Simultaneous Estimation of the Heat Transfer Coefficient and of the Heat of Reaction in Semi-Batch Processes

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1 epartment of Biohemial and Chemial Engeerg Proess ynamis Group () Simultaneous Estimation of the Heat ransfer Coeffiient and of the Heat of eation Semi-Bath Proesses Stefan Krämer alf Gesthuisen Wolfgang Mauntz Sebastian Engell Proess ynamis Group ept. of Biohemial and Chemial Engeerg U ortmund he first two authors now are with IEOS Köln Germany. he third author now is with upont Hamm Germany. PSE Summer Shool Salvador da Bahia 20 Proess ynamis

2 Outle Motivation Modellg of the Proess: CS and PF aet Models System nalysis State Estimation by Extended Kalman Filter ung of the Estimator Influene of the Model of the aet Osillation Calorimetry raditional data analysis dvaned data analysis by an extended model + EKF Summary Proess ynamis

3 Motivation Onle monitorg of onversion (heat of reation) (semi-)bath proesses is very important proess monitorg and ontrol and an be performed by alorimetry. he heat transfer oeffiient is not nown a priori or varies over the bath run. In heat flux alorimetry there are often errors the estimates of the heat of reation due to a wrong heat transfer oeffiient. Estimation of heat of reation and heat transfer oeffiient is needed. Possible approahes: State and parameter estimation by nonlear filterg Osillation alorimetry Proess ynamis

4 Motivation In pratie the followg diffiulties our: he jaet of tehnial reators normally behaves lie a Plug Flow eator (PF) but is modelled as a CS he heat transfer oeffiient () hanges with the bath time espeially semi-bath proesses he flow rate through the jaet fluenes the dynami behaviour of the system signifiantly. hese aspets have to be onsidered the design of the estimator. Proess ynamis

5 d dt Modellg: aet as CS eation alorimetry and state estimation approahes are based on the same physial model. Balanes for the reator and the jaet (CS) Vessel : aet : dh d dt dt V B ρ m B ( V V ) ( ) + ( Q Q ) p p B h ( ) ( m ( ) + ( )) out out p ρ p out B h soure loss... Proess ynamis

6 Modellg: aet as PF Balanes for the reator and the jaet (PF) Vessel : aet : dh d dt dt t V B ρ ρ B ( V V ) ( ) p p v z B + B h h ρ ( t0) out out ( Q Q ) ( ) p soure b +... ( ( t z) ) loss... Proess ynamis

7 CS-Model: Pseudo States Model for state and parameter estimation: We assume that the level the reator h is nown. he model is extended by pseudo dynamis for the unnown parameters. d dt d dt dq dt d dt 0 0 V m B ( ) + Q ( ) p out ( m ( ) + ( )) p ρ p out B h ρ p B h Proess ynamis

8 Proess ynamis CS-Model: Observability nalysis Observability of the CS-model: he nonlear observability map is given by: ( ) ( ) ( ) ( ) ( ) ( ) + ρ ρ + out p p B p loss soure B p out B O m m h Q Q h V y y y y q 2 2 he system is globally observable if an be solved uniquely terms of the state vetor x for. ( ) u x q O U u X x

9 Proess ynamis Observability nalysis he version of the nonlear observability map yields: ( ) ( ) ( ) ( ) ( ) ( ) out p p out p p out B p m y m m y m V y V Q y y ρ he given system is globally observable for all It an be shown that this result holds also for the PF-model if it is disretized by orthogonal olloation with out. 0 0 and V

10 System nalysis ynami behaviour of the system eigenvalues of the learised system f G salg fator m flow normalised jaet flow rate Eigenvalues depend strongly on the jaet mass flow! Proess ynamis

11 Proess ynamis State Estimation: Extended Kalman Filter lgorithm: otation: estimated state at tt + based on measurements up to tt Corretion: Predition: Only (at best) loal stability! ( ) ( ) ( ) ( ) ˆ ˆ ˆ + + P H K I P x h y K x x H P H H P K ( ) ˆ ˆ ˆ ˆ x x x h H x f Q P P u x F x and with x ˆ +

12 ung of the EKF Simulation of a reator (V0 l) with a PF-jaet Estimator based on CS-model for the jaet For a onstant ovariane matrix Q: Performane depends on the jaet mass flow rate. Proess ynamis

13 ung of the EKF daptation of the ovariane matrix of the model error Q to the mass flow rate through the jaet: Q 33 ~ m Proess ynamis

14 Influene of the Model of the aet Simulation of a system with a PF-jaet EKF estimation for with CS or PF-model Large reators or low flow rate of the oolant: esults are poor if a CS model of the jaet is used. Proess ynamis

15 Summary For simultaneous estimation of the heat of reation and the heat transfer oeffiient a CS it has been shown that: the real behaviour of the jaet (CS or PF) must be taen to aount the estimator dynamis have to be adapted to the dynami behaviour of the reator adaptation of Q similar to the hange of the eigenvalues by the jaet mass flow rate results satisfatory estimations. Proess ynamis

16 eap: Calorimetry Energy balanes: eator: () aet: (2) In ase is nown and onstant Eq. () is suffiient. Otherwise Equation (2) has to be added. he model an be exploited by iret Inversion Extended Kalman Filter Proess ynamis

17 Calorimetry esults at a Pilot Sale eator Proess ynamis

18 Heat Balane Calorimetry: Limitations Energy balanes: eator: () aet: (2) Eq. (2) an only be exploited for suffiiently large! Proess ynamis

19 emperature Osillation Calorimetry (OC) Many espeially small (laboratory) reators are operated at large jaet flowrates temperature differene the jaet is too small.. Idea: dd a sosoidal signal to the reator temperature Compute from the frequeny response between the two harmoni signals Proess ynamis

20 OC: Formulae by ietze (996) emperature [ C] δ δ time [s] x 0 4 omputation: Q omputation: From reator heat balane Proess ynamis

21 rawbas of the Method by ietze he method wors well a stationary situation where the temperatures are approximately onstant and does not hange fast. Good estimation of the amplitudes is diffiult transient situations Large deviations slow onvergene Proess ynamis

22 ypial Signals OC Proess ynamis

23 ew pproah to OC lternative evaluation shemes by Wolfgang Mauntz: epresentation of the signal by se plus drift Least-squares estimate movg data wdow Use reator heat balane + its time derivative (2nd order) Movg horizon estimator Proess ynamis

24 Comparison of ifferent Shemes Proess ynamis

25 Experimental eator Proess ynamis

26 ew OC: Experimental esults Proess ynamis

27 Experimental esults: Polymerization esults obtaed with OC and 2nd order model the EKF for a o-polymerization of styrene and butyl arylate the l reator Proess ynamis

28 Summary and Conlusions eation alorimetry is a widely used method to estimate onversion (semi-)bath proesses EKF an estimate Q and simulataneously If the jaet is not behavg as a CS (low flow rates large reators) a PF model of the jaet should be used the estimator If the temperature differene between the jaet let and outlet is small (high jaet flow rate ompared to the volume) traditional alorimetry fails emperature Osillation Calorimetry is a solution to this problem ata analysis usg a seond order derivative model a EKF performs very well also transient situations he exitation signal an be optimized triangular shape Proess ynamis