并行算法在射孔產(chǎn)能研究應(yīng)用

并行算法在射孔產(chǎn)能研究應(yīng)用并行算法在射孔產(chǎn)能研究中的應(yīng)用.天然氣工業(yè),1999;19(6):63～65摘要文章根據(jù)射孔完井的滲流特點(diǎn),利用有限元方法建立了三維單相穩(wěn)定滲流的數(shù)值模型（詳見(jiàn)）,數(shù)值模擬考慮了孔深、孔徑、孔密、孔的相位、污染程度和厚度、壓實(shí)程度和厚度等射孔參數(shù)對(duì)油氣井產(chǎn)能的影響。有限元方程的求解是在曙光1000大型并行機(jī)上利用區(qū)域分解法進(jìn)行的,針對(duì)計(jì)算模型進(jìn)行了并行算法加速比的研究,給出了不同計(jì)算結(jié)點(diǎn)的并行加速比,結(jié)果表明并行算法的計(jì)算速度與串行算法的計(jì)算速度明顯提高;通過(guò)各種射孔方案的計(jì)算,給出了各種射孔參數(shù)對(duì)油氣井產(chǎn)能影響的曲線(xiàn),這些成果對(duì)于油氣田設(shè)計(jì)射孔方案具有一定的指導(dǎo)意義。主題詞射孔射孔參數(shù)并行計(jì)算機(jī)有限元法產(chǎn)能預(yù)測(cè)目前,油氣田上射孔完井是較為廣泛的一種完井方式,射孔參數(shù)(孔深、孔徑、孔密、孔的相位、污染程度和厚度、壓實(shí)程度和厚度等)對(duì)油氣井產(chǎn)能的影響是一個(gè)重要的研究課題。利用數(shù)值方法來(lái)研究射孔產(chǎn)能的機(jī)理起于60年代〔1〕,較全面地考慮各種射孔參數(shù)對(duì)油氣井產(chǎn)能的影響始于80年代〔2〕。由于射孔完井采油氣時(shí)形成的滲流場(chǎng)非常復(fù)雜,這就要求人們把滲流區(qū)域剖分得很細(xì),才能滿(mǎn)足計(jì)算精度。由于受計(jì)算機(jī)內(nèi)存和計(jì)算速度的限制,人們?cè)诮⒂?jì)算模型時(shí),總是要作一些假設(shè)或簡(jiǎn)化。這次我們?cè)谑锕?000上,利用目前普遍使用的區(qū)域分解法〔3〕來(lái)求解有限元方程組,取得了比較好的結(jié)果。通過(guò)各種方案的計(jì)算,給出了各種射孔參數(shù)對(duì)油氣井產(chǎn)能影響的曲線(xiàn),這些成果對(duì)于設(shè)計(jì)射孔方案具有一定的指導(dǎo)意義。計(jì)算模型1.數(shù)學(xué)模型按照射孔完井滲流場(chǎng)的特點(diǎn),數(shù)學(xué)模型采用三維單相穩(wěn)定滲流方程:式中:p為地層壓力,MPa;K為地層滲透率,;μ為地層原油氣粘度mPa;Γ1為已知壓力邊界;Γ2為已知流量邊界(當(dāng)q等于0時(shí),為不滲透邊界);n為Γ2的法線(xiàn)方向;Ω為滲流區(qū)域。2.有限元方程的建立在三維問(wèn)題中最基本的單元是四面體單元,記為(e),它的四個(gè)頂點(diǎn)為有限元剖分的結(jié)點(diǎn),其編號(hào)設(shè)為i、j、k、m,根據(jù)里茨變分原理可得第i個(gè)結(jié)點(diǎn)的有限元方程:同理可寫(xiě)出其他結(jié)點(diǎn)的有限元方程,就形成了有限元方程組。3.滲流區(qū)域的剖分把三維滲流區(qū)域直接剖分成四面體單元,不僅難以繪出醒目的圖示,而且會(huì)使輸入的信息數(shù)量太大,因此在實(shí)際上都采用組合單元,最常用的是六面體單元,每個(gè)六面體組合單元又可剖分成五個(gè)四面體單元(有兩種不同的剖分形式)〔4〕。只要輸入組合單元的信息,可由計(jì)算機(jī)自動(dòng)剖分成基本四面體單元進(jìn)行計(jì)算(可按兩種剖分形式計(jì)算系數(shù)矩陣取每個(gè)系數(shù)的平均值)。六面體組合單元的剖分也是有計(jì)算機(jī)自動(dòng)完成的,剖分的原則是:①在平面上以井為中心,徑向剖分,夾角為10°。再以井為中心,做不同半徑的同心圓剖分,在射孔的頂端比較密,向外向內(nèi)變得比較疏(圖1-a),共有30層;②在垂向上,以ΔZ為步長(zhǎng)進(jìn)行剖分(圖1-b);③根據(jù)射孔的設(shè)計(jì),在每個(gè)射孔處以孔為中心,用四個(gè)不同半徑的同心圓進(jìn)行加密剖分(圖1-b)。這樣就把整個(gè)滲流區(qū)域剖分成不同大小的六面體組合單元。(a)平面上的剖分圖（b）射孔加密剖分圖圖1平面上的剖分和射孔加密剖分示意圖有限元方程組的并行求解方法有限元方程組的求解是在曙光1000并行機(jī)上進(jìn)行的。根據(jù)滲流區(qū)域剖分的特點(diǎn),每一層同心圓上的剖分結(jié)點(diǎn)是相同的,比較適合區(qū)域分解法的并行算法。具體步驟如下。有限元方程組形成一個(gè)N×N的大型稀疏系數(shù)矩陣如下:由于系數(shù)矩陣很大，本文模型的剖分結(jié)點(diǎn)為36×30×20=21600,再加上射孔處的加密結(jié)點(diǎn),若按16個(gè)射孔計(jì)算加密結(jié)點(diǎn)數(shù)為16×32×30=15360,則系數(shù)矩陣是一個(gè)36960×36960的矩陣。