RIGOROUS MODELING OF A HIGH PRESSURE ETHYLENE-VINYL ACETATE (EVA) COPOLYMERIZATION AUTOCLAVE REACTOR. I-Lung Chien, Tze Wei Kan and Bo-Shuo Chen

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1 RIGOROUS MODELING OF A HIGH PRESSURE ETHYLENE-VINYL ACETATE (EVA) COPOLYMERIZATION AUTOCLAVE REACTOR I-Lung Chen, Tze We an and Bo-Shuo Chen Department of Chemcal Engneerng, Natonal Tawan Unversty of Scence and Technology, Tape 6, TAIWAN Abstract: Polyethylene (PE) s one of the most wdely used polymers n chemcal ndustry. In all the PE processes, hgh-pressure autoclave process s generally consdered as the most proftable segment of the polyethylene busness worldwde n recent years. Dependng on dfferent grades of the product, reactor zone temperatures n ths autoclave process can be n the range 5-23 C and pressure n the range of 5-2g/cm 2. In ths paper, rgorous dynamc model of an ndustral ethylene and vnyl acetate (EVA) copolymerzaton reactor wll be establshed. Industral operatng condton data of seven product grades wth melt ndex rangng from ones to over four hundred wll be used as ftted or test data to obtan the ey netc parameters n the model. The predcted outputs of melt ndex, vnyl acetate wt. % n polymer, and polymer producton rate wll be compared to plant data. Copyrght 25 IFAC eywords: Autoclave process; Polyethylene; EVA copolymerzaton reactor; Freeradcal copolymerzaton; Melt ndex.. INTRODUCTION Polyethylene s one of the most wdely used polymers n chemcal ndustry. In all the polyethylene process, hgh-pressure autoclave process s generally consdered as the most compettve and the most proftable segment of the polyethylene busness worldwde n recent years. The autoclave process s extremely flexble n producng varous specalty products. Also, products from autoclave process can be used n varety of hgh-value senstve applcatons because of no resdue of metal-base catalyst whch s commonly used n other polyethylene processes s present n ths polymer. In ths paper, rgorous modelng of an ndustral hgh pressure ethylene and vnyl acetate (EVA) copolymerzaton autoclave reactor wll be establshed. gorous modelng of a hgh-pressure ethylene and vnyl acetate copolymerzaton reactor n the lterature s relatvely scarce n comparson wth the free-radcal polyethylene (PE) reacton. Zabsy et al. (992) revewed the netc model for PE and EVA polymerzaton n a hgh-pressure tubular reactor. Chan et al. (993) usng several contnuous strred tan reactor (CSTR) or plug-flow reactor segments n seres to model the autoclave reactor. In ther paper, pseudo netc rate constants are used to allow for copolymerzaton. Sarmora et al. (2) developed a mathematcal mxng model that descrbes hghpressure polymerzaton of ethylene and ethylenevnyl acetate. The resultng moment model s able to calculate conversons, average molecular weghts, long chan branchng and melt ndexes at any pont n the reactor. Brandoln et al. (2) further developed a mathematcal model able to descrbe the complete molecular weght dstrbutons of polyethylene and ethylene-vnyl acetate copolymers obtaned n hgh pressure autoclave reactors. In ths paper, reactor smulaton ncludng detaled polymerzaton reacton mechansm and also

