Kinetic model of gas phase polymerization of 1,3-butadiene catalyzed by supported rare earth coordin

Vol. 43 No. 5SCIENCE IN CHINA (Series B)October 2000Kinetic model of gas phase polymerization of 1,3-butadienecatalyzed by supported rare earth coordination systemSHEN Zhiquan (沈之荃), LI Weishi (李维实) & ZHANG Yifeng (张-烽)Department of Polymer Science and Engineering, Zhejiang University, Hangzhou 310027, ChinaCorrespondence should be addressed to Shen Zhiquan (email: zqshen@163.net)Received May 10, 2000Abstract Gas phase polymerization of 1 ,3-butadiene (Bd) catalyzed by supported rare earth coor-dination system is studied and a new kinetic model is proposed. Four elementary reactions or proc-esses: the process of exposure and activation of potential active catalytic center, propagation,deactivation and chain transfer reaction to alkyl aluminum, are considered in this model. Someimportant parameters, such as monomer-consuming rate, are well expressed as the functions ofmacroscopic polymerization conditions such as pressure, temperature, and duration. The modelcan simulate the whole polymerization procedure satisfactorily.Keywords: rare earth catalyst, 1,3-butadiene, gas phase polymerization, kinetic, modeling.Because gas phase polymerization is conducted without solvent in the process, the compli-cate procedures of aggregation and separation of polymer from solution, which are needed in so-lution polymerization, are excluded from gas phase polymerization. This leads to not only cuttingdown the cost of construction and operation, but also reducing environmental pollution. On theother hand, it also avoids the shortages of bulk polymerization such as low conversion, polymerquality difficult to control and the danger of violent polymerization, which are due to system vis-cosity enhancing rapidly with the increase of conversion and reaction heat being difficult to dif-fuse in bulk polymerization. Although the gas phase polymerization technology of ethylene andpropylene has been industrialized for a long time, gas phase polymerization of Bd has just beenstudied. However, it represents the trend of Bd polymerization technology.Study on gas phase polymerization of Bd was firstly carried out by Berlin Technical Univer-sity and Bayer Company in 19941. Recently, we have studied it succesfully with supported rareearth coordination catalysts. However, the kinetic study of gas phase polymerization of Bd has notbeen performed except for a preliminary work of Eberstein et al.!21. In this paper, the kinetic be-havior and a whole model of gas phase polymerization of Bd with supported rare earth coordinati-on catalysts are reported for the first time. This model can simulate the whole polymerization pro-cedure satisfactorily.中国煤化工MHCNMHG1 ExperimentalGas phase polymerization of butadiene was carried out in a 150 mL kettle. The monomerpressure and the polymerization temperature were kept constant during the whole procedure. Mo-SCIENCE IN CHINA (Series B)Vol.43lecular weight and its distribution of Poly(Bd) prepared were determined on a WATERS 150CGPC chromatograph under the following conditions: 35"C, THF as eluent, flow rate of 1 ml /min,polystyrene as standard, gel columns of 10, 104 and linear. The Mark-Houwink constants'3] ofhigh-cis poly(Bd) in THF at 35°C are K = 4.57x10- and a = 0.693.2 Modeling principleA growing particle is considered as a“solution”of polymeric continuous phase. All reactionstake place in the intraparticle. The difference between the surface and the bulk of particle is ig-nored in this model. The effective monomer concentration in the particle maintains a certain valuewith respect to the constant pressure of Bd during the whole polymerization procedure. Their re-lationship can be well described by Henry' s law: .M=K.P,(1)where K is the reciprocal of Henry constant.Reasonably, the following three elementary reactions or processes are taken into considera-tion for gas phase polymerization of Bd with supported rare earth coordination catalysts.