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1 ADIPEC 2013 Technical Conference Manuscript Name: Company: FOROIL Job title: Address: 10, rue Lincoln, 75008 Paris, France Phone number: +33 1 80 96 88 88 Email: [email protected] Category: Abstract ID: 412 Title: Learning From Past Data Tells how to Increase Production and Reserves: A Successful Four Year Return of Experience Author(s): Benjamin GUESDON, Stéphane PAIRAULT, Hugues de SAINT GERMAIN, FOROIL This manuscript was prepared for presentation at the ADIPEC 2013 Technical Conference, Abu Dhabi, UAE, 10-13 November 2013. This manuscript was selected for presentation by the ADIPEC 2013 Technical Committee Review and Voting Panel upon online submission of an abstract by the named author(s). Abstract: This paper presents four years of successful implementation of a new methodology for identifying best re-development plans for mature fields. This is based on appropriate learning techniques using mainly past production data. This achieves a 95% forecast reliability for each contemplated plan. Massive computing allows playing 1,000,000s plans and selecting the best. Depending on future actions on the fields (change of injection/production rates, conversion and/or drilling of new wells), this allows identifying production and reserve improvement of +20% to +100% against baseline, hence increasing the ultimate recovery factor. This methodology can be applied to all hydrocarbon mature fields, where reliable production data have been recorded, per well, over typically more than seven years. As this is a learning process, it is valid for identifying the best development plan only with the same recovery technique as experienced in the past. Several operators have successfully implemented this approach since 2009, leading to results already published for two fields, with and without infill drilling. Actual operational results range from +20%, (change of injection pattern and conversions) in San Francisco oilfield, Colombia to +50% (same, plus some infill drilling) in Butte Voluntary Unit, Canada, against baseline.

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Page 1: ADIPEC 2013 Technical Conference Manuscript 20130912 · abstract by the named author(s). Abstract: This paper presents four years of successful implementation of a new methodology

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ADIPEC2013TechnicalConferenceManuscript

Name: Company: FOROIL Job title: Address: 10, rue Lincoln, 75008 Paris, France Phone number: +33 1 80 96 88 88 Email: [email protected] Category: Abstract ID: 412 Title: Learning From Past Data Tells how to Increase Production and Reserves: A Successful Four Year Return of Experience

Author(s):Benjamin GUESDON, Stéphane PAIRAULT, Hugues de SAINT GERMAIN, FOROIL

ThismanuscriptwaspreparedforpresentationattheADIPEC2013TechnicalConference,AbuDhabi,UAE,10-13November2013.

ThismanuscriptwasselectedforpresentationbytheADIPEC2013TechnicalCommitteeReviewandVotingPanelupononlinesubmissionofanabstractbythenamedauthor(s).

Abstract:

Thispaperpresentsfouryearsofsuccessfulimplementationofanewmethodologyforidentifyingbestre-developmentplans for mature fields. This is based on appropriate learning techniques using mainly past production data. Thisachievesa95%forecastreliabilityforeachcontemplatedplan.Massivecomputingallowsplaying1,000,000splansandselectingthebest.

Depending on future actions on the fields (change of injection/production rates, conversion and/or drilling of newwells),thisallowsidentifyingproductionandreserveimprovementof+20%to+100%againstbaseline,henceincreasingtheultimaterecoveryfactor.

Thismethodologycanbeappliedtoallhydrocarbonmaturefields,wherereliableproductiondatahavebeenrecorded,per well, over typically more than seven years. As this is a learning process, it is valid for identifying the bestdevelopmentplanonlywiththesamerecoverytechniqueasexperiencedinthepast.

Severaloperatorshavesuccessfullyimplementedthisapproachsince2009,leadingtoresultsalreadypublishedfortwofields, with and without infill drilling. Actual operational results range from +20%, (change of injection pattern andconversions)inSanFranciscooilfield,Colombiato+50%(same,plussomeinfilldrilling)inButteVoluntaryUnit,Canada,againstbaseline.

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As the best development plan out of 1,000,000s is always a non-intuitive case, it is far better than any traditionalapproach:increaseofproductionagainstthebaselineistypicallytwicelargerthanexperiencebaseddevelopmentplans,underthesametechnicalandfinancialconstraints.

Correspondingreservescanbere-certified,asidentifiedplansensureamorehomogeneousproductionoftheoilorgasinplace.

This approach is a major contribution to the data-driven reservoir modeling, as it introduces an effective physics-constrained learning process. It demonstrates how re-balanced production over amature field can increase reserveswiththesamerecoverytechnique.Itusessmartautomatedwaysofmassivelygeneratingandcomparingdevelopmentplans.

The FOROIL technology is intrinsically secure andallows to completely control the risksof current techniqueson thefield. Indeed, this technology, based on data (facts), is not dependent of human interpretation, and uses the samerecoverytechnologyasalreadyappliedonthefield(acidjobs,waterorgasinjection,gaslift,sidetrackedorhorizontalwells…).Progressivescenariosareintroducedineachfielddependingoninvestmentcapacity.Thetechnologyimprovescurrent technology,patterns (water injection reallocation/newconversions to injection)andallows toknowwhere todrillnewwells.

FOROIL already developed a one-year pilot of selective waterflooding in San Francisco oilfield. Similarly, FOROIL isdevelopingnewmethodstoimplementEORandSAGDprojectsinoilfieldswithinoneortwoyearsinsteadofcurrentlyfiveortenyears.

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Figure1:ActualproductionoftheSanFranciscooptimizedproductionscenario

Figure2:ActualproductionoftheButteVoluntaryUnitoptimizedproductionscenario

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Introduction

Generatingadditionalproductionfrommaturefieldsisbothapriorityandachallenge.Ontheonehand,asnewfindsbecomeevermoreexpensive,maturefieldsaregainingimportanceintheoil&gasindustrywitheachpassingyear.Ontheotherhand,maturefieldsoffernoeasyopportunity:theyusuallysufferfromhigheroperatingcosts,decreasingoilproduction,ageingequipment,andacomplexsubsurfaceconfigurationofpressureandsaturation.Theseissuesjointlycontributetomakingnewinvestmentbothlessattractiveandmorerisky.

Thispaperpresentsabreakthroughtechnologyforincreasingtheproductionofmatureoilandgasfieldswhilereducingtherisksrelatedtothedevelopmentofmaturefields.Thisstillrecenttechnologyhasbeenavailabletotheoilandgasindustry for the past six years and has already been successfully applied on several fields. Two application casescompletedinWesternCanadaandColombiaarereferredtointhepresentpaper.

