Optimization and Control of a Semi-Batch Polymerization reactor

Transcription

1 9th International PhD Workshop on Systes and Control: Young Generation Viepoint Optiization and Control of a Sei-Batch Polyerization reactor T. Miteva, N. Hvala Eail: Teodora.Miteva@ijs.si, Nadja.Hvala@ijs.si Jozef Stefan Institute, Ljubljana, Slovenia Abstract The research ork presented in this paper considers the polyerization plant in MITOL cheical factory in Sežana, Slovenia. This is the leading glue anufacturer in the country ith production rate ore than 90% of its capacity. One of the challenges no is to increase the production rate, hile keeping the quality paraeters at the desired values. A possible approach to reach this goal is by applying better control strategies that ill decrease the batch tie. The underlying research is aied at the design of the process odel and its application in the search for ore optial plant operation. Model siulation results based on real plant data, derived in gpoms odel environent, are presented. I. INTODUCTION The research ork in this paper considers the polyerization process in MITOL, a cheical factory in Sezana, Slocenia. This is the leading glue anufacturer in the country ith the production rate ore than 90% of its capacity. The challenge e are facing no, is to design optial control strategies in order to increase the production rate and decrease the batch tie by keeping the quality paraeters in the desired levels. The production process is sei-batch polyerization process ith initiator and onoer added during the batch. The large quantities of ra aterials and equipent resources prevent us fro perforing experients for batch optiization directly on the plant. Therefore e need a good predictive odel for controlling the input variables (initiator and onoer) and also to control the teperature during the batch. For that purpose a odel consisting of differential and algebraic equations (DAE) have been constructed. The odel predicts four outputs, i.e. conversion, particle size diaeter, solid content and viscosity. That odel as not able to predict the changes in the teperature profile. In order to iprove the predictive capabilities, the odel as extended by adding additional differential equations, that estiate the reactor teperature profile as a function of the concentrations of the reacting cheicals. This paper presents the extended odel using first principle odeling (energy balance). II. PLANT POCESS DESCIPTION IN MITOL The process presented hereby is a polyerization of vinyl acetate by using potassiu persulfate (PS) as initiator and polyvinyl alcohol as protective colloid. The production process is sei-batch polyerization. In the beginning initial aounts of onoer and initiator are added into the reactor as ell as the hole aount of polyvinyl alcohol and ater. The reactor is closed and the heating starts. The heating of the reactor is done by puping hot ater in the heating around the reactor. The hot ater is puped ith a teperature of 90 C. When the teperature in the reactor reaches approxiately C, the operator stops the hot ater. The exotheric reaction and the heat of the reaining ater filling the heating coat, continue to rise the teperature. After the reactor teperature reaches a certain level, the reaining onoer starts to be puped into the reactor ith a continuous flo of 370 kg/h. The onoer flo rate is controlled by a PID controller acting on the pup. The teperature of the added onoer is ith outdoors teperature, fig. 1. Fig. 1 Schee of the polyerization reactor in MITOL In the beginning of the reaction, the teperature can reach 82 C, but afterards, for the product quality reasons, it is necessary to keep the teperature beteen C. Teperature control is perfored by anually adding a sall aount of initiator every tie hen the teperature decreases. When all the onoer is added into the reactor, a larger aount of initiator is added in order to terinate the reaction. The teperature is then allo to reach 90 C. The reaction is consider as finished hen the teperature starts

