservoirengineercandiagnose85SeeAppendicesCandD.86IhavederivedalltheequationsIusebyhand,andhavenotreliedoncommercialpressuretransientanalysissoftware.Suchsoftwarerequiresanassumedflowrate(see,forinstance,M.Levitandeposition[56];page216,lines19,20).87Bourdetetal.(1983;1989).


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pressure theGovernment investigatorsassumed that the rise in reservoirpressurewas thesameasinthecappingstack,withalowerderivative.Thiscorrespondstoahigherpermeabilityofaround560mD.95Thisalmostexactlymatchesthe550mDusedbyDr.PooladiDarvish96and593mDemployedbyDr.Hsieh:97theydid indeedmatchthepressure,butthewrongpressureto find the wrong permeability, which lay outside the averages from log and coremeasurements. The flow rate isproportional to thepermeability,so their simulationmodelssignificantlyoverestimatedtheflowrate(andhencecumulativeoilreleased).

Figure4.12.Thepressurederivativeandthepressureriseplottedasafunctionoftimesincechokeclosure.Theredpointsare thederivativemeasuredat the capping stack,while the crosses show thedownhole (reservoir)pressurederivative,which is higher, indicating lower permeability. I show best match predictions to the reservoir behaviour using bothrectangular(blacklines)andlinearflowmodels(redlines).Thelinearflowmodelshowsadeviationatearlytimes,sinceitcannotrepresentthetransitiontoradialflow.

4.3.9Reservoirpressurepredictions.Theanalysisofthepressureinthefirstday(86,400s)hassomeuncertainties:coolingfromtheocean,thethermalpropertiesoftheannulusaroundthewell,andthecomplexsequenceofflowratesduringchokeclosureallimpacttheearlypressuretransient.IconsiderthepermeabilitycalculatedintheexpertreportofDr.Gringarten,238mD,whichavoidstheseproblemsthrough using downhole pressure measurements, more robust than my determination presented95Assumingaradialflowstabilizationinthecappingstackderivativeof32psiinFigure4.12.96Dr.PooladiDarvishsbasecasemodel[PD],AppendixIII,slide8.97Exhibit8615(10/22/2010HsiehDraftReport,Table2)[67].

Radialflow

ChannelflowDownholederivative

Cappingstackderivative

Downholepressureincrease


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above,althoughmyvalueliesinhisstatisticalrange.98Theemphasisofmycalculationswillbeonlatetimes,beyondaday,whenthereislinearflow.Aclosematchtothepressureinthisregimeisimportanttodeterminethefinalreservoirpressureandthelocationofthefarreservoirboundary.Mybasecaseassumesaconstant(albeitunspecified)flowrate.Theflowratehistorydoesimpactthepressureresponse,asstatedabove. However,fortimesbeyondadayorso,thepressureresponse isgovernedbytheaverageratealone.99Figure4.13showsthedownholepressureplottedagainsttimecomparedtothepressurepredictedbymymodel:theinsetshowsthepressurepredictionforlatertimes,indicatingthatthepressurestabilizesto its finalvalueof10,433psiaround threemonthsafterchokeclosure. The final reservoirpressurethatIuseinmymaterialbalancecalculationrangesfrom10,433to10,531psi,dependingonwhichsetsofthefluidpropertiesareused.100TheGovernment reportsallestimatea final reservoirpressure that liesbelowmyvalues.101Noneofthese reports compare their predictions to the data using the Xray examination of the pressurederivative.102Dr.Hsiehomittedthisanalysis,eventhoughtheBPengineerswithwhomhewasworkingdidusederivativeplots.103However,myvalue is lowerthanthevaluepresented inapressreleasebyBP:industrystandardtechniquespredictthefinalreservoirpressuretobeapproximately10,600psi.104IfindalowerfinalpressurethanthatderivedbyBP,resultinginahighercalculatedcumulativeflow.Dr.HsiehandDr.PooladiDarvishsignificantlyoverestimatedthepressuredropandconsequentlyoverstated the oil released; this effect is quantified in the summary table in Section 2. Drs. Kelkar &Raghavanmade twoerrors thatpartiallycancelled: theyunderestimated thehead,butslightlyoverestimated the pressure rise, leading to a more reasonable final assessment of pressure drop (seeAppendixB.4).