2 dynamc component balance and energy balance wll be establshed for an ndustral autoclave reactor. Industral operatng condton data of seven product grades wth melt ndexes rangng from ones to over four hundred wll be used as ftted or test data to obtan the ey netc parameters n the model. The predcted outputs of melt ndex, vnyl acetate wt. % n polymer, and polymer producton rate wll be compared to plant data. The organzaton of the paper s as follows. The detaled rgorous dynamc model of an ndustral autoclave reactor s gven n Secton 2. Smulaton results of the ftted model n comparson wth the plant data s shown n Secton 3. Some concludng remars are drawn n Secton PROCESS MODELING The overall process of ths ndustral ethylene-vnyl acetate copolymerzaton process can be seen n Fgure. In ths paper, the detaled dynamc model of the autoclave reactor wll be developed. The autoclave reactor s modeled as seven constantlystrred zones wth flow from top zone down. Bacmxng flow from lower zone upward s also allowed. The combned feed (INL) ncludng ethylene, vnyl acetate, chan modfer, and nert s fed nto the frst fve zones. The peroxde ntator and solvent (INI) s fed nto three of the seven zones. The temperatures of these three zones are controlled by the ntator flow addton rate. The detaled segmented model of ths autoclave reactor s shown n Fgure 2. For each zone, the dynamc component balance and energy balance are smulated wth the free-radcal polymerzaton netc mechansm as below: d[ X ] V = F [ X ] F [ X n n out dt ] + V r out dt V ρ Cp = ρ F Cp T n n n n dt ρ F Cp T out out out out () + V R P Hr (2) In the two equatons above, s the reactor zone number and [X] means the concentraton of each component. The overall mass balance of each zone s assumed to be at quas steady state wth the total nlet flow to each zone ncludes possble feed flow rate nto ths zone, possble ntator feed nto ths zone, the outlet flow from the above zone, and the bac-mxed flow from the zone below as n the followng Eqn. (3): F [ X ] n n INI INI INL INL = F [ X ] + F [ X ] + ( α ) F [ X ] + α + F+ [ X ] out out + (3) In ths equaton, α s the fracton of total zone outlet flow bac nto the above reactor zone. The netc mechansm ncludes the followng elementary reactons: decomposton of ntators, propagaton, chan transfer to monomer, chan transfer to modfer, chan transfer to polymer, termnaton by dsproportonaton, termnaton by combnaton, and β-scsson of termnal radcals. Pseudo netc rate constants are used to allow for copolymerzaton. The detaled netc mechansm can be seen below: Intaton: d I 2R () R ( ) + M R () Fgure. The overall EVA polymer process. Propagaton: p R + M R ( x+ ) Termnaton by combnaton: + + tc R R ( y) P ( x + y) Termnaton by dsproportonnaton: td R + R ( y) P( x) + P ( y) Chan transfer to monomer: cm + M P + R() Fgure 2. Detaled autoclave reactor model Chan transfer to modfer: ct + T P + R ()

3 Chan transfer to polymer: cp R + P ( y) P( x) + R ( y) β-scsson of termnal radcals: β P ( x ) + R () + In the netc mechansm above, subscrpt stands for the number of long chan branches, x s the chan length measured as number of monomer unts n the chan. Each netc rate constant s a pseudo netc rate constant. For example: P = (4) pφ f + p2φ2 f + p2φ + p22φ2 where f and φ are defned as: M f =, f (5) = M + M2 p2 = φ2 = p2 f + p2 φ f, φ wth M as ethylene and M 2 as vnyl acetate. (6) The reacton rate, r, n the dynamc component balance equaton can then be calculated. The components consdered n Eqn. () nclude: two monomers, ntator, modfer, solvent, nert, and also free-radcals and polymer. For examples, the reacton rates for free-radcals and polymer are calculated as below: r = 2 fd [ I] δ δ xv P[ M ][ ] R P[ M ][ ( x )] V tc[ ][ V td [ ( x)][ V cm[ ][ M ]( δ x) cm[ [ M ] δ δ xv cp[ ]( δ x) y[ P ( y)] = y= cp[ x[ P ] V ct[ ][ T]( δ x) ct[ [ T] δ δ xv β [ ]( δ x ) β [ δ δ xv ct[ ][ T ] β[ ( x + )] V (7) x rp = tc [ R ( y)][ + ( x y)] td[ ( x)] [ R ( y)] 2 = y= = y= cm[ ][ M ] V cp[ xp cp[ ( x)] y[ P( y)] = y= (8) where [ s the overall free-radcal concentraton, δ s the ronecer s Delta, and double sum s for the summaton of all chan length and all number of long chan