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1、[4]ReactModelsfaSeriesofContinuousStirredTankReactswithaGasLiquidSolidLeachingSystem:PartI.SurfaceReactionControlV.G.PAPANGELAKISG.P.DEMOPOULOSInthisthreepartseriesofarticlescomprehensivethreephasesteadystatehydrometallu
2、rgicalreactmodelsofthecontinuousstirredtankreact(CSTR)typearedevelopedappliedtoacommercial(pressureoxidation)process.Thekeyfeaturesofthedevelopedmodelsarethecouplingofbothmassheatbalanceequationsthedeionofthenonisotherma
3、lperfmance(autothermal)ofamultistagecontinuousreactthetreatmentofmultimineralfeedmaterials.Themodelconsidersonlytheoxidationreactionsbecausetheymainlyaffectthethermalbalanceofthereact.Thestoichiometriesintrinsickiicsofth
4、eheterogeneousleachingreactionswhichareestablishedviaindependentexperimentsarethefoundationofthedevelopedmodel.Athreephase(gls)reactionprocessmightbecontrolledbyeithersurfacereactioncontroli.e.therate(s)oftheheterogeneou
5、sleachingreaction(s)bygastransfercontroli.e.therateoftransferofthegaseousreactantintotheliquidphase.Inthepresentarticle(PartI)thecaseofsurfacereactioncontrolistreated.Thearticleaddressesinparticularthefollowingtopics:(1)
6、itoutlinesthebasicmassheatbalanceequationswhichdescribetheperfmanceofamultistageleachingreact(2)itpresentsacontinuousfunctiontodescribetheparticlesizedistributionofthefeed(3)itdevelopsonthebasisofprobabilitytheynumbermas
7、sparticlesizedensityfunctionswhichgivethesizedistributionofparticlepopulationsreactingaccdingtothesurfacereactioncontrol—shrinkingcemodel.I.INTRODUCTIONTHEbasicframewkfmodelingasinglestagecontinuousstirredtankreact(CSTR)
8、fanexothermicleachingprocesswhichiskiicallycontrolledbysurfacereactionhasbeendescribedpreviously.mHereextensionismadetoacadeofcontinuousreacts.Thedevelopmentofmathematicalexpressionsismadefthegeneralcaseinvolvingthefollo
9、wingheterogeneousreaction:A(aq)bB(s)cC(aq)dD(aq)[1]ItisrecognizedthatreactantA(aq)mightbepresentintheaqueousphasebecauseofanotherheterogeneousprocessoccurringsimultaneouslywithReaction[1].FexamplereactantA(aq)mightbefmed
10、viaatransferstepfromthegastotheaqueousphase:A(g)—A(aq)[2]Throughoutthisarticle(PartI)itwillbeassumedthattherateofReaction[2]issofastthattheoverallprocessislimitedbytheheterogeneousrateofReaction[1].Thatistheprocessiscont
11、rolledbysurfacereaction.Thecaseofgastransfercontrolwillbeconsideredinacompanionarticle(PartII121).FinallythemodelequationsdevelopedinPartsIIIarebeingusedinafollowuparticle01whereaspecificthreephasesystemofchemicalV.G.PAP
12、ANGELAKISAssistantProfessiswiththeDepartmentofChemicalEngineeringAppliedChemistryUniversityofTontoTontoONMSS1A4Canada.G.P.DEMOPOULOSAssociateProfessiswiththeDepartmentofMetallurgicalEngineeringMcGillUniversityMontrealPQH
13、3A2A7Canada.ManusubmittedAugust21991.METALLURGICALTRANSACTIONSBreactionsencounteredinthepressureoxidationofmixedpyritearsenopyriteconcentratesissimulated.Theassumptionsmadepreviously111arealsovalidhereunlessotherwisestat
14、ed.Themainobjectiveremainstoassesstheperfmanceofthereactseriesindertoidentifyappropriatefeedconditionsfautogenousstablesteadystateoperationwithanacceptablefinalconversionofthesolids.Sincethereactivityofthesolidsdependson
15、theirsurfaceareaclosemonitingoftheparticlesizechangewithtimebecomesofcriticalimptance.Itisindeedtheobjectofthisarticletodeveloptheequationswhichdescribetheevolutionoftheparticlesizedistributionofsolidsreactingunderchemic
16、alreactioncontrolinareactcade.H.THEBASICMASSHEATBALANCEEQUATIONSItisassumedthatthereexistsaseriesofLCSTRsasshowninFigure1eachofarbitraryvolumeVcsTR1(1L).Theexitstreamofeachreactconstitutesthefeedtothenextone(nointerstage
17、recyclingofanykindisassumedtotakeplace).ThefollowingsteadystatemassbalanceequationcanbewrittenfthesolidphaseofReaction[1]inthethreact.—Fi—briSi=0[3]Similarlytheadiabaticheatbalanceequationfthethreactisgivenby(Fi_jCp)(T1—
18、T1_1)wherethelefthsideofEq.[4]representstherateofVOLUME23ADECEMBER1992847f?_1(d0)istheparticlesizedensity(PSD)function(basedonthemassofparticles)attheexitofthe1—1threact.TheincpationofacontinuousPSDfunction—fm(do)inEq.[1
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