Anoptimizedre-developmentplanwasengineeredforeachofthosewaterfloodedmatureoilfields.InSanFranciscooilfieldcase,Colombia,theimplementedplanincludednoinvestment(onlyare-organizationofthewaterfloodingregime,inparticularthroughtheconversionofproducersintoinjectors).Theresultwasanincreaseofmorethan20%oftheoilproductioncomparedtobaseline.InButteVoluntaryUnit,theimplementedplanincludedlimitedinvestment(fournewinfillwellsandfourconversions).Theimplementationofthisplanprovedverysuccessfulandresultedinmorethan50%production increase, pursuant to the initial prediction. This technology is also intrinsically secure and allows tocompletelycontroltherisksofcurrenttechniquesonthefield.

Thestakes for theoil fields ispresentedfirst.Thefollowingtwosectionsprovidedetailsaboutthemainpillarsof thetechnology:(i)thegeneralworkflowforafieldmassiveoptimizationproject,and(ii)themethodologytoobtainthebestpossibledevelopmentplanunderspecifiedconstraints.Thelastsectionisdevotedtopresentingtheimplementationofthescenariosintheoilfields.

1) AtstakeforSanFranciscooilfieldandButteVoluntaryUnit

a) AtstakeforSanFranciscooilfield

The San Francisco field was discovered in 1985 in Colombia (Figure 1) and has been producing from the Caballosformation. This is a highly heterogeneous reservoir in a fractured anticlinal, 3000 feet deep. The initial pressurewas1100psiawithanapproximatebubblepointpressureof950psiaandoilqualityvaryingfrom23°to28°degreesAPI.Thefieldhasbeenunderawaterfloodschemesince1989.Thecurrenttotalfluidproductionis250,000bblwithanaveragewatercutof96.7%.

By 2008, the operator, Hocol S.A., had drilled a total of 193 wells consisting of 128 active producers and 76 activeinjectorswithvariedresults.Dueto theheterogeneityof the field,complicatedbydense faultingandwater injectionunder an unfavorablemobility ratio, the operator needed to determine the candidates for the upcoming conversioncampaign;notonlythelocationoffuturewellsbutalsowhatinjectionandproductionratestoimplement.

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Before the study,Hocolmadeadisappointing infill drilling campaign. Then theydidnot expectmore good infill. ThestudyconfirmedtheHocolidea.AccordingtopreviousstudiescarriedoutintheSanFranciscofield,itwasapparentthatthereshouldbeapossiblegaininre-arrangingthewater-floodingscheme,inordertobetterdrainsaturation-favorableareas,detrimentallytootherlessattractiveareas.Thiswouldhavetobedoneundertechnicalconstraints,notonlyperwell,butalsofortheoverallfield,inparticulartotalinjectionandproductionrates.Also,thefinancialconstraintwastominimizecapitalexpenses.

Oneofthekeypracticalanddifficultquestionswastodefinehowmanyproducersshouldideallybeconverted,whereandwhen.Astherewere99activeproducers,therewere299possibilities(about1030),withouteventakingintoaccountwhentoconvertthem.Ofcourse,thisisevenmuchmorecomplex,asaconversionneedstobebestimplementedwithevery relevant rate of neighboring producers needing to be consequently adjusted. Also, other injection ratesmightneedtobechangedelsewhere,duetoasurfacelimitation(totalinjectionrate)orasacontributiontothereadjustmentoffieldstaticpressure.

Obviouslythelocationofproducerstobeconvertedhasaclearimpactonfieldtotalproduction.Theoptimumnumberof conversions to be carried out also matters very much: if there are too few conversions, opportunities of betteramanagingpressureandsaturationwillhavebeenmissed.Worsewouldbetoconverttoomanyproducers:themostcertain consequence of a conversion is the corresponding loss of its oil production. It needs to be compensated bybetterproducerselsewhere. Ifoneproducertoomanyisconverted,thecorrespondingincremental lossofproductionwillnotbecompensatedbyotherproducers:moneyspenttoproducelessoil.

Therefore,amassiveoptimizationprocessisparticularlyappropriateforSanFranciso.Asexplainedbefore,thisrequires,first,arelevantunderstandingofthefieldmechanisms,andthentheuseofanOptimizationEngine™.

b) AtstakeforButteVoluntaryUnit

ButteVoluntaryUnitisaconventionaloilfieldlocatedinWesternCanada.Itstartedproductionin1967andwaswaterfloodedfrom1970onwards.Thefieldwasoriginallydevelopedwith160-acrespacinginthe60’sand70’s,followinganinverted9spotpatternfor injection.80-acredownspacingwascompletedduringthe80’s,and40-acredownspacingwas in progress since the early 2000’s. InMay 2009, 82wells had been drilled (in the scope of study), of which 53producersand12injectorswerestillactive.Themostrecent investments,ninewellsdrilledin2004and2005,provedinsufficienttomitigatethenaturaldecline.Thefieldwasproducing624bbl/doilwith83.5%watercut.

ButteVoluntaryUnitwasbelievedtostillhavepotentialforimprovementunderwaterflooding,anditwasenvisagedtoconvert several more wells in order to complete a line injection pattern aligned with a North-East / South-Westpermeability trend of the reservoir. However, a fieldmodel did not exist yet, so itwas an excellent case for using abespoke tool to accurately forecast future oil production per well and calculate the costs and benefits of differentpossibleconversionplans,andtheexpectedyieldofdrillingnewinfillwells,accountingfortheirimpactonsurroundingwells.

The technologydescribed in thispaperwas suited fordesigning thedevelopmentplanof the field, andwas selectedwiththeobjectiveofmitigatingthenaturaldeclineofoilproductionwithorwithoutinvestment.Withoutinvestment,bymaking the best use of already existing hardware, taking advantage of local heterogeneities and re-shuffling the

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injectionandproductionschemesinordertomaximizetheoilproduction(re-allocationofflows).Withinvestment,byimplementingthebestpossibledevelopmentplan inorder tomaximizetheNetPresentValueof theButteVoluntaryUnit. Specifically, define the best set and locations for new investment including conversions, drilling of new infillproducers(orpossiblyinjectors),andifappropriateincreasingtheinjectionandliquidtreatmentcapacitiesofthefieldbeyond the current limits. The actual end result identified, forecasted, and achieved was a gain in excess of 50%additionaloilproduction(withnewwells)asillustratedonFigure2.

