Modeling and Simulation of Ethylene Polymerization in Industrial Slurry Reactor Series

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1 CATALYSIS, KINETICS AND REACTION ENGINEERING Chiese Jural f Chemical Egieerig, 21(8) (2013) DOI: /S (13) delig ad Simulati f Ethylee Plymerizati i Idustrial Slurry Reactr Series ENG Weijua ( 孟伟娟 ) 1,2, LI Jiaei ( 李建伟 ) 1,*, CHEN Biahua ( 陈标华 ) 1 ad LI Hg ( 李洪泊 ) 2 1 State Key Laratry f Chemical Resurce Egieerig, Beijig Uiversity f Chemical Techlgy, Beijig , Chia 2 Yasha Brach, Beijig Research Istitute f Chemical Idustry, Chia Petrleum & Chemical Crprati, Beijig , Chia Astract A five-site cmprehesive mathematical mdel as develped t simulate the steady-state ehavir f idustrial slurry plymerizati f ethylee i multistage ctiuus stirred ta reactrs. re specifically, the effects f varius peratig cditis (i.e., ifl rates f catalyst, hydrge ad cmmer) the mlecular structure ad prperties f plyethylee (i.e.,,, plydispersity idex (I PD ), melt idex, desity, etc.) are fully assessed. It is sh that the prpsed cmprehesive mdel is capale f simulatig the steady-state perati f a idustrial slurry stirred ta reactr series. It is demstrated that chagig the catalyst fl rate, chages simultaeusly the mea residece-time i th reactrs, hich plays a sigificat rle the estalishmet f plyethylee architecture prperties such as mlecular mass ad I PD. The melt idex ad desity f plyethylee are maily ctrlled y hydrge ad cmmer ccetrati, respectively. Keyrds imdal plyethylee, multiple tas i series, simulati, plymerizati 1 INTRODUCTION High plydispersity imdal plyethylee prducts have imprtat applicatis i areas such as thermfrmig ad l mldig. T prduce this prduct, several reactrs i series may e utilized. By suitaly adjustig the temperature ad ccetrati f chai trasfer aget (i.e. hydrge) i each reactr, a imdal prduct ca e taied [1-4]. The mlecular mass distriuti f the fial prduct may e regulated y adjustig the relative amuts f plymer prduced i each reactr y chagig the residece time i each stage, usig differet reactr temperatures. Several prcesses ca e used fr the prducti f imdal plyethylee. Ethylee ca e plymerized i a variety f evirmets, icludig liquid r gaseus reactrs ith little restricti. Slurry plymerizati f ethylee i multiple stages f ctiuus stirred-ta reactrs (CSTR) usig hetergeeus Ziegler-Natta catalysts is a cmm prcess fr the cmmercial prducti f high plydispersity imdal plyethylee. Simulati mdels are imprtat tls fr the develpmet ad ptimizati f plymerizati prcesses ecause they ca descrie catalyst perfrmace ad plymer prperties as a fucti f plymerizati ietics ad prcess cditis [5-10]. As the plylefi idustry mves tards the prducti f resis ith mre cmplex micrstructures, these mdels ecme essetial fr prcess uderstadig ad prduct desig. Ftes ad edes [5] develped a cmplete dyamic mdel fr ctiuus slurry ethylee plymerizati reactr t predict the prducti rates as ell as the umer ad mass mlecular mass averages f the fial plymer. Khare et al. [6] used a plymerizati prcess simulatr t descrie the steady-state perati f a idustrial slurry reactr ad aalyze prducti rates ad certai ey mlecular prperties f the fial plymer material [average mlecular mass ad plydispersity idex (I PD )]. The mdel as ale t simulate the trasiet perati f the plymerizati plat s as t suggest mdificatis f the perati cditis i rder t icrease the plymer prducti rate. Ati et al. [7] develped a cmprehesive mdel fr the ethylee/1-utee cplymerizati i a idustrial slurry plymerizati reactr fr liear l desity plyethylee sythesis. The mdel as ale t descrie the dyamic evluti f the mlecular mass averages, cmmer ctet, particle size averages, melt idex, ad desity f the fial plymer resi. Nipu ad Suil [8] develped a mdel f slurry plymerizati f ethylee i a multistage CSTR t fid the effect f stageise variati f the partial pressure f ethylee ad/r hydrge plymer plydispersity ad rate f plymerizati. Oly sigle-site type catalyst as mdeled i their r. I this paper, a five-site cmprehesive mathematical mdel has ee develped t simulate the steady-state ehavir f a idustrial imdal highdesity plyethylee prcess. I particular, the mdel ca t ly predict the prperties f the plymer that is prduced i each reactr ut als estimate the prperties f the fial prduct. The effects f catalyst fl rate, hydrge ad ethylee mlar rati, cmmer ad ethylee mlar rati the plymer mlecular structure ad prperties ere als ivestigated. Received , accepted * T hm crrespdece shuld e addressed. lij@mail.uct.edu.c

