Student: Fredrik Gjertsen

1. Midtermpresentation, master thesis Student: Fredrik Gjertsen Titleofthesis: Models for on-line controlofpolymerizationprocesses Supervisor: Prof. Sigurd Skogestad, NTNU Co-supervisor: Peter Singstad, Cybernetica AS Goal: To extendestablishedknowledge and processmodelsonsemi-batch emulsioncopolymerization to formulatemodels for tubularreactors for similar systems.

2. Agenda The background for thework The purpose ofthethesiswork Strategiestowardsachieving proper processmodels Results so far Thoughtsonhow to implementthemodels in an on-line simulator for optimization and control

3. Background • Same chemicalprocess as previouslystudied • Emulsioncopolymerization • Summer internship & specializationproject • Previouslystudied as a semi-batch process • Part ofthe European researchproject COOPOL • The semi-batch reactorsetup is thesetupofprimaryinterest, butnewreactorsetups, i.e. tubularreactorsarealsoexplored.

4. Purpose ofthework The purpose ofthework is to establish an efficientmodel for a smart-scaletubularreactor to be used for on-line optimization and control. Modelingapproaches: • Finitedifferences (The Numerical Method of Lines) • Incrementalmodelwith variable transformation, yielding a modelofmovingcontrolvolumes • Mass diffusioneffects for thereactorareexploredusingexperimental RTD data, and theestablishedmodelsarecompared to this. • For the purpose ofcontinuousreactors, micellarnucleation is included in themodel as an alternative to seededpolymerization.

5. Mathematical modeling • Startingpoint: An arbitraryvolume, for whichtheamountof an arbitrary (intensive) quantity (φ) is considered. • (a shellbalance is an alternative approach to theexact same result)

6. A quicksummary • The tubularreactor is described by partialdifferentialequations in both time and space • More complexityintroduced, compared to semi-batch setup • System(s) ofordinarydifferentialequations is preferred • Whatstrategyshould be used to reducethemodel? • Discretization in spaceshould be performed • Numericalefficiency is important • Using experimental RTD data for thereactor, themixingeffectsofthereactorcan be accounted for in each case (eachmodel) • Is theeffectivemassdiffusion negligible?

7. Approach 1: Finitedifferences (referred to as the NMOL approach) • Partialdifferentialequationsarediscretized in space, yieldingordinarydifferentialequations in time for eachdiscreteposition. • This strategy is referred to as theNumerical Method of Lines, which is a traditionalapproach to solvepartialdifferentialequations. • In practice, thisapproach is similar to thewell-known tanks-in-series strategymodel. • Calculations show that a largeamountofdiscretizationpoints is needed • This mayconstitute a problem withrespect to implementingthemodel on-line

8. Approach 1: Finitedifferences • Approximation basedon Taylor series: • Tanks in series RTD:

9. Residence time distribution, finitedifferences • In doing an RTD experimentusing an inert tracer compound, therequirednumberof tanks in series, i.e. thespacingofthe spatial discretization, can be determined. • Calculations show that a largeamountofdiscretizationpoints is needed

10. Transformationof variables • Runningan inert tracer compoundthroughthereactorcanindicatethe RTD ofthereactor. • Note: No netgenerationof inert in thereactor. • Transformationofthemodelequations to an alternative coordinate system: • The equation is now separable, and can be solvedanalytically. • Important: This specificequation is for an inert tracer componentonly, and theequationwill be more complicated for a reacting species.

11. Residence time distribution, changeof variables Simulationwitheffectivediffusivityadjusted:

12. Approach 2: Mobile (finite) controlvolumes (referred to as the MCV approach) • Each discretecontrolvolumebehaves like a (small) traditional batch reactor, withordinarydifferentialequations in time for themodelequations. The positionsofthecontrolvolumesvarythroughoutthereactor. • The controlvolumesare not physicallyconnected, meaningthatmodel outputs at specificpoints in space, e.g. reactoroutlet, must be theresultof an interpolation. • Experimental RTD can be utilized to determinethesize and internalspacingbetweenthemovingreactor units. • How many units areneeded, and howlarge (long) shouldthey be?

13. Residence time distribution, MCV

14. Thoughtsoncontrollerimplementation • Numericalstability and efficiency • Some parts ofthemodelare sensitive to stiffness • A lowdemand for computationaleffort is desired • Functioning estimator • The estimator must run smoothly and not intervenewiththeorderingofmovingcontrolvolumes in the MCV approach. • The controller tuning is not trivial/obvious

15. Controller performancesimulationstrategy Measured plant behavior Controller action Controller and estimator algorithms, governed by a numericallyefficientmodel. Plant*representation, governed by a less numericallyefficient, butperhaps more accurate, model. * In thiswork, the plant is theisolatedbehaviorofthe single reactor in mind.

16. Summary • The NMOL model is less numericallyefficientthanthe MCV model. In order to getsatisfyingperformance for the NMOL approach, thenumberofdiscretizationpointsneeds to be significantlylowerthanwhatthe RTD experimentssuggest (in order to achievecorrectmixingconditions). • A proposal is to usethe less numericallyefficientmodel (NMOL) as a plant replacementmodel and the MCV model for on-line control purposes. • Nextsteps: - Off-line parameter estimationusingexperimental data - ImplementationwiththeCybernetica CENIT software for control studies. Temperaturecontrol, feedratecontrol to achievebetterconversionof monomer, etc.