branches. The reacton rate constants are expressed n Arrhenus form as: ( Ea + PVa ) / RT = A e (9) In order to calculate the number average of molecular weghts and the weght average of molecular weghts of ths system, the moment equatons are utlzed n ths paper. The followng double moments for the radcal and polymer dstrbutons are defned as n the followng Eqns. () and (). m n λ m, n = x () = x= m µ m, n = x P () = x= n where the frst ndex corresponds to the branch dstrbuton whle the second one corresponds to the length dstrbuton. In Eqn. (), λ, s actually the overall free-radcal concentraton, [. Applyng quas steady state assumpton (QSSA), the moments of radcal, λ, can be calculated. For example, m, n 2 fd [ I].5, = ( ) tc + td λ (2) All dynamc moment balance for the polymer, µ m, n, can also be developed from Eqns. (), (8), and (). Wth the moments of radcal and polymer, the number average of molecular weghts ( M ) and the weght average of molecular weghts ( M expressed as: n w ) can be µ, + λ, M n = M mon (3) µ + λ,, µ,2 + λ,2 M w = M mon (4) µ, + λ, where M mon s the average molecular weght of the monomers as: [ M] MW + [ M 2] MW M 2 mon = (5) [ M] + [ M 2] The number-average long-chan branchng frequency for every one thousand carbon atom can be expressed as: µ, + λ, LCB = 5 (6) µ, + λ, The melt ndex from plant data can be calculated accordng to an emprcal correlaton n McAuley, et al. (99) as: M Melt Index = n (7)

4 The comonomer wt. % n the polymer (CW) can be calculated as:. Notce that the plant data has been scaled for propretary reason. CW = r M r M rm 2 2 (%) (8) Table. Plant outputs for seven grades 3. SIMULATION RESULTS The ndustral plant that we wor wth has a propretary steady-state model to predct ther plant output condtons. We acqured ther nput data whch needed to feed nto ther model and then usng our model for the output predcton. The followng Fgure 3 contans some component concentratons for comparson purpose. The component concentratons nclude: [I] for ntator; [M] for ethylene; [M2] for vnyl acetate; [T] for chan modfer; [N] for nert; and [S] for solvent. From ths fgure, one would observe that our model predcted reasonably well n comparson wth the propretary plant steady-state model. [I] mol/cum [M2] mol/cum 7e-6 6e-6 5e-6 4e-6 3e-6 2e-6 e new model predcted plant model predcted new model predcted plant model predcted [M] mol/cum [T] mol/cum new model predcted plant model predcted new model predcted plant model predcted Producton Rate (g/h) MI Comonomer wt. % Grade Grade Grade Grade Grade Grade Grade From the senstvty analyss of the netc parameters, the followng Table 2 ndcates the most nfluental elementary reactons for the three plant output varables. In ths table, propagaton reacton and termnaton by dsproportonaton reactons are most mportant for the producton rate predcton. Thus, these netc parameters are adusted frst to ft the plant producton rate. Sum of squared predcton error s used for the mnmzaton search. Table 2 also ndcates that propagaton, chan transfer to modfer, and β-scsson of termnal radcal reactons are most mportant for the melt ndex predcton. Thus, the netc parameters for the chan transfer to modfer, and β-scsson of termnal radcals reactons are adusted further for the melt ndex predcton. [N] mol/cum new model predcted plant model predcted [S] mol/cum new model predcted plant model predcted Fgure 3. Comparson wth propretary plant model for a product grade. Table 2. Most nfluental elementary reactons. Plant output data Producton Rate Melt Index Comonomer wt. % Most nfluental elementary reactons Propagaton, termnaton by dsproportonaton Propagaton, chan transfer to modfer, β-scsson of