BiochemicalBiochemical ReactorsReactorsModelingModeling andand SimulationSimulation

M.CM.C. . LuisLuis E. CastroE. CastroUniversidad Universidad AutonomaAutonoma de de

CoahuilaCoahuila

ObjectiveObjective

§§ TheThe objectiveobjective ofof thisthis talktalk isis toto illustrateillustrate a a visual visual metodologymetodology ((SimulinkSimulink) ) toto modelmodel andandsimulatesimulate a a biochemicalbiochemical reactor, in reactor, in orderorder totoinvestigateinvestigate hishis dynamicdynamic behaviorbehavior andand steadysteadystatestate responseresponse

BackgroundBackground

§§ BiochemicalBiochemical reactorsreactors are are usedused in a in a widewidevarietyvariety ofof processesprocesses, , fromfrom wastewaste treatmenttreatmenttoto alcohol alcohol fermentationfermentation..

§§ BiomassBiomass ((cellscells) consume ) consume substratesubstrate ((sugarsugaroror wastewaste chemicalschemicals) ) andand produce more produce more cellscells..

DiagramDiagram§§ A A typicaltypical control control andand instrumentationinstrumentation

diagramdiagram, , withwith biomassbiomass concentrationconcentration as as thethe measuredmeasured output output isis shownshown belowbelow

ModelModel

§§ TheThe modelingmodeling equationsequations forfor thethe bioreactorbioreactorareare

§§ dXdX//dtdt = (u = (u –– D)XD)X

§§ dSdS//dtdt = = D(SfD(Sf –– S) S) –– uXuX/Y/Y

WhereWhere§§ TheThe statestate variables arevariables are

§§ X = X = biomassbiomass ((cellcell) ) concentrationconcentration§§ = = massmass cellscells//volumevolume

§§ S = S = substratesubstrate concentrationconcentration§§ = = massmass substratesubstrate//volumevolume

§§ TheThe manipulatedmanipulated inputinput isis D = D = dilutiondilution raterate§§ = F/V = = F/V = volumetricvolumetric flowflow raterate/reactor /reactor volumevolume

§§ TheThe disturbancedisturbance inputinput isis§§ SfSf = = substratesubstrate feedfeed concentrationconcentration

KineticsKinetics

§§ TwoTwo possiblepossible expressionsexpressions forfor thethe specificspecificgrowthgrowth raterate are are MonodMonod andand substratesubstrateinhibitioninhibition kineticskinetics, , wichwich includeinclude, , amongamongothersothers

§§ U = U = umaxumax S / (S / (KsKs + S) + S) …….. .. MonodMonod

§§ U = U = umaxumax S / (S / (KsKs + S + K1 S+ S + K1 S22))…… substratesubstrateinhibitioninhibition

SteadySteady StateState andand DynamicDynamic BehaviorBehavior

§§ WeWe use use thethe followingfollowing parametersparameters forfor a a modelmodelwithoutwithout substratesubstrate inhibitioninhibition, , forfor thisthis studystudy§§ UmaxUmax = 0.53 = 0.53 hrhr--11§§ KsKs = 0.12 g/= 0.12 g/literliter§§ K1 = 0.4545 K1 = 0.4545 literliter/g/g§§ Y = 0.4 (Y = 0.4 (biomassbiomass yieldyield))§§ DilutionDilution raterate = D = 0.3 = D = 0.3 hrhr--1 = 0.3/1 = 300/10001 = 0.3/1 = 300/1000

ModelModel ((MatlabMatlab SimulinkSimulink®®))

D ModuleD Module

Load Load ScenariosScenarios ModuleModule

dXdX//dtdt = (u= (u--D)XD)X

dSdS//dtdt = = D(SfD(Sf--S) S) –– uXuX/Y/Y

LoadingLoading ScenarioScenario 11

§§ 1.1.-- Sine Sine wavewave loadload§§ SfSf = 2 + 4sin(0.1t)= 2 + 4sin(0.1t)

ModelModel response response underunder L1, X L1, X vsvs tt

ModelModel response response underunder L1, S L1, S vsvs tt

LoadingLoading ScenarioScenario 22

§§ 1.1.-- StepStep loadload§§ SfSf = 4.0 g/= 4.0 g/literliter

ModelModel response response underunder L2, X L2, X vsvs tt

ModelModel response response underunder L2, S L2, S vsvs tt

SteadySteady statestate conditionsconditions

§§ TheThe processprocess has has thethe followingfollowing steadysteady--statestatesolutionssolutions ((operatingoperating pointspoints).).

§§ L2 L2 scenarioscenario..

§§ X = 1.5374X = 1.5374§§ S = 0.16S = 0.16

ConclusionsConclusions§§ ItIt waswas shownshown thethe usefullnessusefullness ofof thethe productproduct MatlabMatlab SimulinkSimulink forfor

modelingmodeling time variable time variable andand steadysteady statestate conditionsconditions forfor a a MonodianMonodianChemostatChemostat withoutwithout recirculationrecirculation

§§ TheThe simulinksimulink platformsplatforms allowsallows toto use use directdirect visual visual instructionsinstructions forfor modelmodelallall operationsoperations involvedinvolved in in thethe solutionsolution ofof differentialdifferential equationequation’’ss systemssystemsdirectlydirectly

§§ SimulinkSimulink allowsallows toto investigateinvestigate differentdifferent load load scenariosscenarios

§§ SimulinkSimulink uses uses solversolver schemesschemes wellwell documenteddocumented in in otherother partsparts ((SeeSee by by exampleexample, , BurdenBurden & & FrairesFraires))

§§ TheThe dynamicdynamic behaviorbehavior andand steadysteady statestate conditionsconditions waswas shownshown onongraphicgraphic formform..

ReferenceReference

§§ TheThe parametersparameters usedused in in thisthis module module werewerepresentedpresented in in thethe followingfollowing paperpaper ((ourour resultsresultsshow show consistencyconsistency withwith thethe correspondentcorrespondentresultsresults presentedpresented therethere))

§§ AgrawalAgrawal, P , P andand H.CH.C. . LimLim, , ““AnalysesAnalyses ofofVariousVarious control control schemesschemes forfor continuouscontinuousbioreactorsbioreactors”” Adv. Adv. BiochemBiochem. . EngEng. . BiothechnolBiothechnol, , 3030, 61, 61--90, (1984)90, (1984)

ContactContact

§§ LuisLuis E. CastroE. Castro--SolSolííss

§§ M.CM.C. . EnvironmentalEnvironmental EngineeringEngineering (ITESM 2000)(ITESM 2000)§§ Civil Civil EngineeringEngineering (UA de C, 1990)(UA de C, 1990)

§§ Departamento de Postgrado e InvestigaciDepartamento de Postgrado e Investigacióónn§§ Facultad de IngenierFacultad de Ingenierííaa§§ Universidad AutUniversidad Autóónoma de Coahuilanoma de Coahuila

§§ ee--mail: netzerohunt@hotmail.commail: netzerohunt@hotmail.com