2) WorkflowofaMatureFieldMassiveOptimizationProject

a) TypicalWorkflowofaMatureFieldMassiveOptimizationProject

Optimizingamaturefieldmeansidentifyingthebestsetofinvestmentsthatshouldbecommittedtothefield,andhowtomakethebestpossibleuseofavailableresourcestoexploittheremainingprofitableopportunities.Thefullmassiveoptimizationworkflowforamaturefieldconsistsofthefollowingsteps:

1.Buildtheproductionforecasttool2.Buildanautomatedsearchengine(optimizationtool)linkedwiththeproductionforecast3.Runtheoptimizationtooltoidentifythe“optimizedscenario”ineveryproposeddevelopment“strategy”4.Decidetheretained“strategy”(andoptimizedscenarioaccordingly)5.Conducttheimplementationonthefield

Thestepsandterminologyareexplainedherebelow.

Step1. Assessingopportunities requires in the first placebeing able to forecastwhatwill be theoutcomeof actionstakenonthefield,suchasdrillingnewproducers,convertingsomeproducerstoinjectors,orapplyinglargechangestoindividual injection and production rates of wells. It is actually possible to build a reliable and accurate productionforecasttoolforamaturefield(Ref.1).Thisisthefirstpillarofthetechnologydescribedinthispaper:maturefieldslendthemselvestoaparticulartypeofmodeling,basedoneducatedlearningfromhistoricalproductiondata.Thismakesitpossibletoachievehighreliabilityandadequateaccuracyoftheproductionforecast,evenforlargechangesappliedtothe setof activewells and to thewells’ in andout flows. Step1of theprocess consists indeveloping such so-calledproductionforecasterforthefield.

Step2.Onceanaccurateproductionforecasttoolhasbeencreatedforthefield,thequestionremainsofhowtoidentifythebestdevelopmentplan.Inamaturefield,thereusuallyexistahugenumberofoptionsthatmaybeenvisaged.Forinstance, a large number among the producers can be a priori considered equally good candidates for conversion.Likewise, when the drilling pattern is already rather comprehensive,many potential drilling locations at half-spacingseemequallyreasonableatfirstsight.Furthermore,thehighwelldensitycancreatestrongcross-flowsbetweenwellsvia the reservoir. In addition tophysical interactions, the often-limited fluid processing capacity in effect createsoperationalinteractions:assoonasanewproducerorinjectoriscreated,onehastore-allocateallflowsofotherwellstostaywithintheglobaltreatmentcapacity.Thus,apowerfulproductionforecastisnotsufficient.Oneneeds,andthis

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isthesecondpillarofthetechnology,anautomatedsearchenginethatwillextensivelyexploretheimmensespaceofpossibledevelopmentplans,andfindoutthebesttrade-offbetweenallcompetingconstraints.

Step3.Achievingthe“besttrade-off”requiressettingacleargoal.Itiswise,inordertodevelopadeepunderstandingofavailableopportunitiesandknowinglymake investmentdecisions,to investigatedifferentdevelopmentstrategiesandcomparethebestsolutionforeachone.Typically,onewillwanttoexplorethefollowingstrategies:

• Varythesetofinvestmentallowed:noinvestment,conversionplanonly,drillingandconversionplan…• InvestigatethedifferencesbetweenpursuingmaximumoilproductionandmaximumNetPresentValue.• Tunethetotallevelofinvestment.• Varythefutureoilpriceassumptioninordertochallengehowrobustaplanistoadownturninoilprice.• Pursuethehighestreturnoninvestmentratherthanthehighesttotalvalue.

Each “strategy” is defined on the one hand by a set of technical and financial constraints, on the other hand by anoptimizationtarget(oil,NetPresentValue,returnratio).Thereexistbillionsof“scenarios”thatmaybeenvisaged,andone“optimizedscenario”thatachievesthemaximumtargetcompliantwiththeconstraints.

Step4.Eventually,thesolutiontobeimplementedonthefieldisnotdirectlydictatedbyamachine:theselectionofthestrategyfinallyretainedis inessenceanassetmanagementdecisionthattakesintoaccountthelevelofspendingandriskpermitted,andtheexpectedfinancialresultbothinvolumeandinreturnratio.Beforereachingthisfinaldecision,itmaybenecessaryto investigatevariationstothestrategies initiallyproposed.Theexact“implementationscenario” isdefinedindetailasaresultofstep4.Itneedstobesecuredbysensitivityanalysescarriedoutbyreservoirengineers,using the forecaster tool, in order for this scenario to be resilient to operational uncertainties. Step 4 also entailssecuringthenecessarybudgetandresources,andrealizingthedetaileddesignofworkstobeconductedonthefield.

Step5.Whiletheretained“implementationscenario”isbeingimplementedonthefield,itisnecessarytokeeptheplanalwayscurrentandconsistentwiththeevolvingrealityofthefield.Theactualavailabilityofmeans(existingwellsandnewplannedwells)mustbemonitored.Thebestallocationofavailablemeansmustbere-optimizedregularly(monthlyto quarterly) to take into account technical incidents or favorable contigencies. Importantly, the constraints deemedapplicableatthetimeofinitialoptimizationmustbereviewed,andtheimplementationscenariomustbere-optimizedincaseofmaterialchange inconstraints.Therefore, thebestproductionsettingsarealwayspursued,consistentwiththerealsituationonthefield.

Evenifthetwoaforementionedoilfieldsaredifferent(geology,exploitationstrategy…),themethodologyremainsthesameforallmaturefieldsstudied,leadingtooptimizationofproductionleversalreadyusedinthepast.

Foroil also develops techniques to support the development of recovery methods for which no historcal data areavailableyetonthefield,asillustratedbyasecondstudyinSanFranciscooilfield.

b) SanFranciscooilfieldPhaseII:anexampleofapilotforunconventionalrecoverywithoutpriorhistoricaldata

The San Francisco Upper Caballos formation produces from 8 different sand bodies, KCUA-KCUF. These sands differpetrophysicallyandinsaturations.Withover15yearsofwaterinjection,recentILTswereproofthatseveralsandshad

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not experienced good waterflooding, mainly due to their less favorable petrophysical properties. A methodology toidentifyremainingsaturationspersand,aswellasdesigninjectionpatternsthatwouldremedythiswillbepresented.

Thefirstoptimizationproject intheentireKCUformationallowedtodefinetherightbalancebetweenproducersandinjectors and all appropriate injection rateswas identified (2008, ref. 1). A furtherwaterflood improvementwas thesubject of a second optimization project called San Francisco Phase II. This entailed selectively readjusting andamplifyingtheinjectionandproductionperlayer,andfine-tuningthehorizontalandverticalinjection-pattern.