( i ) Process of exposure and activation of potential catalytic centers. In the case of gasphase polymerization of Bd by supported rare earth catalysts, the catalytic centers deposit on theouter and inner surfaces or in the cavity of the carrier. Monomer diffuses from outer to inner of theparticle in a slow rate. Therefore, some zones in inner have no monomer at the very beginning ofthe polymerization. Consequently, no polymerization has happened at the catalytic centers in thesezones, which is regarded as the potential catalytic centers. However, the monomer reaches thesezones gradually along with the polymerization proceeding. In such a case, these centers have φp-portunities to meet with monomer. They become the“true”active propagation centers right afterreacting with monomer. This is consistent with the multigrain model4+. 51 and multilayer model6.7.The process is called the exposure and activation of potential catalytic centers, as expressed in thefollowing:C+M- Ake→>P*where C is the number of potential catalytic centers, and ke the rate constant.(il ) Propagation. The propagation reaction isP1-1+Mk。P%where kp is the rate constant of propagation, and P" the number of active propagation chains with中国煤化工polymeric degree of n.(ii) Deactivation. It is reported!21 that thereMHCNMHGionreationinthegasphase polymerization of Bd. To take it into account, we consider the following deactivation reac-tion:No.5KINETIC MODEL OF BUTADIENE GAS PHASE POLYMERIZATION479P*_kg>Pnwhere Pn is the terminated polymer chain with polymeric degree of n, and kg the rate constant ofthis deactivation reaction.Besides, chain transfer reaction exists in this polymerization system, but mainly toward alkylaluminuml8.9. We assume that the active propagation chain，Pi, and the terminated polymerchain, Pn , are yielded in such chain transfer reaction, as shown in the following:P,*+Al-kr→P, +P*where kr is the rate constant of chain transfer reaction.Thus, we have the variation rate of potential catalytic center:dC=-k。MC,(2)Itthe variation rate of active propagation chain with polymeric degree of 1: .d=k.MC-kpMP* -kgP° -k[AI]P* +2kk.[I]P"，(3)the variation rate of active propagation chain with polymeric degreeof n( n>2):中e =KkMP"1-k,MP" -kgP”" -k[AIp",(4)dtand the variation rate of the terminated polymer chain with polymeric degree of n:I=kgP* +k.[AI]P,*(5)The above polymerization mechanism indicates that the monomer consumes in both pro-cesses of exposure and activation of potential catalytic centers and propagation step. Thus, mono-mer-consuming rate can be expressed asRm=k。MC+ SkMP" =k_MC + kpMP*,(6)n=lwherer=之?is the total number of active propagation chain.. n=lThe number of potential catalytic centers can be obtained from the integration of eq.(2), as .shown in the following:(7)中国煤化工where Co is the initial number of catalytic centers:THCNMHGrization.From eqs. (3) and (4), we can easily get the varation rate ot total number of active propaga-tion chains, P*:SCIENCE IN CHINA (Series B)Vol. 43.dP*dEp:n=1=k。MC-kqP*(8)dtThis is a one-order linear differential equation. It can be solved with eq. (7) givingp°=.k。MC、,[exp(-k.M)- exp(-ka1].(9)kg-k。MThus, the monomer-consuming rate can be well expressed as the functions of polymerization du-ration:kpkeM2CqRm =k.MCo exp(-ke Mt)+-kg-k.M. [exp( -k。M1)- exp(-kg1)].(10)Integrating R. over 1, the polymerization yield is obtained askpM -kgM +kjkpk。M2Yield=Co1 - exp(-k.Mt)]+ .. C。.[1-exp(-kg1)]. (1)kg- k。Mk.(ka-k。M) .From eqs. (3), (7) and (9), we obtainp*=A+keMCo exp(-k.Mr)--Aexp( -kgt)A2-keMA2 -kdA +k。MC。+|A2-kgA2 -k.M|exp(-A21),(12)whereAl=kw[AI]k.MCkj-k。MA2 =kpM +ks + kt[I].Thus, the expression of P" , as shown in the following, can be derived from that of the P* basedon the recurrence of eq. (4): .kp 'M n-(A + k。MCo)kqp-'M"-'Ap"=k-exp(- -k.Mt)--exp(- kat)(A2-k。M)"(A2-k.)"A +k.MCo_ |+kp-'M"-l exp(-A2)0 i[(A2-kg)"-i (A2-k。M)"-i」(n≥1).(13)Integrating eq. (5), the number of terminated polymer chain with polymeric degree of n is ob-tained:中国煤化工”M"-(A +k_MCG)(A-k.M)n_P=--exp6.MYHCN M H Gl-exp(-kx1)]k_M(A2 -k&M)"ndV2 ^dA +k。