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1、T.P.2732THEAPPLICATIONOFTHELAPLACETRANSFORMATIONTOFLOWPROBLEMSINRESERVOIRSA.F.VANEVERDINGEN,SHELLOILCO.,HOUSTON,ANDW.HURST,PETROLEUMCONSULTANT,HOUSTON,MEMBERSAIMEABSTRACTdiffusivityequation.Multiple-phasefluidflowhasnotbeenconsidered.Forseveralyearstheauthorshavefeltthe
2、needforasourceApreviouspublicationbyHurst'showsthatwhenthepres•fromwhichreservoirengineerscouldobtainfundamentalsurehistoryofareservoirisknown,thisinformationcanbetheoryanddataontheflowoffluidsthroughpermeablemediausedtocalculatethewaterinflux,anessentialtermintheintheu
3、nsteadystate.Thedataontheunsteadystateflowarematerialbalanceequation.Anexampleisofferedinthelit•composedofsolutionsoftheequationeraturebyOld'inthestudyoftheJonesSand,SchulerField,O'P+~oP=oPArkansas.Thepresentpapercontainsextensivetabulatedor'rOratdata(fromwhichworkcurve
4、scanbeconstructed),whichdataTwosetsofsolutionsofthisequationaredeveloped,namely,arederivedbyamorerigoroustreatmentofthesubjectmat•for"theconstantterminalpressureca;;e"and"theconstantterthanavailableinanearlierpublication.'TheapplicatIonofterminalratecase."Intheconstantt
5、erminalpressurecasethethisinformationwillenablethoseconcernedwiththeanalysispressureattheterminalboundaryisloweredbyunityatzeroofthebehaviorofareservoirtoobtainquantitativelycorrecttime,keptconstantthereafter,andthecumulativeamountofexpressionsfortheamountofwaterthathas
6、flowedintothefluidflowingacrosstheboundaryiscomputed,asafunctionreservoirs,therebysatisfyingallthetermsthatappearintheofthetime.Intheconstantterminalratecaseaunitratematerialbalanceequation.Thisworkislikewiseapplicabletoofproductionismadetoflowacrosstheterminalboundaryt
7、heflowoffluidtoawellwhenevertheflowconditionsare(fromtimezeroonward)andtheensuingpressuredropissuchthatthediffusivityequationisobeyed.computedasafunctionofthetime.ConsiderableefforthasDIFFUSITYEQUATIONbeenmadetocompilecompletetablesfromwhichcurvescanThemostcommonlyencou
8、nteredflowsystemisradialflowbeconstructedfortheconstantterminalpressureandconstanttowardthewellboreorfield.The