2 9th International PhD Workshop on Systes and Control: Young Generation Viepoint to decrease again. The ain variables affecting the duration of the reaction and possibly used in the batch optiization are: reactor teperature, flo rate of the onoer and the addition of the initiator. The quality of the product is defined by the folloing paraeters: conversion into polyer, particle size distribution, viscosity and solid content. here d is the initiator decoposition rate constant, T is the reactor teperature and Tstart is the teperature hen an appreciable decoposition is observed. The addition of the initiator is calculated fro the eight change of the initiator dozing tank (fig. 1) III. ENEGY BALANCE The current odel is based on a ore coplex one described in previous papers [1][2][3]. In the first odel the onoer flo rate, the initiator addition and the teperature in the reactor ere taken as inputs into the systes. The data for the ere provided fro the real plant in MITOL. In that case the teperature in the reactor as not estiated by the odel. In order to observe the changes in the teperature as a result of onoer and initiator addition, e took out the teperature as input and rather estiate it fro the energy balance odel. The odel is applied ithin a odel predictive optiization schee aied to search for an optial policy of anipulating initiator and onoer feed rates. The polyvinyl alcohol covers the particles, providing steric stabilization. The partition of the PVOH beteen the ater phase, the droplets and the particles is odelled ith the Languir odel [16], based on adsorption isothers. Fig. 2. Estiating the initiator profile fro the eight of the initiator tank Having this profile e are able to estiate the initiator profile and it is: [ G ] + [ G ] A [ G] Aps G = ad [ G] MWPVOH c ad 0 V gd Vd + 1+ (1) Where [G ] is the concentration of PVOH in the ater phase, gd is the partition coefficient on the droplets, A c is the equilibriu coverage of the particles and G 0 is the total ass opvoh The ass of the initiator in the reactor (I) is increased by the flo addition of initiator (I e ) and decreased by its theral decoposition [9][10]. To obtain the concentration of the initiator (I ) in the aqueous phase e divide by the volue of ater (V ). di [ ] e d [ I ] V = I k (2) I = I V To account for higher rate of decoposition of PS at higher teperature e use the folloing function: 2 T Tstart T Tstart d = (4) (3) Fig 3 Estiated teperature profile The feed rate of the onoer (Q ) is an input to the odel; its values are read fro a database containing real data fro the plant. The onoer in the reactor (M) is consued in the ater phase due to the initiation, propagation and chain transfer reactions, and, above all, in the particle phase, the ain locus of polyerization. The equation for the onoer is given by: dm k pp = Q ( M NoC [ M p ] n ( PSDi ) V ) i= 1 k k i i + k p M + k 1 ( M 1 ) + ( M ) tr 1 + The energy balance odel is based on reaction heat capacity and the energy produced and consued during the reaction. The latter include the folloing: - Heating of the reactor through the heating - Producing heat in the exotheric reaction (5)

3 9th International PhD Workshop on Systes and Control: Young Generation Viepoint - Heating the incoing onoer - Cooling the reactor by the reflux in the condenser - Heat losses to the surroundings The reaction heat capacity is calculated by the onoer in the reactor, the converted into polyer onoer, initial aounts of ater and polyvinyl alcohol and their heat capacities as follo: = MMW Cp + M MW Cp + V Cp + PVOHCp (6) on conv pol ater pol The heating of the reactor through the heating is given by: Δ H = ( T T ) (7) here T is the teperature in the reactor and T is the teperature in the reactor. The changes in the latter are odeled as follo: = )( T T ) (8) ( The energy needed to heat the incoing onoer is represented by the flo rate of the onoer, its olecular eight, heat capacity and teperature: Q MW Cp T (9) on on The losses due to the reflux fro the condenser are also taken into account. It is estiated by the flo coing in the condenser and out of the condenser, the heat capacity of the condenser and the teperature of the reflux going through the condenser. Q cond = Q Cp ( T T ) Q (10) FC Cout Cout Cin FCλ here λ is the vaporization heat and it is calculated by the folloing equation: 2 λ T Cout T (11) = Cout The heat losses through the surroundings are also odeled and are: Q loss = C ( T T ) (12) 3 ext The energy balance odel is divided into three parts depending on the stage of the process and the reaction (fig. 3) Fig. 4 Three phases odel separation The first part of the odel starts hen e close the reactor and start heating it up ith hot ater through the heating. This first part of the odeled reaction ends hen the hot ater stops to be puped in the and ait till the teperature reaches around 80 C. In that first part the heat losses are negligible and also there is no flo through the condenser. Therefore the energy balance odel in that first part is given by: ΔH r r pol d + T C ΔH 3 = Q MW Cp on T on (13) The left side of the equation account for the changes in the internal energy of the reactor, hich is due to the changes of the reactor teperature (first ter) and the change of its heat capacity (second ter) The second part of the odeled teperature profile starts at the end of the first part and ends at the first initiator addition during the batch. In that part the reactor is no ore heated through the heating, the losses are negligible, as ell as the flo through the condenser because the reaction has just been started. The energy balance odel includes only onoer enthalpy and the reaction heat. The equation is the folloing: d + T = QMWCponTon C 4 ΔH rr (14) pol The energy balance for the third and last part of the odeled reaction takes into account the reflux though the condenser and the heat losses through the surroundings. The equation has the folloing for: C d + T = QMWCponTon (15) 5ΔH rrpol Qcond C Q 6 loss Model paraeters in the equations (3-13) are taken fro the literature [4] or estiated based on real plant data (C 3, C 4, C 5, C 6 ), so that a satisfactory agreeent beteen the process