GlobalMethodologyAselective,optimizedinjectionandproductionprogram(inlimiting/stoppinginjection/productionatcertaindepths)hasbeendevelopedby:(i)Usinglogtestsavailableandbycarryingoutafivemonthfieldtest,inordertocollectspecificproductiondatacomingfromselectiveinjectionandproduction,andimprovedoil-cutand/orliquidproduction;(ii)Reducingconstraintsrelatedtosurfaceequipment(waterinjection)inordertofurtherboostoilproduction,throughamassiveoptimizationoftheinjectionpattern.

Deliverablesofthisprojectwere:

• A well-selective intervention pilot which allowed learning about of reservoir behavior from well response toproduction/injectionparameterchangesatindividuallayersoftheUpperCaballos(KCU)formation;

• Recommendationforfurtherlayer-selectiveinjectionandproductionjobs;• Alearningprocessderivedfrompastbehaviorofthewholefieldandfromthepilotresults,leadingtoacustomized

ProductionForecasterTMforfieldwideoptimizations.• Asaresultofamassiveoptimizationprocess,quantifiedandpreciserecommendations(injection/productionrates)

inorder tooptimize the injection schemeover the full field,with available facility capacity/limitations taken intoaccount.

The pilot phase aimed at identifying and stimulating layers having the best oil-increment potential. A in-housemathematicalapproach,basedonunevenperforationsofproducers,wasusedtochooselayerswiththebestoilcutatpresent.

Layer-selectiveproductionpilotplanThepilotwillprovideafirstestimateoflayercontributionandpossibleimprovementintermsofoilproduction.Data are gathered by stimulating specific layers in somewells – producers and injectors – andmonitoring effects inproduction.Inordertooptimizeproductiongainsduringthepilotphase,highest-potential layersarefirst identifiedtoconductthepilot.Thegoalistoidentifyandstimulatetheselayers.The different actions are linked to responses, in order to refine the Production ForecasterTM. Individual actions arechangesinflowrateofindividuallyselectedlayersinproducersandinjectors.Thisisachievedthroughacidstimulationandflowcontrolinselectiveinjectionwells.Responsesareidentifiedaschangeinfluidflow–interactionbetweenwells–andoilvs.waterdistribution(OilCut).

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KeylearningsfromSanFranciscoIIproject

With over 15 years of water injection, recent ILTs were proof that several sands had not experienced good waterflooding, and would benefit from a vertical conformance improvement program. A methodology was developed toestimate,basedonproductiondatawell (re-)perforationhistories, the remainingsaturationsper sand layer.Thiswasvalidatedby a selective stimulationpilot,which in turngeneratednew information for refining themodel andwaterinjection.ThisshowshowFOROILdevelopsnewmethodstoimplementnewEORandSAGDprojectsinoilfieldswithinoneortwoyearsinsteadofcurrentlyfiveortenyears.

3) Technology/Modelization

a) AchievingReliableandAccurateProductionForecast

Arecenttechnologybreakthrough.Thefieldoptimizationworkflowheavilyreliesonareliableandaccurateforecasttool(production forecaster). The technology behind the production forecaster is based on the principles of statisticallearningtheory(Ref.2)andwasdevelopedforhydrocarbonfieldsduringthefirstpartofyears2000’s.ThistechnologyappliestomatureenoughfieldsonlyandhasbeenavailabletotheOil&GasIndustryforthepastsixyears.Theessentialfeaturesoftheproductionforecasteraredevelopedinthepresentsection.

Datadrivenanalysis.Most importantly,theproductionforecaster isbasedona(production)datadrivenanalysis.Thiscontrasts with traditional grid simulators, which first rely on many assumptions or indirect measurements aboutsubsurfaceproperties,andinvolvealargenumberofparametersveryremotelyrelatedtotheproductionofwells.Theideaistoacknowledgethatforamatureenoughfield,historicalproductiondatahaveaccumulatedenoughinformationto account for all relevant phenomena at stake in the field, under a given recovery technique. Obviously, there arelimitations, because the field has to be mature and can be modeled only for actions similar to those alreadyencounteredinthepast.Forinstance,itcouldnotbeusedtopredicttheeffectofdeployingapolymerfloodifthelatterwasnevertriedonthatfieldinthepast,atleastinapilotarea.

Limitthemodelcomplexity.Theproductionforecasterisamaterialimprovementofthemethodsofstatisticallearningtheoryappliedtoagivenhydrocarbonfield.Basicstatistical learningtheoryconsists ingeneralizingthebehaviorsofasystembasedon learning froma limited setofobservation samples.Amajor theoremof this theoryemphasizes theparamountimportanceofmodelingonlythosebehaviorsnecessarytoaccountforthetrainingsampleset.Thismeansthatonemustabsolutelyavoidusingaspaceofsolutionswider thanthestrictminimum.Looselyspeaking,onemustbuild the simplestpossiblemodelembarkingonly themost relevantphenomenaat stake in the field. If the so-calledVapnik-Chervonenkisdimensionofthespaceofsolutionsissubstantiallylargerthanthenumberofindependenttrainingsamples,thereisnocontrolledboundontheexpectationdifferencebetweenmodelandrealityinfutureexperiments.In other words, one must avoid a model too general and too complex with respect to the limited set of availablesamples.Thisisrelatedtothewellknownproblemof“over-fitting”:ifamodelcanbeparameterizedtomatchperfectlyallpastdataforeverywellandeverymonth,chancesaretheparameterizationishighlyambiguousandsowillbetheforecast(Ref.3).Meshedsimulators,whichuseastandardsetofreservoirequations,tobeparameterizedwithrockand

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fluidpropertiesdiscretizedonafinegrid,definitelyareover-complexwithrespecttothestatisticalrichnessembeddedinthehistoricaldataofafield,howevermature.

Purestatisticsisnotenough.Yet,oneshouldnotbelievethatapurelystatisticalapproachmadeonpast-observeddataisenough.Vapnikhimself,thefatherofstatisticallearningtheory,recognizesthefollowing(Ref.4):“Learningtheoryhasonecleargoal:tounderstandthephenomenonofinductionthatexistsinnature.Pursuingthisgoal,statisticallearningtheory has obtained results that have become important for many branches of mathematics and in particular forstatistics.However,furtherstudyofthisphenomenonrequiresanalysisthatgoesbeyondpuremathematicalmodels.Asdoes any branch of natural science, learning theory has two sides: (1) themathematical side that describes laws ofgeneralizationwhicharevalidforallpossibleworlds,and(2)thephysicalsidethatdescribeslawswhicharevalidforourspecificworld,theworldwherewehavetosolveourappliedtasks.”