98Dr.Gringarten[ACG]quotesarangeof170329mD.99SeeAppendixE.100Thefluidpropertiesdeterminetheconversionfromcappingstacktoreservoirproperties(AppendixB)andsothepredictionsaredifferentforthethreesetsofmeasurements.InthisSectionIshowmodelcomparisonsusingtheCoreLabsproperties;myanalysisis,however,performedforallthreesetsofdata.101Dr.Hsieh,10,267psi(seeExhibit8617(Hsiehpressureanalysis))[44];Dr.Griffiths,10,310psi[SKG]AppendixF,page39;Dr.PooladiDarvish[PD],AppendixV,slides4and5:10,053to10,382psifromhissimulations;Drs.KelkarandRaghavan[KR],page23:10,23510,396psi.102Dr.PooladiDarvish[PD]presentedapressureandderivativematchforhisanalyticalmodel,AppendixII,slides30and31;however,forallhissimulationruns,heonlyshowedmatchesofpressurealone.103SeeDr.Merrillsdeposition[55],page344,line18whereDr.MerrillmentionsBourdetderivativeplots.104BPpressrelease,page6,secondparagraph[50].


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Figure 4.13. Downhole (reservoir) pressuredata (crosses) compared to thepredictedpressure for linear (red line) andrectangular (black line)models. The inset shows theextrapolation to late timeshowing that the final reservoirpressure(10,433psi)isreachedaround3monthsafterchokeclosure.

4.3.10Pressuredrop:1,3251,423psi.105Forcompleteness,weendthissectionwithTable4.5,whichpresentsthe finalreservoirpressureandpressuredropp (the initialpressure,11,856psi,minusthefinalpressure)usingthethreesetsoffluiddata.Thepressuredropisthethirdandfinalcomponentinthematerialbalanceequation:itsvalueliesbetween1,325psiand1,423psi.

Property HighcaseCoreLabs

MiddlecaseIntertek

LowcaseSchlumberger

AveragevaluesFinalreservoirpressure,pf(psi) 10,433 10,502 10,531 10,489

Pressuredrop, p(psi) 1,423 1,354 1,325 1,367Table 4.5. Final reservoir pressure and pressure drops determined from the pressurematch for the three sets of fluidproperties.

105Thesevaluesarefoundusingthelinearflowmodel.SeeAppendixD,TablesD.2andD.3.


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5. ConfirmingtheconsistencyofthecalculationswithotherevidenceBeforewemultiplyourthreenumberstogethertocalculatetheoilreleased,weneedtopausetocheckifthedifferentinputstoourcalculationaremutuallyconsistent.Itisstandardinreservoirengineeringtocheck if thepredictionsof thepressureanalysisagreewith thegeologyof the reservoir.Wehaveassembled the pieces of theMacondo jigsaw in this analysis; nowwewill analyzewhether they fittogethertoconstructacoherentpictureofthereservoir. ThisvitalassessmentwasnotperformedbyanyoftheGovernmentinvestigators:suchacheckwouldhaveshown(aswewillshowhere)thattheiranalysiswasincompatiblewiththemeasurements.InSection4.1weshowedhowtheGovernmentinvestigatorsassumedwithoutgeologicanalysisthatthetotalreservoirvolumewasconnectedtothewell.InSection5.1,Iwillcombinetheseismicandpressureanalysistoshowthatthereservoirisnot100%connected.InSection5.2Iwillexplainhowmyapproachofusingtherangeofvalues fromthedata foreachparameterendsupdefiningarangeofcalculatedflowvolumesthatismorecertainandreliablethanotherapproachestouncertainty.5.1 Crosscheckingseismicandpressuretransientindicationsofreservoirsize,dimensionsandconnectivity5.1.1Reservoirlength.Itcouldbepossiblefortheconnectedreservoirtobeshorterthanthelengthofthe field. For example, in the seismic interpretation introduced in Section 4.1, faultsweremappedcuttingacrosstheaxisofthechannelorientation.Iwouldarriveatamuchsmallerconnectedreservoirandlowerconnectedoilvolume(andhencecumulativeflow)ifIadoptsuchanassessment.Figure5.1showsaBPinterpretationoftheseismicsurveywhereindividualchannelsareidentified.TheanalysissuggestedthatthechannelswerenotnecessarilycontinuousinaNorthSouthdirection.Fromthis,BPmadeanassessmentof theareaconnected to theMacondowellbefore thecappingstackpressuredatawasavailablethatgavevaluesbetween50and225acres.106Bycomparison,theentirearea inBPsseismicanalysis ismuch larger4,482acres. If IweretousethesmallerconnectedareasuggestedinthisBPstudy,thecalculatedvolumeofoilreleasedwouldbeatmostbetween80,000and440,000stb.WhileBPsanalysisisnotunreasonablefromageologicalstandpoint,IwillshowinthisSectionthatthepressureresponseclearlyindicatesthattheconnectedareaisconsiderablylargerthanthis.Thus,Iwillnotconsiderthepossibilitythatthereservoiriscompartmentalizedbyafaultorotherbarriercuttingacrossthechannels.Instead,Ibelievethepressuretransientevidence(outlinedbelow)suggeststhatthe limitationonconnectivity isassociatedprincipallywiththereservoirwidth,that is,how far itextendsEastWestorNESW.