MG_t- K~"M"-(A2 - k,M)exp6A2)2(n≥1). (14)台(A2-ky)"- (A2 -kgM)"-+」o j:A5No.5KINETIC MODEL OF BUTADIENE GAS PHASE POLYMERIZATION481As we know, two kinds of chains with polymeric degree of n exist in the system at the sametime. Therefore, the total number of chains with polymeric degree of nis P" + P. Thus, the av-erage molecular weights (Mn and M w ) and the distribution index (MWD) can be expressed bytheir definitions:M、厂,n(P" +P,)Mn =(15)C(":+R,)M2 n2(P,; +Pn)Mw =-(16)2n(P" +P,)n=lEn(p;*+P,). 2(P;+ P)Mw_ nMWD =(17)Mn72|之,n(P," +Pn) ._ n=lwhere Mw is the molecular weight of Bd.Eqs. (1), (7), (9)- -(11), (13)- (17) construct a whole new model for gas phase polymeriza-tion of Bd with supported rare earth catalysts. In these expressions, the concentration of catalyst,total number of active propagating chains, monomer-consuming rate, yield, number of activepropagating chains with polymeric degree of n, the terminated polymer chain with polymeric de-gree of n, molecular weight and its distribution are all described as the functions of the macro-scopic conditions, such as pressure and polymerization duration. The practical polymerizationprocedure can be well simulated by using these expressions, if the values of K,ke, kp. ks, and ku areavailable.3 Determination of model parameters and discussionThe monomer- consuming rate was determined after the following way: close the monomer-inlet valve at time of t, then measure the interval time,△t;, for the minute decrease of system pres-sure,△P. Since Bd monomer can be absorbed or dissolved by poly(Bd) particles, the concentra-tion of monomer in polymer matrix will change \中国煤化工riation of gas pressureduring the measure of monomer-consuming rate.:TYHCN M H Gconsuming amoumt isthe total variation of the monomer concentration occurring both In gas phase and in polymer ma-trix. Thus, the monomer-consuming rate, Rmi, at the time of t; can be calculated as .482SCIENCE IN CHINA (Series B)Vol. 43.APVg. KAPVp .Rm =ZRTNt;Ot;(18)where Vg and Vp are the butadiene volume of gas phase and the volume of the polymer matrixrespectively, and Z is the compressibility factor of Bd gasltlo. Although K is unknown, Rmi can becalculated by a given initial value of K, followed by integrating Rm over polymerization time.Based on the comparison of the integral with practical yield as shown in table 1, the value of K ismodified and the above steps are repeated until the integral approaches practical yield with satis-factory approximation. Then, the value of K is the reciprocal of Henry constant at those polymeri-zation conditions like temperature, pressure, etc. The instantaneous monomer-consuming ratesunder various polymerization pressures and temperatures were determined, as shown in fig. 1. All .curves are similar in their shapes, but distinguish from each other with different values and posi-tions of climaxes as well as different variation rates. The values of K under these polymerizationTable 1 Gas phase polymerization of Bd with supported rare earth coordination catalystsat various temperatures and pressuresT/C .40506070P/MPa0.20130.201 30.11630.15130.251 3Yield /kg PBd1 043540244611815693519Mw x10+58.552.459.830.833.044.7Mn x10-15.616.(18.814.3MWD3.763.283.183.734.603.11Polymerization conditions: Cn= 1 mol Nd, 1.5 h.conditions (as shown in table 2) were also6robtained. It is found that K increases with龄。rising of the polymerization temperature.The effective concentrations of monomer inpoly(Bd) matrix (M) calculated by eq. (1), asalso displayed in table 2, are quite high and心increase at lower temperature or higher pres-2sure.The data in fig. 1 were ftted by eq. (10).The values of modeling parameters obtained10002000300040005000are listed in table 2 and the fitting curves aret/sFig.1. Variation of monomer-consuming rate during polymeri-displayed in fig. 1. It can be seen that thezation procedure. Polymerization conditions: C= 1 mol Nd.