Petroleumphysicsmustbeembarked.Inordertoapplythetheoryforpracticalpurposes,onemustinvolvethephysicallawsthatgovernthespecificproblemathand.IncontrasttoexistingstatisticalapproachesappliedintheIndustry,theproduction forecaster does exactly this and honors the main laws of petroleum physics, which severely bind thecomplexityof themodel, in contrastwithpure statistical generalizationaswouldbedonewithneuralnetworks. Thesystemicconsistencyoftheforecastisguaranteedbytheveryconstructionofthesolutionspace.Thisalsoexplainswhya good accuracy is achieved not only in forecasting future field operation close to current conditions (typically, abaseline),butisalsodemonstratedforsubstantialchangesagainstbusinessasusual,likelargeinjectionandproductionratevariations,conversionsofproducersintoinjectorsornewinfillwells.

b) SelectedFeaturesoftheButteVoluntaryUnitProductionForecaster

Datasettolearnfrom.Thegeologicalcontextsupportsthegeneralunderstandingofthefieldbutisnotconsideredpartofthetrainingdatasetassuch.Thecoredatausedforbuildingtheproductionforecasterconsistsof:

• A fact sheet, summarizing the field development and production history. This allows identifying the effects ofdeliberatehumandecisionsnotdirectlyrelatedtoreservoirdynamics.

• Oilandrockphysicalproperties(PVT,viscosity,porosity,permeability).• Pastproductiondatabaseforeverywell,permonthandperphase(oil,water,gas,injectedwater,injectedgas,gas

lift…).• Test bookswith production control parameters:monitoring of bottom hole flowing pressure and head pressure,

pumpsettings(cyclesperminute,strokeperminuteandstrokelength).• Logofwellwork-overs(recompletion,pumpupsize,stimulationorcleaningjob,conversion).• Positionsofwells(atperforations,orfulldraindeviationforhorizontalwells)onastructuralmap.• Reservoirpressuremeasurements,inasmuchasavailable.

Useful additional data include the prior understanding of the drainage mechanism, aquifer influence and oil watercontacts, and everything that can be used as a tracer, such as water salinity when there exists a contrast betweenformationwaterandalienwaterfedintotheinjectionsystem.

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Reservoirpressure.Reservoirpressuremeasurementsareoftenscarce,althoughitisacriticaldynamicalvariableofthefield.FortheButteVoluntaryUnit,theavailablereservoirpressuremeasurementsconsistedofabout80staticgradientorbuild-uptestsspanningfrom1970to2008.Availabletestsprovidedusefulcontrolpointsontherangeofreservoirpressure experienced locally. The production forecaster provided effective pressuremaps of the field, showing high-pressureregionsintheeasternandwesternpartofthefield.

Well-well cross-flows. Observed in the historical production data, inter-well cross-flow was properly modeled in theButteVoluntaryUnitproductionforecaster.Achangeinwellflowcanpropagatethroughoutthefield,for instanceviathe reservoir pressure, and in fact account for effective well-well influence that are not limited to the nearestneighbours. Producers farther away are of course less sensitive to such local change of injection. However, theirresponseisnotnilbecausetheentireButteVoluntaryUnitisconnectedviathecirculationofmultiphasefluids.

Fromanoperationalviewpoint,whileitisnaturaltoincreaseinjectioninordertosupportnearbyproduction,itismuchlessintuitivetoreduceaproducer’soutflowforthesamepurpose.However,thisalternativewayofsupportingthefieldpressure is a lever used by the optimization toolwhen seeking an optimum compatiblewith the total field injectionconstraint,orcompatiblewiththelocationsofexistinginjectorswhenconversionsarenotallowedortoocostly.Note,however,thattheresponsetimesdifferbetweenbothcases.Indeed,theproductionforecastermayinvolveseveraltimescalesinconjunction,ifitprovesnecessarytoaccountfortheproductiondata.ThisisthecasefortheButteVoluntaryUnitproductionforecaster,andthetime-dependentresponseofneighbors isquitedifferentwhenvaryingan injectorthanwhenvaryingaproducer.

Water cut dependency on liquid rate. Another important behavior that was observed in the production data, andrendered in the production forecastmodel, is the existence of a strong relationship between thewater cut and theliquidrateformanyproducers.Forseveralwells, it isobservedontheproductiondatathatthewatercuthasbeeninthepastsubjecttosuddenincreaseresultingfromarelatedincreaseoftheliquidproduction.Furthermore,thiseffectisreversibletosomeextent,sothatthewatercutresumesalowervalueshortlyafterreducingtheliquidproductionrate.

Two-stagewaterbreakthrough.Carefulanalysisoftheproductiondatarevealedtheexistence,forasetofwellslocatedin thecenter-westpartof the field,ofa two-stageevolutionof thewatercutover thewell lifecycle.Theproductionforecasterembarksthisbehavior,whichiswellestablishedbytheproductiondatainalimitedandidentifiedpartofthefield.

c) IdentifyingtheBestDevelopmentPlan

Distortedreservoirconfiguration.Oilandgasmaturefieldshavedevelopedduringthecourseoftheirproductionhistory(typically more than ten years) a high degree of complexity. When first starting production, reservoir pressure isuniform, but heterogeneities exist in the petrophysical properties of the reservoir. Aftermany producers have beendrilled and operated for a long time, distorsions have developed since thewells have locally depleted the field anddecreased saturation in a non-uniform fashion. Injectors also heavily impact both reservoir pressure and saturation.Quiteoften, the impactofhumandecisionshavealsostronglydistortedthereservoirconfiguration:partsof the fieldmighthavebeendevelopedbydifferentoperatorsunderdifferentconcepts,a temporarydownturn inoilpricemight

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havecancelledinvestmentopportunitiesthatwereneverconsideredagainafterwards,lagginginjectioncapacitymighthaveledtoconcentratingvoidagereplacementonlyinselectedareasofthefield,etc.Asbothsaturationandpressurehavegrownheterogeneous,theprecisewayofproducingthefield,thatis,theexacttuningofeveryindividualinjectionorproductionrateperwell,mattersalotmore(Reference1).Capabilitytoimproveproductionbyrevisitingproductionandinjectionratescanincreasethereservestypicallyby+10%to+20%.