106BPHZN2179MDL04440238(BPseismicsurveypresentation,slide3and4,respectively)[17].OtherestimatesoftheconnectedoilvolumemadeduringthespillbyBPinclude650acresseeDr.Levitansdeposition[56];page95,lines7,8whichisstillmuchlowerthanindicatedbythepressureresponseoncethewellwasclosed.


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Onceweknowthetimestoseetheboundariesofthe(connected)reservoir,weneedtoderivetherateatwhich thepressuresignalpropagates. Ifweknow thisspeedand the times, thenwecan find thephysical locationsof theseboundaries. In Sections 4.3.4 and 4.3.5wediscussed that this rate is afunctionofpermeability. Higherpermeabilityallows faster flowandamorerapidpropagationofthepressuresignal.Hencehigherpermeabilitygivesalargerareaandgreaterconnectivity.Thespeedofthepressuretransientisalsoafunctionoftherockcompressibility.Amorecompressiblerock retards thespeedofpressure transmission. Hence reservoirengineersusea term forpressuretransient speed called diffusivity, which proportional to permeability but inversely proportional tocompressibility.108Withourpressuretransientdeductionsof times tohitboundaries,combinedwithpossible rangesofvaluesfordiffusivity,Icancalculatealikelyupperboundonthereservoirsconnectivity.IwilltakethelargestpermeabilityvaluefromtheexpertreportofProf.Gringarten:329mD.109ThisisabovethevalueIdeducedfrompressureanalysis(300mDseeSection4.3)andfromdownholemeasurements(219mDseeAppendixA.5).Usingthisupperboundonpermeability,theconnectedareaIcalculatevariesfrom1,931to2,590acres(seeTable4.1).1105.1.3Meanderingflowpath.Figure5.1showsthatthepressureresponse(andtheoil)doesnotmoveinastraightlineitfollowsthewindingpathofthesandstonechannels.Hencethepressuresignal(andthe flowingoil) travelsa longerthanstraightlinedistance. Tocalculate thepath length Ihave takensomeofthechannelsindicatedinFigure5.1andmodelledtheirshapeassinewaves.Thisisastandardgeometricapproachingeology.111Icalculatethatthetruedistancetravelledisaround14%longerthanastraight line.112Inreality,theflowpathcouldbemoretortuousstill,takingdetoursalong locallythethickestsandsinthreedimensions.IusedthissinuosityinconstructingmymodelinFigure4.5.5.1.4Combiningpressureandseismicanalysistodeduceconnectedarea. InFigure5.2,the leftsideoverlays the reservoir size estimated from pressure analysis onto the size predicted by the seismicanalysis. Thehorizontal lines indicatethewidthofthefieldas interpretedfromthepressureanalysis.The pressureinferred size is smaller,which suggests that the field is poorly connected, requiring areductionofthe initialvolume input formaterialbalance fromthevalueusedbytheGovernment. ApossiblereasonisshownontherightsideofFig.5.2,mygeological(clay)model,showinghowindividualoilfilledchannelsmaybedisconnectedlaterallyfromthewell.

