Forthethree-dimensionalcompressiblemulticomponentdisplacementproblemweputforwardthemodifiedmethodofcharacteristicswithfiniteelementoperator-splittingproceduresandmakeuseofoperator-splitting,characteristicmethod,calculusofvariations,energymethod,negativenormestimate,twokindsoftestfunctionsandthetheoryofpriorestimatesandtechniques.OptimalorderestimatesinL^2normarederivedfortheerrorintheapproximatesolution.Thesemethodshavebeensuccessfullyusedinoil-gasresourcesestimation,enhancedoilrecoverysimulationandseawaterintrusionnumericalsimulation.