Huge combinatorial complexity. In a mature field, while on the one hand, outstanding opportunities for drilling(respectivelyconversion)arenotobvious topinpoint, thereareontheotherhandmanyequally reasonable locations(respectively wells) to consider as valid candidates for infill drilling (respectively conversion). This leads to a hugecombinatorialcomplexityofpotentialdevelopmentplans.Considerforinstanceacombineddrillingandconversionplaninvolving 8 newwells among 20 sweet spots locations and 7 conversions among 69 candidates: this represents 136hundredthousandbillionpossibleplans.Andthiscoversonlythemaininvestmentdecisions:thereremainstofinetuneeveryindividualwellflow.Evenwithverygoodinsight,ordinaryreservoirengineeringmethodscannotpossiblyassessasizeablefractionofthatandfindtheirwaytothebestplan.

Fastforecast.Itisausefulconsequencethattheproductionforecasterdescribedintheprevioussection,whichwasfirstdesigned to achieve best possible production forecasting accuracy, is actually very quick to compute, owing to thecomparativesimplicity imposedonthemodel.Moderatecomplexitymakes itpossibletorunaforecast inamatterofsecondsonup-to-date farmsof computers.Themethodalso relieson recentprogressachieved incomputingpower,and it would not have been practicable in the early 2000’s. State-of-the-art calculation software is used, includingprocessing routines for large databases, farmed multicore microprocessors and parallel computing. It really is thecombination of a reliable production forecast tool based on recent mathematics, the comparative simplicity of theresulting model, and the advent of ever more powerful computers, which made the whole technology nowadaysrealizable.

Optimizationknow-how.Inspiteofsuchcomputingspeed,itremainsimpossibletocomprehensivelyrunallimaginablescenarios in the numbers exemplified above. Nor is it smart to pick and test thousands of them randomly like in aMonte-Carloapproach,asthereislittlechancethiswouldcaptureaverygoodscenario.Specificoptimizationtechniquesneed tobedeveloped, inorder toproperly explore the vast amountof possibilities in an informedmanner, so as toachieve comprehensiveness and relevance in the choice of scenarios to be played. A hybrid threefold optimizationtechniquewasdevelopedinordertoselectandplayhundredsofthousandsofproductionscenarioscombiningheuristic,deterministic,andnon-deterministicapproaches.

Inorderto limitthenumberofproductionscenariostorun,reservoirengineeringreasoning isusedtosetsomerulesand discard “unefficient” scenarios without running them. This is the heuristic component: optimizing an oilfield isdifferentfromoptimizingsomeabstractprobleminabsolute,andallowseducatedsimplificationsapriori.

Deterministicmethodsarealsoused to rapidly converge towardsa localoptimum.Suchmethodsareclassicallyusedwhen thereexists a singleoptimum in a locally convex landscape,which canbe found througha continuouspathofconsecutive scenarios. At each step, the next scenario is a small variation from the previous one, and there aresystematicwaysofexploringaroundbynottestingallclosescenariosinordertoconvergetowardsthebest.

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However, one should not remain trapped around a local optimum and must be able to consider radically diffentsolutionsthatcannotbeidentifiedbyastep-by-stepcontinuoussearch.Non-Deterministicoptimizationtechniquesarerequiredwhenbinarydecisionsmustbeevaluated(suchasdrillinganewlocationorconvertingawell).

d) TheFieldOptimizationTool

Massive Optimization in practice. The massive optimization exercise is to some extent reverse to the forecastingexercise.Whenbuildingtheproductionforecaster,inputsaregivenandtheforecastermustbedesignedandcalibratedsoastodelivercomputedoutputs.“Inputs”meansallproductioncontrolparametersdefininghowwellsareoperatedovertime,whichcommonlyconsistof:

• Actualavailabilityofeverywell(productionorinjectionhours).• Actualdatesandlocationsofconversionsperformed,newwellsdrilled,andotherwork-overs.• Productionparametersapplied,forinstancebottomholeflowingpressuresandinjectionrates.

Outputsarethecomputedproductionratesofeachphase(oil,water,andgaswhenrelevant),monthly,foreverywell.Once theproduction forecasterhasbeenmadeavailable, thegamebecomes to findout thebest setof inputs tobeenforcedinthefutureinordertogenerateoutputsofmaximumpossiblevalue.Theglobalvalueofoutputsisevaluatedbya“gain”functionsuchascumulatedoilproductionorfinancialNetPresentValue.

Constraints. Both technical and intentional constraints are imposed on inputs and outputs. Wells are subject toindividualtechnicalconstraints:

• (Producers)Minimumbottomholeflowingpressure,for instancerelatedtothebubblepointandtotheminimumacceptablesubmergenceofpumps.

• (Producers)Maximumliquidproductionrate,relatedtothemaximumpumpthroughput,andsometimestothewelldesignandcompletion.

• (Injectors)Maximuminjectionpressure,relatedtothenetworkdesignatthesurfaceend,andrelatedtotherockfracturingthresholdatthebottomend.

• (Injectors)Maximuminjectionrate,forinstancerelatedtothechokesandtubingdiameter.

Onemustalsobecautioustousetheproductionforecasterwithinitsvaliditydomain,thatis,nottoofarawayfromtheconditions seenduring the learningperiod in the trainingdata set (yet these canbe far fromcurrentoperation). Forinstance,injectionratesofexistinginjectorsareintentionallylimitedto130%oftheirhistoricalmaximum,inthespecificcaseoftheButteVoluntaryUnit,andaceilingisalsosetontheratesofnewinjectors,consistentwithotherinjectionratesinthearea.

Perhapsmoreimportantthanindividualwellconstraintsaretheglobalfieldconstraints,becausethosedrivetheneedforanoptimumallocationoflimitedsharedresourcesamongwells:

• (Field)Maximumfluidprocessingcapacity.• (Field)Maximuminjectioncapacity.

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Schedulingconstraintswereenforcedinordertoproduceonlyrealizablescenarios:

• Thestartingdateofinvestmentallowedforapriorpreparationperiod.• Thenumberofdrillingwaslimitedpermonth(rigavailability),andperyear(durationofthefrostperiod).

Finally,intentionalconstraintsserveatdefiningdifferentdevelopmentstrategies:

• “Noinvestment”strategy:onlyre-allocationofinandoutflows,noconversionordrillingisallowed.• “Nonewwell”strategy:re-allocationandconversionsareallowed,butnotinfilldrilling.• “Fullinvestment”strategy:re-allocation,conversions,andinfilldrillingareallowed.• “Xnewwellsstrategy”:re-allocation,conversions,anddrillinguptoXnewwellsareallowed.