為了減少計(jì)算機(jī)內(nèi)存和計(jì)算結(jié)點(diǎn)之間的信息傳遞,在實(shí)際形成系數(shù)矩陣時(shí),本文僅儲(chǔ)存非零元素,用兩個(gè)指示數(shù)組來(lái)確定元素的具體位置,用一個(gè)N×1的一維數(shù)組來(lái)儲(chǔ)存與每個(gè)結(jié)點(diǎn)有關(guān)的結(jié)點(diǎn)數(shù);用一個(gè)N×22的二維數(shù)組來(lái)儲(chǔ)存與每個(gè)結(jié)點(diǎn)有關(guān)的具體結(jié)點(diǎn)號(hào),這兩個(gè)數(shù)組可在形成系數(shù)矩陣時(shí)同時(shí)形成。一般剖分成六面體組合單元每個(gè)結(jié)點(diǎn)周?chē)?6個(gè)結(jié)點(diǎn),但通過(guò)四面體建立基本單元后,實(shí)際上只有18個(gè)結(jié)點(diǎn)與其有關(guān),在射孔處有些結(jié)點(diǎn)周?chē)?3個(gè)結(jié)點(diǎn),實(shí)際有關(guān)的結(jié)點(diǎn)也僅有22個(gè)結(jié)點(diǎn),所以,系數(shù)矩陣變成了一個(gè)N×22的矩陣。一維指示數(shù)組二維指示數(shù)組系數(shù)矩陣用超松弛迭代法求解有限元方程組,程序并行化采用部分重疊的區(qū)域分解法,具體做法如下:首先按30層同心圓狀剖分不同層上的結(jié)點(diǎn),平均地加載到不同計(jì)算結(jié)點(diǎn)上。比如加載到4個(gè)計(jì)算結(jié)點(diǎn)上,1～8層加載到0號(hào)計(jì)算結(jié)點(diǎn)上;8～15層加載到1號(hào)計(jì)算結(jié)點(diǎn)上;15～22層加載到2號(hào)計(jì)算結(jié)點(diǎn)上;22～30層加載到3號(hào)計(jì)算結(jié)點(diǎn)上;每迭代一次,就將重疊層上的計(jì)算結(jié)果相互傳遞,取算術(shù)平均值作下一次迭代的初值,計(jì)算中僅需傳遞重疊層和相鄰層,如上面重疊層(8、15、22層)和相鄰層(7、9、14、16、21、23層)。表1是不同計(jì)算結(jié)點(diǎn)數(shù)計(jì)算時(shí)的并行加速比(串行程序計(jì)算時(shí)間與并行程序計(jì)算時(shí)間之比)對(duì)比表,表明隨著計(jì)算結(jié)點(diǎn)的增多,計(jì)算速度明顯加快。表1并行計(jì)算加速比對(duì)比表計(jì)算結(jié)點(diǎn)數(shù)1234568101530計(jì)算時(shí)間(min)計(jì)算加速比78.91.0051.61.5335.92.2029.12.7125.73.0722.43.5219.24.1115.94.9613.35.9311.07.17射孔參數(shù)對(duì)油氣井產(chǎn)能的影響這次研究所選取的數(shù)據(jù):地層滲透率為0.01、油氣井半徑(Rw)為0.1m;根據(jù)前人的研究經(jīng)驗(yàn)影響半徑(有限元計(jì)算的外邊界)取30倍的油氣井半徑,即SRw=30Rw;影響半徑處的地層壓力與射孔內(nèi)的壓力差為4MPa。在以上假定條件下,我們研究了射孔參數(shù)的變化對(duì)油氣井產(chǎn)能的影響。圖中的產(chǎn)率比是計(jì)算的射孔產(chǎn)能與裸眼井穩(wěn)定流產(chǎn)能的理論值之比。圖2是在沒(méi)有污染和壓實(shí)的情況下,射孔密度為每米16個(gè)孔,孔徑為4mm,90°相位時(shí)射孔深度與孔徑的變化對(duì)產(chǎn)能的影響曲線(xiàn),從圖中可看出,射孔深度和孔徑對(duì)產(chǎn)能的影響都比較大。圖3是在沒(méi)有污染和壓實(shí)的情況下,射孔密度為每米16個(gè)孔,孔徑為4mm,90°相位時(shí)射孔相位不同對(duì)油氣井產(chǎn)能的影響曲線(xiàn),圖中表明0°相位產(chǎn)能最低,螺旋式90°相位產(chǎn)能最大。圖2射孔深度和孔徑對(duì)產(chǎn)能影響曲線(xiàn)圖3射孔相位對(duì)產(chǎn)能的影響曲線(xiàn)圖4污染程度對(duì)產(chǎn)能的影響曲線(xiàn)圖5壓實(shí)程度對(duì)產(chǎn)能的影響曲線(xiàn)圖4是不考慮壓實(shí),僅考慮污染的情況下,射孔密度為每米16個(gè)孔,孔徑為4mm,90°相位,污染深度為0.3m時(shí),不同污染程度對(duì)產(chǎn)能的影響曲線(xiàn),圖中Kd代表污染區(qū)滲透率與原地層滲透率的比值。圖中可看出,在射孔深度小于污染深度時(shí),污染程度對(duì)產(chǎn)能的影響較大;而射孔深度大于污染深度時(shí),污染程度對(duì)產(chǎn)能的影響較小。圖5是不考慮污染,僅考慮壓實(shí)的情況下,射孔密度為每米16個(gè)孔,孔徑為4mm,90°相位,壓實(shí)深度為0.004m時(shí),不同壓實(shí)程度對(duì)產(chǎn)能的影響曲線(xiàn),圖中Kc代表壓實(shí)區(qū)滲透率與原地層滲透率的比值。圖中可看出,壓實(shí)程度對(duì)產(chǎn)能的影響較大,這是因?yàn)閴簩?shí)區(qū)包圍了整個(gè)射孔。以上研究表明,利用并行算法求解地下滲流方程計(jì)算速度比串行算法的計(jì)算速度明顯提高,因此,并行算法應(yīng)該在射孔產(chǎn)能研究、油氣藏?cái)?shù)值模擬等研究中被推廣應(yīng)用。本文給出的各種射孔參數(shù)對(duì)射孔產(chǎn)能的影響結(jié)果對(duì)油氣田設(shè)計(jì)射孔方案具有一定的指導(dǎo)意義。ABSTRACT:ThemainreasonsofthewellsloughoccurredinthecourseofdrillingunderthecomplexgeologicalconditionsineastSichuanregionandseveralcommontypesofwellslou-gh(causedbyhigh-angleformation,byeasy-to-hydrateformation,bygroundstressandbyengin-eeringfactorsetc.)areanalyzedinthispaper.Theanti-sloughingmethodsforeastSichuanregion(i.e.usinganti-sloughingdrillingfluid,determiningreasonabledrillingfluiddensityandfindingzonewithsmallerstressetc.)andtheprobleminpreventingandtreatingwellsloughandresearchdirectioninfutureareintroducedalso.SUBJECTHEADINGS:Sichuanbasin,East,Complexstructure,Anti-sloughingdrillingfluid,TechniqueAPPLICATIONOFFULL3-DFRACTURINGDESIGNSOFTWARETOULTRADEEPWELLFRACTURINGDESIGNABSTRACT:Becausethepumppressureandtemperatureatthetimethatultradeepwellfra-cturingoperationismadeareveryhigh,iffracturingengineercannotexactlypredicttheoperatingpumppressureandthetemperatureprofileinfractures,itisdifficulttomakeafracturingdesignsuitedtoultradeepformation,leadingtofailureintheoperationfinally.Inviewofthe.Character-risticsoftheultradeepwellsinTarimDHoilfield,anoptimumfracturingdesignforthethreewaterinjectionwellshasbeenmadethroughaccuratelypredictingtheoperatingpumppressure,understandingthetemperatureprofileinfracturesandmasteringthefractureextendinglawbyuseoffull3-Dfracturingdesignsoftware(TerraFrac)andbycombinationwiththeresultsinreserv-oirsimulation.Thefieldoperationcametoasuccessfulconclusionandobtainedanobviousaugmentedinjectioneffectbyuseoftheboostingpumpfracturingunitandthepremiumandlow-damageneworganicfracturingfluidsystemsuitedtoultradeepformation..SUBJECTHEADINGS:Ultradeepwell,Threedimensional,Fracturingdesign,Pumppressure,Temperature,Fractureextension.APPLICATIONOFPARALLELCOMPUTATIONMETHODINPERFORATIONPRODUCTIVITYRESEARCHABSTRACT:Accordingtotheseepagefeatureofperforationcompletion,a3-Dsinglephaseandstableseepagenumericalmodelhasbeenestablishedbyuseoffiniteelementmethod.Theinfluenceoftheperforationparameters(perforatingdepth,perforationdiameter,shotdensity,perforationphase,degreeofdamageandthicknessoftheintervaldamaged,aswellasdegreeandthicknessofcompactionetc.)onoilandgaswell′sproductivitywasconsideredinnumericalsimulation.ThesolutionoffiniteelementequationwasacquiredbyadoptingparalleldomaindecompositionmethodinDawn1000.Takingaimatthecomputationmethod,astudyofthespeedupratioofparallelcomputationwasmade,givenouttheparallelspeedupratioatdifferentcomputingnodes.Theresultsshowthatthecomputingrateofparallelmethodisobviouslyfasterthanthatofserialone.Throughthecomputationsofvariousperforationplans,thecurvesreflectingtheinfluenceofvariousperforationparametersontheproductivityofoilandgaswellshavebeengivenout,whichisofacertaindirectivefunctionfordesigningtheperforationplansofoilandgasfields.SUBJECTHEADINGS:Perforation,Perforatingparameter,Parallelcomputation,Finiteelementmethod,Productivityforecast.COUPLINGANALYSISOFTHEPRESSUREANDTEMPERATUREINGASWELLBOREHOLEABSTRACT:Thedistributionsofthepressureandtemperatureinawellborearetwoimportantparametersinthemanagement,designanddynamicanalysisofgaswells.Inthispaper,acoup-linganalysismodelforthepressureandtemperatureingaswellboreholeisestablishedthroughovercomingtheshortcomingsofpreviousarticlesinthepressureandtemperaturecalculationandsyntheticallyconsideringtheinterrelationbetweenthepressureandtemperature.Thismodeliscomposedofpressurecalculationmodelandtemperaturecalculationone.Forthepressurecalculationmodel,theeffectofkineticenergychangeisconsidered.Forthetemperaturedistri-butionmodel,itisassumedthattheheattransferinwellboreissteady-stateoneandthatintheadjacentformationsistransientone,andtheeffectoftheheatcausedbyfrictiononthedistribute-ionofthetemperatureinwellboreisconsideredalso.Thewholewellboreisfirstdividedintoseveralintervalsbeforethedistributionsofthepressureandtemperaturearecalculated,andthen,thephysicalpropertyparametersofeachintervalareacquired.Becausetheseparametersarealsothefunctionsofthepressureandtemperature,whereasthepressureandtemperaturearetheunknownnumbersnecessarytobeacquiredinthecalculation,thus,itcanbeseenthatthepressureandtemperaturearecoupledwitheachotheranditisnecessarytouseiterativemethodtosolvethem.Themethodforacquiringtheinitialvalueofthetemperatureiniterativecalculationisgivenoutinthispaper.Finally,themodelisverifiedbyuseofthepracticaldatafrom6wellsinSichuangasfields,whichshowsthatthemodelisofahigheraccuracy;itscalculationmethodissimpleanditiseasytobeoperated,thusitcansatisfytheengineeringneedsintheanalysisandcalculationofthepressureandtemperaturedistributionsinproducingandtestingwells..SUBJECTHEADINGS:Gaswell,Borehole,Pressure,Temperature,Thermalstability,Heattransfer,CouplingMODULARIZEDDESIGNOFTHETECHNOLOGI2CALPROCESSOFGASGATHERINGSTATIONABSTRACT:Atpresent,oilandgasproductionismainlyconcentratedintheregionswithcomplextopographyandveryharshclimate(suchaspolarregion,seas,oceansanddesertetc.),thustherearegreattechnicaldifficultiesintheproduction;theconstructionvolumeistremendo-us;