4 9th International PhD Workshop on Systes and Control: Young Generation Viepoint and the odel as obtained. The values of the odel paraeter are given in Table I Table I Paraeter Value k i MW [gol -1 ] ρ p [g l -1 ] 3.70E k' i [l ol -1 s -1 ] 3.70E+04 tr [l ol -1 s -1 ] 1.75E-04 pp [l ol -1 s -1 ] 3700 Cp pol [kj kg -1-1 ] 1.77x10-2 Cp on [kj kg -1-1 ] 1.77x10-2 Cp out [kj kg -1 ] x10-2 Cp ater [kj kg -1 ] T ext [] ΔH r [kj ol -1 ] C 3 (diensionless) 0.50 C 4 (diensionless) 0.35 C 5 (diensionless) 0.60 C 6 (diensionless) Depending on the batch The output quality paraeters are also odeled. The conversion is given by: With the presented odel e are able to get relatively good estiates of the reactor teperature. Fro Figure 3 it can be seen that the estiated profile follos the dynaics of the real one. Not so good estiates are obtained at the beginning and at the end of the batch. At the beginning of the batch, the ost influential part of the odel is the heating of the reactor through the heating. So ost probably, the corresponding odel paraeters still need to be estiated ore precisely. The agreeent of the odel is also not good in the last part of the estiated profile. This is hen the hole aount of onoer has been already added in the reactor and a larger aount of initiator is put to finish the reaction. There are to possible reasons that the perforance of the odel in this part is not so good, i.e., (i) the actual heat losses are higher than estiated, (ii) the final addition of initiator as saller than calculated. For the latter e have to take into account that the aount of initiator is obtained fro the eight change of the dozing tank, so there ight be soe disparity of the final addition because of its larger aount. The obtained odel still needs fine tuning of paraeter values and close inspection of the initiator addition x 100 M c = (16) M t Matheatically express the particle size diaeter is: D pu 6000M cmw = πρ p N P 1/ 3 (17) Solid content: M cmw + G0 SC = M MW + G + V t 0 (18) Fig. 5 Initiator addition, onoer flo rate and the teperature prfile during the batch The viscosity is calculated by: 0 υ = (19) 2 1 υ sc sc ref IV. ESULTS The presented odel as siulated using gpoms [5][6] odeling tool. Model siulations ere perfored based on real plant data. The flo of the added onoer during the batch as easured, hile the addition of initiator as calculated fro the eight change of the initiator dozing tank. The reactor teperature and initiator flo rate during the batch are shon in Figure 2. Fig. 6 Modeled teperature profile vs. real plant teperature profile The overall odel as also used to calculate the product quality paraeters. Table II shos the validation of the odel for one batch for siulation tie of seconds.

5 9th International PhD Workshop on Systes and Control: Young Generation Viepoint The ranges for the outputs are the folloing: the conversion for all the batches is over 99%, the solid content is beteen 44-46%, the range of the viscosity is For the viscosity and the solids content, laboratory analyses ere perfored at the end of the reaction. These easureents are norally perfored after ixing several batches and therefore no individual data is available. Table II Output variables real plant data and estiated data Batch No. Conversion (%) Solids Content (%) Viscosity (Brookfield 200C, 50rp), (Pas) eal Modelled data eal Modelled eal Modelled Fro the table e can see that the odel output variables are in good agreeent ith real plant data. To obtain these results it as necessary to adjust the C 6 paraeter for each batch. This could be attributed to the variable and increased fouling of the reactor alls beteen cleaning periods. The average odel error for conversion and solids content is around 2% and for the viscosity around 15%. Soe bigger deviations can be noticed for batch 1214 for all output variables. V. CONCLUSION A odel for polyerization of vinyl acetate has been developed. The odel has to inputs flo rate of onoer and flo rate of initiator addition. The outputs of the presented odel are four conversion, particle size diaeter, solid content and viscosity. The overall odel has thirteen differential equations, sixty-three algebraic equations and nine adjustable paraeters. In this odel e are able to observe teperature profile and based on it apply the control of the initiator addition and estiate ore precisely the sufficient aount of initiator hich needs to be added during the batch. The odel has been validated on data of five batches taken fro the real plant. The presented teperature profile is quite satisfactory and also the odel output variables are in the range. The ork continues ith the design and testing of initiator and onoer control strategies. ACNOWLEDGMENT The support of the European Coission in the context of the 6th Fraeork Prograe (PISM, Contract No. MTN-CT ) is greatly acknoledged. NOMENCLATUE I Moles if initiator in the aqueous phase ol I e Flo ate Initiator ol/ sec I Concentration of the initiator in the ol l-aq -1 aqueous phase k d Initiator decoposition rate constant sec -1 V Volue of the ater L T start Starting teperature [] Q Flo ate Monoer ol/ sec M Moles of onoer dissolved in the ol aqueous phase Total concentration of priary radicals ol l-aq -1 fro initiator Overall concentration of oligoeric ol l-aq -1 radicals (M and M ) M i Monoeric radicals of chain length i ol l-aq -1 [M p ] Concentration of onoer in the polyer ol l -1 phase PSD(i) Moles of particles of group i ol T Teperature in the reactor [] eaction heat capacity kj kg -1 Q Flo rate of onoer ol s -1 MW Molecular eight of onoer gol -1 Cp on Specific heat capacity of onoer kj kg -1 Cp pol Specific heat capacity of polyer kj kg -1 Cp out Specific heat capacity of the onoer kj kg -1 going in and out of the reactor T on Teperature onoer [] ΔH r Heat of polyerization kj ol -1 r pol Polyerization reaction rate - ΔH Heating through the heating kj ol -1 Q cond eflux through the condenser kj kg -1 Q loss Heat losses to the surroundings [] T Teperature in the reactor [] k' i ate constant for propagation of onoeric radicals l ol -1 s -1 pp ate constant for propagation in the polyer phase l ol -1 s -1 k i ate constant for propagation of initiator radicals l ol -1 s -1 tr ate constant for chain transfer to onoer l ol -1 s -1 D pu Diaeter of an unsollen polyer c particle M c Total oles of onoer charged in the ol reactor M t Total aount of onoer added to the ol reactor N P Nuber of particles Adi. G 0 Total as of polyvinyl alcohol ol ν Viscosity of the latex Poise ν o Viscosity of the ater Poise sc Solids content Adi. ρ p Polyer density Polyer Handbook

