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1、StochasticAnalysisofaThree-PhaseFluidizedBed:FractalApproachThree-phasefluidizedbedshaveplayedimportantrolesinvariousareasofchemicalandbiochemicalprocessing.Thecharacteristicsofsuchbedsarehighlystochasticduetotheinfluenceofavarietyofphenomena,includingthejettingandbubblingofthefluidizingme
2、diumL.T.Fanandthemotionofthefluidizedparticles.Anovelapproach,basedontheDepartmentofChemicalEngineeringconceptoffractals,hasbeenadoptedtoanalyzethesecomplicatedandstochasticcharacteristics.Specifically,pressurefluctuationsinaD.Neogigas-liquid-solidfluidizedbedunderdifferentbatchoperatingco
3、nditionsM.YashimahavebeenanalyzedintermsofHurst’srescaledrange(R/S)analysis,R.Nassarthusyieldingtheestimatesfortheso-calledHurstexponent,H.ThetimeDepartmentofStatisticsseriesofthepressurefluctuationshasalocalfractaldimensionofd,=KansasStateUniversityManhattan,KS665062-H.AnHvalueofsignifies
4、thatthetimeseriesfollowsBrownianmotion;otherwise,itfollowsfractionalBrownianmotion(FBM),whichhasbeenfoundtobethecaseforthethree-phasefluidizedbedinvestigated.Introductionphenomena,includingthejettingandbubblingofthefluidizingGas-liquid-solidfluidizedbedshaveemergedinrecentyearsmediumandthe
5、motionofthefluidizedparticles;pressureasoneofthemostpromisingdevicesforthree-phaseoperations.fluctuationsaredirectconsequencesofthesephenomena.Itwas,Suchdevices,illustratedinFigure1,areofconsiderabletherefore,naturalthatstatisticalmethodswereemployedexten-industrialimportanceasevidencedbyt
6、heirwideuseforsivelytoinvestigatethepressurefluctuationsinfluidizedbeds.chemical,petrochemicalandbiochemicalprocessing(see,e.g.,TheearliestattemptsweretodefineindicesforthequalityofFanandNewcomer,1981).Asthree-phasereactors,theyhavefluidizationthroughstatisticalanalysisofthepressurefluctua
7、-beenemployedinhydrogenationandhydrodesulfurizationoftions(ShusterandKisliak,1952;Bailieetal.,1961;Sutherland,residualoilforcoalliquefaction,inturbulentcontactingabsorp-1964;Winter,1968;Moritomietal.,1980).Whiteheadetal.tionforfluegasdesulfurization,andinthebi