108UsingEq.(C.4).109TheGringartenreport[G]hasarange170329mDwithamostlikelycaseof238mD.Technically,thismeansthatthereisa10%probabilityofthepermeabilityexceeding329mD.110SeeAppendixD.1forthemathematicaldetailsofhowdistancesandareasarecalculated.111See,forinstance,Posamentier(2003),DystraandKneller(2008).112SeeAppendixD.1forthemathematicaldetails.


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lowpermeabilityshale.114 InFigure5.2, Ihave indicatedbythe lilacovals regionsofthe fieldthatIconsiderareunlikelytobeconnectedtothewell.

3. Theclearsignatureofchannelflow,therestrictedwidthofthechannel,andevidenceofnoflowboundariesalongallsidesoftheregionconnectedtothewell,stronglyindicatethatthereisnoaquifersupport.Thereisnoevidencethatweareseeingadrainageregionthatextendsbeyondtheoilfield.

Wewillnowaddresspossibleobjectionstothisinterpretation.1. Permeability.ThehighernumbersforpermeabilityassumedbytheGovernmentexpertswould

suggesthigher connectivity. However,Prof.Gringartens reportuses a superiormethod fordeducing permeability that is based on prespill measurements and dynamic flowing data,considered thegold standard forpermeabilityassessment. Hederivesapermeabilityof238mD. Iamusingahighervalueof329mD theupperendofhis range. It isnotpossible toreconcile significantly higher permeabilities of 500 mD and above as used by theGovernment investigators115withmeasurementsonrocksamplesfromMacondo(average364mD),log(downhole)analysis(average219mD),116andmypressureanalysis(300mD,Section4.3).There is another source of evidence that the Governments high permeabilities are highlyimprobable.Ifthepermeabilityhadbeen500mDorhigher,thentheeffectofwellcoolingmaywellhaveexceededtheslowreservoirpressureriseafterchokeclosureonJuly15th2010.Thecappingstackpressuremighthavestabilizedandthenfallenslightlyinthefirstday.Thisislikelytohavebeenmisinterpretedasa signofpoorwell integrity, the chokewouldhavebeen reopened,andoilwouldhavecontinuedtospill,unnecessarily, intotheGulfuntilthereliefwellwasdrilled.117

2. Compressibility. As discussed earlier, some Government experts asserted a highercompressibility,leadingtoahighercalculationofcumulativeflow.However,thiswouldleadtoaslowermovingpressuresignal,sincethediffusivityisinverselyproportionaltocompressibility.Hence, their assumption of higher compressibility must result in an interpretation of thepressure transient yielding a smaller calculated drainage region. A low compressibility, incontrast,allowsthepressuresignaltotravelfasterandencountermoreofthefield.Noticetwocompetingeffectsofcompressibility:whileforafixedoilvolumeandpressuredropahighcompressibilityleadstomoreoilreleased,ahighcompressibilityindicatesasmalleroilvolume.So,allowingamuch largercompressibility is inconsistentwith theseismicextentof the field,unlessthefieldispoorlyconnected.

114Posamentier(2003).115SeeAppendicesFandG.116SeeAppendixA.5.117SeeAppendixB.3forafullerdiscussion.


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3. Aquifer. Duringthe incident, investigatorsfromboththeGovernmentandBPconsideredthatanaquiferdrivecouldprovidepressuresupportandadditionalrecoveryinMacondo;118thiswasa reasonablehypothesis to consider,but the impactof theaquiferwould requireproductionperiods of some years, while the pressure response indicates flow boundaries wereencounteredduringthetimescaleoftheincident.Foranaquiferlocatedtothesidesandendofthemainoilbearingchannelstocontributetooilproduction,thepressureresponsehastopassthroughpoorlyconnected,lowpermeabilityregionsbetweenchannels,orpassbeyondthelongitudinal extent of the reservoir. This flow response takes several months or years tocontributenoticeablytoproduction.ThisconclusionisconsistentwiththemodellingworkofalltheGovernmentinvestigatorsandtheanalysisperformedshortlyaftercappingstackclosurebyBP. BPsreservoirengineerDr.Merrillsaysthatheexcludedanaquifer119astheeasiestandsimplestwaytomatchthemeasuredpressures.