“Gain”functionandfinancialparameters.Asageneralrule,optimizationsoughttomaximizetheNetPresentValue,inorder to account for all operational and capital costs of the optimized scenario, and assess the financial value ofproposed development opportunites.However, computing theNet Present Value involves additional assumptions, inparticular about future oil price: for strategies involving no ormoderate investment (“no investment” and “no newwell”) itmade sense to run theoptimization also formaximizingoil production regardless of the (limited) costs, andindependentlyfromtheexpectedsalepriceofoil.

TheNetPresentValuefunctionincludedafaithfulrepresentationofallcostsincurred.Operatingcostshadafixedpartrelatedtothenumberofactivewellsandavariablepartproportionaltoproduction.Capitalexpenditureswerespecifiedfor drilling, conversions, and enhancing the field injection capacity (thus releasing the current constraint). Royaltiesapplicabletoeachwell(dependingondrillingdate,location,andcumulatedvolumeproduced)wereexactlyencoded.Asis customary in the industry, a financial discount rate was used to account for the time value of cash flows. It isextremely important, in order to reach trustworthy conclusions, that the Net Present Value reflects the economicalrealityofthefield.Ofcourse,futureoilpriceisalsoakeyassumption:sensitivityofoptimizedscenariostovariationoftheoilpricewasalwaysassessed.

Candidateopportunities. Asoutlinedabove,manypotential opportuniteswere available. In amature field, onemustavoidfilteringoutoptionsapriori,becauseinvestmentopportunitiesareneitheroutstandingnorobviouslyinvalid.Thisis the very reasonwhy a fine forecastmodel and apowerful optimizer areneeded. For theButteVoluntaryUnit, allproducers(69,includingsuspendedones)wereconsideredforconversion,andacomprehensivesetofsweetspots(20)wasconsideredfordrilling.

Fullinvestmentoptimizedscenario.GiventhecomputationalspeedoftheButteVoluntaryUnitmodelatthetimeofthestudy, most optimization runs spanned 20,000 to 30,000 iterations. Since each iteration manages 20 scenarios inparallel, thisrepresented400,000to600,000differentsscenariosconfigured,run,andevaluatedundereachstrategy.Thiswassufficienttoconvergetotheoptimizedscenario,thankstotheadvancedoptimizationalgorithmsused.

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The “full investment” optimized scenario entailed drilling eight new infill wells, converting five active producers toinjectors, and re-opening two suspended producers as new injectors. As explained in the next section, a balanceddecisionwasmadeinfavorofahigherreturnratioforamorelimitedinvestment,andtoimplementafirstbatchoffournewinfillwellsandfourconversions,focusingonthemostprofitableopportunitiesinpriority.

4) Implementationinthefieldsandresults

a) MassiveoptimizationoftheSanFranciscofield

AspecificOptimizationEngine™hasbeencalibratedusingheuristic,deterministicandnon-deterministicmechanisms,asexplainedabove.The“costfunction”:tomaximizethecumulativeoilproductionofthefullKCUreservoiroverthenextfiveyears,startingfromOctober2008.

Technical constraints for wells were defined according to their historical values, in such a way that the ProductionForecasterTMonlycalculateswithinaspacewhichhasbeenlearntfrominthepast:injectionratescanvaryfromzerototheir maximum historical value (+ 20%), and bottom-hole flowing pressures (BHFP) of producers are kept aboveminimumobservedvalues.

For any setof technical and financial constraints, theOptimizationEngine™has computedhundredsof thousandsofdifferent production scenarios (hence the “Massive Optimization” name). This striking and exceptional amount isactuallypossible,astheProductionForecasterTMshowsquiteahighcomputationalspeed:ittakeslessthanonesecondto calculate a production scenario over five years, for a given set of production parameters. Apart from smartprogramming, such speed is essentially due to the limited number of parameters (related to a small enough VCdimension)thatisnecessaryforbuildingthemodeloftheProductionForecasterTM.

Identificationofthebestproductionscenario

Theconstraintsdefinedforthescenariostocomplywithwere:

• Technicalconstraintsforproducersandinjectorssameasinthebaseline.• Conversionofproducersallowed.• Newinfillwellsnotconsidered.

Aftercalculating400,000scenarios,theoptimizationprocessconvergedtoabestscenarioshowinga1.2mmboabovethe baseline, that is +12% of the remaining reserves. This scenariowould require the conversion of seven identifiedproducers, at thebeginningof the implementationperiod. Injection andproduction rates aredefined for everywell,overfiveyears.

It appears that theOptimizationEngine™recommends to fully rebalance the injectionandproduction ratesperwell.Thenorthernpartofthefieldhasexperiencedaglobalreductioninfluids,inordertofavorbetterareasinthesouthernpart.

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Implementationandresults

Theoptimized scenariohasbeenquickly andeffectively implementedover the courseof 3months.Of course, therewere some instanceswhereproductionparameters couldnotbeexactly implemented in the field, inparticularwhatconcernsinjectionrates.Regularre-optimizationscenarioshavebeencalculatedoverpassingmonths,inordertotakeinto account such limitations and opportunities to injectmore (or less) than the original constraints. This is possiblebecausetheOptimizationEngine™isquicktorun.

Actual production results in the field very closelymatch the forecast for the optimum scenario: expected additionalproduction has been achieved indeed. This is pictured (Fig. 1) as green bars against the baseline in blue and theoptimizedscenarioingreendots.

b) MassiveOptimizationoftheButteVoluntaryUnit

Thetechnologypresented in thispaper is strongly result-oriented. It is intendedtoyieldpragmatic recommendationsquicklyapplicableonthefield.Wereviewinthepresentsectiontheactualstagesandprogressundergonethroughouttheproject.Themainphasesandmilestonesoftheprojectaresummarizedbelow.

InitialStudy

The initial studywas completedwithin four (calendar)months, from June to September2009, anddelivered the keyexpected conclusions. A blind test allowed improving and validating the production forecaster, the baseline oilproductionwasdetermined,andallpotentialopportunitieswereidentified.

• Amongst69candidatewellsforconversion,fiveprofitableconversionswereidentified.• Amongst20candidatesweetspotsforinfilldrilling,eightdrillinglocationswereidentifiedandranked.• Fourconversionsandtwodrilling locationswouldsurvivethe lowestoilpriceassumption,whileaninthprofitable

drillinglocationwasidentifiedunderthehighestoilpriceassumption.• Drilling newwells triggered the need for additional supporting injectors (in general, two more conversions with

respecttoaplaninvolvingonlyconversions).