termnal radcals Propagaton Industral operatng condton data of seven product grades wth melt ndexes rangng from ones to over four hundred wll be used as ftted data to obtan the ey netc parameters n the model. The plant output nformaton ncludes the producton rate (g/hr), melt ndex, and comonomer wt. %. The plant outputs for the seven grades are lsted n Table Fnally, a combned obectve functon s used to obtan the above netc parameters agan wth values obtaned from the last two optmzaton searches as ntal guess for the fnal combned optmzaton. The combned obectve functon s defned as:

5 2 2 7 plant predcted plant predcted PR OF = P MI MI mn A = plant plant, Ea, Va P MI 2 plant predcted CW CW plant CW (9) The results from the optmzaton search requred two netc parameter sets to properly ft the wde range of plant data. One netc parameter set s used for the lower melt ndex operatng condtons (Grades, 2, and 3). The other netc parameter set s used for the hgher melt ndex operatng condtons (Grades 4, 5, 6, and 7). The ftted results can be seen n the followng Fgures 4 and 5. Notce that all plant outputs are predcted very closely to the plant date. Ths ndcated that ths dynamc model s qute relable for later study to fnd optmum operatng condton moves durng grade transtons. 4. CONCLUSIONS In ths paper, rgorous dynamc model of an ndustral autoclave reactor for the producton of ethylene-vnyl acetate copolymer has been establshed. Ths reactor model ncludes detaled polymerzaton reacton mechansm and also dynamc component balance and energy balance. In order to calculate the number average of molecular weghts and the weght average of molecular weghts of ths system, the moment equatons are also utlzed n ths paper. Industral operatng condton data of seven product grades wth melt ndex rangng from ones to over four hundred has been used to obtan the ey netc parameters n the model. The predcted outputs of melt ndex, comonomer wt. % n polymer, and polymer producton rate are compared closely to the plant data. Two sets of model parameters are used to ft these wde ranges of operatng condtons. Ths dynamc model can be used n a later study to optmze operatng condton moves durng grade transtons and also for developng plantwde control strategy of the overall copolymersaton process. Model-predcted ProdRate 2 G Model-predcted MI G ACNOWLEDGEMENT Ths wor s supported by Natonal Scence Councl of the R. O. C. under grant no. NSC E Plant ProdRate Plant MI REFERENCES Model-predcted ProdRate Model-predcted CoWt Model-predcted CoWt G Plant CoWt Fgure 4. Model predcton for lower melt ndex grades Plant ProdRate Model-predcted MI Plant MI Brandoln, A., C. Sarmora, A. Lopez-Rodrguez,. S. Whteley and B. Del Amo Fernandez (2). Predcton of molecular weght dstrbutons by probablty generatng functons. Applcaton to ndustral autoclave reactors for hgh pressure polymerzaton of ethylene and ethylene-vnyl acetate. Polymer Eng. Sc., 4, 8, 43. Chan, W. M., P. E. Gloor and A. E. Hamelec (993). A netc model for olefn polymerzaton n hgh-pressure autoclave reactor. AIChE J., 39,,. McAuley,. B., J. F. MacGregor and A. E. Hamelec (99). A netc model for ndustral gas-phase ethylene copolymerzaton. AIChE J., 36, 6, 837. Sarmora, C., A. Brandoln, A. Lopez-Rodrguez,. S. Whteley and B. Del Amo Fernandez (2). Modelng of molecular weghts n ndustral autoclave reactors for hgh pressure polymerzaton of ethylene and ethylene-vnyl acetate. Polymer Eng. Sc., 4, 6, 48. Zabsy, R. C. M., W. M. Chan, P. E. Gloor and A. E. Hamelec (992). A netc model for olefn polymerzaton n hgh-pressure tubular reactors: A revew and update. Polymer, 33,, Plant CoWt Fgure 5. Model predcton for hgher melt ndex grades.