中国煤化工e quite small, and all30C, 0.201 3 MPa, O, 40C, 0.201 3 MPa; O, 50C, 0.201Fncided well with theMPa; ( ), 60"C, 0.201 3 MPa;口, 70C, 0.201 3 MPa;v , 50":THCNMHGcpuuuncilal uaia. itierefore, the above ki-0.116 3 MPa;+, 50"C, 0.161 3MPa; <, 50C, 0.251 3 MPa;一，netic model can be used to elucidatingsimulation. x x -|1-experimental phenomena and to predictingNo.5KINETIC MODEL OF BUTADIENE GAS PHASE POLYMERIZATION483Table 2 V alues of modeling parameters at various temperatures and pressuresKx10-sk.x10/L 1 mol-' 'sT/"CP1 MPaM/mol●L'k/L 'mol''sl kx10/s-+ kx/mol-'.s+/mol. LI . Pa-0.201 32.244.510.85土0.075.9士0.71.2士0.1401.693.401.31土0.0410.9士0.73.7士0.218.81.422.861.61土 0.0619.7土1.34.3土0.352.0601.22.540.98土0.0253.1土2.48.1土0.389.6701.172.361.30士0.0275.4+ 3.315.7+ 0.6500.11631.453.67土0.1719.2士0.44.3土0.1 .0.15131.392.102.43土0.0618.5土0.54.1土0.20.251 31.373.440.78土0.0617.7土0.44.9土0.7polymerization rate satisfactorily. For example, it is found that the rate of polymerization is quitelow at the beginning, then increases rapidly toward its climax. This is caused by the process ofexposure and activation of potential active centers, which is quite slow in comparison with thepropagation step. However, the gradual decrease of polymerization rate after its climax is mainlydue to the deactivation of active centers. Since the effective concentration of Bd monomer inpoly(Bd) matrix at 30°C is rather high and the rate constant of deactivation, kg, is far less than thatat other temperatures, the polymerization proceeds in a distinguishing high rate. However, lowyield and catalytic activity appear in the case of 70"C, which is due to the big value of rate con-stant of deactivation, resulting in the rapid decrease in polymerization rate (table 1).There is no obvious relationship between ke and temperature or pressure, as shown in table 2.Clearly, it indicates that the process of exposure and activation of potential catalytic centers is notonly affected by temperature and pressure, but also subjected to the practical operation conditionslike stirring effect, amount of carrier, and so on, which need to be further investigated.The correlation between the other rate constants and temperature can be well expressed byArrhenius equation:一E。k=ko exp|RT(19)8rwhere ko is frequency factor and Ea is activa-tion energy. Thus, we havelnk=Ink。--(20) 鸢0After linear regressing the data of Inkp, Inkgand Ink calculated from table 2 under thesame pressure, as shown in fig. 2, the activa-中国煤化工3.153.203.253.303.35tion energy and frequency factors of propa-MHCNMH GorK-gation, deactivation and chain transfer reac-tion are obtained as Ep=57.7kJ/mol, Koo= Fig.2. Plotoflnk, lnko andInkw. vesus 1/T: O.InK;●Ink;▲4.74x10l0L *mol-1 s+; Es =51.7 kJ/mol, kaoInkr484SCIENCE IN CHINA (Series B)Vol.43.1.01 1000=1.1x10*s-1; E=67.8 kJ/mol, kto=4.28x 10120.8C800600虽4 Application of model心0.4-Yield,400The practical polymerization experiment三of concrete conditions can be well simulated0.2-200by using this model. For example, the variationPof catalyst amount， total number of active0.001000 2000 3000 4000 5000 6000propagation chains and yield during the whole1/spolymerization procedure under the Bd pres-Fig. 3. Application of the model. Conditions of simulation: sure of 0.201 3 MPa at 50°C, as shown in fig.3,50'C, 0.201 3 MPa Bd, Co= 1 mol, others are shown in table 2.can be predicted by this model with theparameters listed in table 2.Acknowledgements This work was supported by the Ministry of Science and Technology of China (Grant No.G1999064801), National Natural Science Foundation of China (Grant Nos. 29734130, 29974024), Ministry of Education (GrantNo. G98402) and Commission of Science and Technology of Zhejiang Province.References1. Sylvester, G., Vermalekeu, H., Eur. Pat. Appl., EP647, 657.2. Eberstein, C., Garmatter, B., Reichert, K. H. et al, Gas-phase polymerization of butadiene, Chemie Ingenieur Technik,1996, 68: 820.3. Wilson, D. J. A rare earth catalyst system for the polymerization of 1,3-butadiene: the effect of different carboxylates,Polymer, 1993, 34( 16): 3504.4. Floyd, S.. Choi, K. H, Taylor, T. 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