ScenarioSelection

Basedontheaboveconclusions,thereremainedtoselectexactlywhichscenariotoimplementontheButteVoluntaryUnit,dependingontheallowedlevelofinvestmentandexpectedreturnratio.AdetailedcomparisonofmoreandmorecomprehensivedrillingplanswascompletedintermsoftotalNetPresentValuegainontheonehand,andreturnratioontheotherhand.Theseadditional investigationsandoptimizationrunswerecompletedfromOctober2009toApril2010.

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During that period, intensive use wasmade of the production forecaster in order to evaluate the pros and cons ofvariousideasorvariantstotheproposeddevelopmentstrategies.

Thescenarioselectionperiodwasalsousedtosecuretheresourcesandlegalauthorizationforimplementation,andtoinvestigate more detailed questions that had not been embarked in the production forecaster. For instance, theconditionsofcasingswerenotavailable foreverywellat thetimeof the initialstudy: theycouldnowbereviewed indetailfortherestrictedsetofproposedconversions,togetherwithcostsandrequirementsfortying-inthenewinjectorstothesurfacenetwork.

Likewise,aprecisedesignprojectwaspreparedfortheproposednewinfillwells.

Eventually,areasonablyambitiousdevelopmentplanwasdecided,namely:

• Drillfournewinfillwells,outoftheeightproposedinthefullinvestmentoptimizedscenario.• Performfourconversions,outofthesevenproposedinthefullinvestmentoptimizedscenario.• Carryouttheinjectionfacilityupgrade,asproposedinthefullinvestmentoptimizedscenario.

Implementation

Moving on to field implementationwas importantly delayed by the harsh reality of terrain. Indeed, although a clearcourseofactionwasdecidedsinceApril2010,exceptionaladverseweatherconditions impededactualdeploymentofnewinvestmentandproductionsettingsonthefielduntilsummer2011.Duringthattime,notonlywasitimpossibletocarryoutsignificantfieldworks,evennormalmaintenanceofexistingwellswasjeopardizedbythepooraccessibilitytothe field. The spring and summer of 2010were extremely rainy and the ground resulted constantly flooded,makingaccess to the fieldeither impossibleor forbidden inorder toavoidexcessivewearoutof roadsand tracks.Then, thewinter of 2011 was unusually mild, so the ground rarely frozen, a mandatory condition for rigs to operate. Thus,althoughsomewellscouldbedrilledandsomenewinjectorscouldbeequipped,noneofthemcouldbetied-intothefacilitiesuntil later thatyear.Onecan seeon the fieldproductioncurve (Figure1) that theButteVoluntaryUnitwasproducinglessthanitsbaselineduringthatperiod.

Eventually,fromJune2011onwards,thegrounddriedoutandnormaloperationscouldberestored.Newinjectorsandnewproducersbecame livebetween JuneandAugust 2011, andnewproduction settings – essentially the individualinjectionsrates–couldbeenforced.Still, therevisedbaselineshowsa littlekinkreflectingagroupofwellsthatwerestilldownduringtheautumnof2011,awaitingrepairinJanuary2012.

Quicklyaftertheactualdeploymentofnewproducersandinjectors,theoilproductionsoaredtoalmost800bbl/d,backtolevelsunseenfortheprevioussixyears.Figure2shows(reddots)thelatestproductionforecastoftheimplementedoptimizedscenariofortheyearstocome.Thedemonstratedadditionalproductionis+63%abovethebaseline.

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ConclusionThis paper presents a technology developed and industrialized in the recent years for increasing the production andreservesofmature fieldsand reducing the riskof current techniquesused in the field.This technology is intrinsicallysecureandallowstocompletelycontroltherisksofcurrenttechniquesonthefield.Indeed,thetechnology,basedondata(facts),isnotdependentofhumaninterpretationandappliessamerecoverytechnologyasalreadyappliedonthefield(acidjobs,waterorgasinjection,gaslift,sidetrackedorhorizontalwells…).Progressivescenariosareintroducedineach fielddependingon investmenthypotheses.Thetechnologyadjustscurrent technology,patterns (water injectionreallocation/newconversionstoinjection)andallowstoknowwheretodrillnewwells.

Said technology relies on twomain breakthroughs. Firstly, the ability to create, for eachmature field, a reliable andaccurateproductionforecasttool.Secondly,usingthisforecasttoolcombinedwithpowerfuloptimizationtechniques,toidentify the most valuable future development scenario to implement on the field, among a huge number ofpossibilities.

Thistechnologyisnowfullyvalidatedandprovenonseveralfields.ItisillustratedinthepresentpaperbytwosuccessfulapplicationstoconventionalwaterfloodedmatureoilfieldsinColombiaandinWesternCanadaandasuccessfulone-year pilot of vertical conformance optimization in San Francisco oil field. Future development is to extend thistechnologytoEORandSAGDinmatureoilfieldstoreducethetimeoftheimplementationtooneortwoyears,insteadcurrentlyfiveortenyears.

References:

1. AndrésFelipeSuárez,DavidSoto,&HubertBorja,SPE,HocolS.A.;RemiDaudin,FOROIL“MassiveOptimizationTechniqueImprovesProductionofMatureFields:SanFrancisco,Colombia”.SPE-138979-PP.

2. VladimirN.Vapnik,“TheNatureofStatisticalLearningTheory”,SecondEdition,Springer,1999.

3. Z.Tavassoli,JonathanN.Carter,PeterR.King,“ErrorsinHistoryMatching”,SPEJournal,Vol.9,No.3,September2004(pp.352-361).

4. VladimirN.Vapnik,“StatisticalLearningTheory”,Wiley,1998(p.721).

ThispaperincludessomepartsofthefollowingSPEpapers:

1. AndrésFelipeSuárez,DavidSoto,&HubertBorja,SPE,HocolS.A.;RemiDaudin,FOROIL“MassiveOptimizationTechniqueImprovesProductionofMatureFields:SanFrancisco,Colombia”.SPE-138979-PP.

2. DavidSoto,AndresFelipeSuarez,PE/HocolS.A.;RemiDaudin,StéphanePairault,FabriceSorriaux/FOROIL“Sand-SelectiveOptimizationMethodologyreducesWaterCutandImprovesProductioninMatureFields:SanFrancisco,Colombia”.SPEWVS017

3. S.Pairault,R.Daudin,FOROIL“SmartLearningfromPastDataYields50%IncrementalOilProduction”SPE164919-MS