4. Analysis of the implicitGovernment premise that thewell drained the entirewidthof thefield. I have calculated that approximately half thewidth of the field near thewell iscontacted.120Todoublethis,sothatthewholewidthisencountered,wouldrequireanincreaseofmyvalueofwbyafactoroffourfromaround17hourstomorethanthreedays.121Despitetheambiguitiesassociatedwith the interpretationof thepressure responseatearly times, aclearindicationofchannelflowisencounteredwithinaday.Furthermore,Ihaveassumedthatthe average permeability across or between channel complexes (including low permeabilityshalethatseparatesindividualchannels)isthesameasthepermeabilityalongachannel.Thisagainisunlikely,122andsoifanythingmycalculatedwidthislikelyanoverestimate.

5.1.5Deducingconnectivityfromtheoverlayofpressureandseismicanalysis.Iwilltakeagenerousapproach,whichwhileitlikelyoverstatestheconnectedoilvolumeprovidesarobustupperbound.AsoutlinedinSection4.1,Iplacetheoilconnectedtothewellintheareapredictedfromthepressureanalysis. Iassumethatoutsidethisarea,theoildoesnotflowtothewell. Thethicknessoftheoil intheseregions isassumedtobe10ftonaveragethis isthelimitoftheseismic interpretation.123Theoverallaveragethicknessofthewholefield44ft,whilethethicknessatthewellis93ft,soIamplacingvery littleoiloutside themain, connected channels.124 I find a connectivityofbetween87 and90%dependentonthefluidproperties.125 Ifind it implausiblethattheconnectivity isbetterthanthis:theseismicinterpretationplacesoilfurthertotheEastandWestofthewellthancanbepossiblyconnectedto it. I cannot,however,excludea lower casewithmore restricted connectivity,basedon themostlikelyvalueofpermeabilityintheGringartenreport.118BPHZN2179MDL06566208(BPPreDrillReview,slide18)[31].119Dr.Merrilldeposition[55],page442,line27.120Windicatesthetransitionfromradialflowtochannelflowandso,technically,isusedtofindtheconnectedreservoirwidthnearthewell.121Sincethisisadiffusiveprocess,totraveltwicethedistancetakesfourtimeslonger.122SeeBPsgeologicalreview;[39],slide2.123SeeBPsgrossrockvolumeassessment;[30],slide1,mostlikelycase:10ftcutofffootprint(noisebackground).124SeeTableA.3and[31],slide15.125SeeAppendixD.1.6forthemathematicaldetailsandTableD.4forthevalues.


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My assumptions are consistent with the upper bound of permeability. I can only allow a largerconnectedareabyreducingthecompressibility.Thismayallowmoreoiltobeconnected,butlessoilisreleasedforagivenpressuredrop.Thetwoeffectscancelout.Or,Iallowalargerpermeability,outsidethevaluesassignedbyrobustpressureanalysisanddownholemeasurements.Itisnotpossibletouseplausiblerockandfluidpropertiesandallowacumulativeoilreleasethatliesabovemyrange.5.2 Consistencywithflowratehistory5.2.1 Pressureanalysisandflowratehistory.Iwillnowmentiononelast,further,consistencycheckrelatedtothepressureanalysis. Thepressurewasmatchedbyamathematicalmodelthatassumedafixed (albeitunspecified) flow rate. Toyieldmycalculationof totaloil released, if the flow ratewasconstant, itwas in the rangeof34,000 43,000 stb/day. This is inconsistentwith theGovernmentassumptionofflowratesthatwereeitherconstantordecreasingovertimewithfinalvalueofaround50,000stb/day.Ifthisfinalflowrateiscorrect,thenmyanalysisassertsthattheflowratemust,overall,haveincreasedonaverageduringthespillperiod.InAppendixE.2Imatchthepressureresponseusingdifferentpossibleflowratehistories.Thisapproachisstandard inpressuretransientanalysis,where formanyreasonstheflowatanygivenwellmayvary. Icanobtaingoodmatches forvarious flow ratehistories, including thosewitha final flow rateconsistentwithGovernmentestimates,whilearrivingatmymidrangecalculationoftotaloilreleased.Furthermore, analysis of the accident suggests that oil flow into the wellbore was initially highlyrestricted,buttherestriction(s)haddisappearedbytheendofthespill,as indicatedbythe injectivitytest justbeforecementing thewell,whichshowedn

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