6 9th International PhD Workshop on Systes and Control: Young Generation Viepoint EFEENCES [1] F. Aller al al., Modeling of seibatch vinyl acetate eulsion polyerization in an industrial reactor, CHISA 2006, August 2006, Prague - Czech epublic [2] T. Miteva,. Alvarez, N. Hvala, D. ukanja, Modeling of Polyvinyl Acetate Polyerization Process for Control Purposes, ESCAPE18, 1-4 June 2008, Lyon, France [3] F. Aller, G. andare,, L. F. Blázquez Quintana,, D. ukanja,, V. Jovan, and M. Georgiadis, Model-based optial control of the production of polyvinyl acetate. European Congress of Cheical Engineering (ECCE-6), Copenhagen, Septeber, 2007 [4].C. Berger and G. Meyerhoff, Polyer handbook, 3 th edition, Wiley, Ne York 1989 [5] Process Systes Enterprise Ltd., gpoms Industry User Guide, 2004 [6] Process Systes Enterprise Ltd., gpoms Advanced user Guide, 2004 [7] C.M Gilore, G.W. Poehlein and F.J. Schork, Journal of Applied Polyer Science, 48, , [8] C.M Gilore, G.W. Poehlein and F.J. Schork, Journal of Applied Polyer Science, 48, , 1993 [9] Polyvinyl Alcohol: Properties and Applications, edited by A. Finch, John Wiley and Sons Ltd, 1973 [10] N. Praojaney, Ph.D. thesis, Lehigh University, [11] J. T. O Donnell and. B. Mesrobian. Vinyl acetate eulsion polyerization. Journal of Polyer Science, Vol. 28, , [12] M. B. Urquiola, V. L. Dionie, E. D. Sudol, M. S. El-Aasser, Journal of Polyer Science: Part A: Polyer Cheistry, 30, 12, , 1992 [13] M. B. Urquiola, V. L. Dionie, E. D. Sudol, M. S. El-Aasser, Journal of Polyer Science: Part A: Polyer Cheistry, 30, 12, , [14] M. B. Urquiola, V. L. Dionie, E. D. Sudol, M. S. El-Aasser, Journal of Polyer Science: Part A: Polyer Cheistry, 31, 6, , [15] S. Dunn and P. A. Taylor. The polyerization of vinyl acetate in aqueous solution initiated by potassiu persulphate at 60ºC. Makrool., 83, , 1965 [16] Charles D. Ianuel, Cajetan F. Cordeiro, Sehkar S. Sundara, Edard S. Meados, Tiothy J. Croley, Francis J. Doyle III. Modeling of particle size distribution in eulsion co-polyerization: coparison ith experiental data and paraetric sensitivity studies, Coputers and Cheical Engineering, 26, , 2002 [17] H. Yildiri Erbil, Vinyl acetate eulsion polyerization and copolyerization ith acrylic onoers, CC Press LLC, 2000