2 Chi. J. Chem. Eg., Vl. 21, N. 8, August Figure 1 Prcess fl diagram fr the series reactr 1 mmer, hydrge ad slvet; 2 mmer, cmmer, hydrge ad slvet; 3 CSTR; 4 flash drum; 5 vlatile remval; 6 cetrifugal separatr; 7 slvet recycle; 8 ligmer separati ad plymer et cae dryig 2 ODEL DEVELOPENT 2.1 deled series reactr prcess I Fig. 1, a schematic represetati f a idustrial slurry-phase lefi plymerizati reactr series is illustrated. The prcess csists f t jaceted CSTRs, here gaseus mmer, cmmer ad hydrge diffuse i the liquid phase slvet (hexae) ad react at the surface f slid catalyst micrgrai, resulted i the frmati f the plymer slids. Ra materials feed t the first CSTR ad the slurry prduct is the pumped t the secd CSTR, hich als receives fresh mmer ad slvet. The secd reactr is t fed ith fresh catalyst as the catalyst frm the first reactr is sufficiet t ctiue the plymerizati prcess. The cmmer is 1-utee, ad it eters as a feed stream t the secd reactr ly. The vapr utlet frm each reactr uderges clig ad recycles t the reactr ilet. The slurry stream leavig the secd reactr eters a flash uit fr remval f vlatiles. The resultig stream eters a cetrifugal separatr, hich remves ad returs hexae t the reactr ilets. The temperature i th the reactrs eeds t e the same. The hydrge partial pressure is als differet i t reactrs, permittig the prducti f plymers ith differet average mlecular mass i the t reactrs. This results i a imdal mlecular mass distriuti fr the fial plymer prduct. Typically, plyethylee f l mlecular mass ad high desity are prduced i the first reactr f the series, cmmly perated at high hydrge ccetrati. O the ther had, i the secd reactr f the series, l hydrge ad high cmmer ccetrati result i the prducti f high mlecular mass ad l desity plyethylee. Typically, idustrial slurry-phase CSTRs perate at C, pressures f Pa ad a plymer-slids ccetrati f apprximately 350 g plyethylee (L hexae) Kietic mdelig fr Ziegler-Natta catalyst Hetergeeus Ziegler-Natta catalyst is ppular amg plylefi catalysts ad used fr the prducti ver tes f milli ts f plyethylee per year [11, 12]. Fr hetergeeus Ziegler-Natta catalysis, eve the same catalyst particle, differet active sites ca have differet prpagati rate cstats, hich ca give rise t very rad mlecular mass distriutis [13]. The mechaisms (Tale 1) descried here are similar t thse utlied y cauley et al. [14], hich has ee used successfully t descrie the ehavir f idustrial reactrs. The asece f a site activati step i the prpsed mechaism is explaied y the assumpti f the existece f a preplymerizati peratial stage efre the reactr feedig. Tale 1 Kietic mechaism f ethylee/1-utee cplymerizati ver a Ziegler-Natta catalyst Prcess Equati chai iitiati P + 0i P chai prpagati chai trasfer t hydrge (H 2 ) sptaeus chai trasfer chai trasfer t mmer deactivati 0 i 1i pij Pi, + j P + 1, j th Pi, + H2 D + P0 ts Pi, D + P0 tmij i, + j + 0 d Pi, D + Cd P D P 2.3 Determiati f ietic parameters We use the ase set f ietic parameters i the pe literature as iitial values i the mdel ad the apply a iterative methdlgy t adjust them t match mdel predictis ith plat data. Adjust the rate cstats fr chai prpagati t match the cversis f mmer ad cmmer. The primary reactis affectig mmer ad cmmer cversis are thse fr mmer-mmer ad mmer-cmmer prpagatis, respectively, due t the high mmer ccetrati relative t that f cmmer. Adjust the rate cstat fr sptaeus catalyst deactivati t match the prducti rate f high desity plyethylee (HDPE). Adjust the rate cstat fr chai trasfer t hydrge ad t mmer t match the umer-average mlecular mass prduced at each site type. The detailed prcedures ere descried i Ref. [6].

3 852 Chi. J. Chem. Eg., Vl. 21, N. 8, August 2013 Gel permeati chrmatgraphy (GPC) as used t get the mlecular mass distriuti (D) f the plymer ad a statistical algrithm as used t decvlute the plymer D t determie the miimum umer f catalyst site types that gives a accurate represetati f the mlecular mass distriutis geerated y Ziegler-Natta catalysts, as ell as the mass fracti ad umer average mlecular mass f plymer prduced y each site type. The csiderati f these site types, each ith its respective reactivity, eales us t mdel the rad mlecular mass distriuti f the HDPE accurately. Fur prduct grades (t parallel ad t series cfiguratis) ere used fr determiig the ietic parameters. Fig. 2 illustrates the D predicted fr each site type, as ell as a cmparis f the predicti f the verall D ith the experimetal curve. The results idicate that a five-site mdel ca accurately descrie the mlecular mass distriuti f this particular sample. I Fig. 3, the effect f the umer f differet catalyst active sites the percetage square errr deviati f experimetal ad predicted D values is depicted. It is evidet that as the umer f catalyst active sites icreases t five, the percetage deviati errr decreases t a miimum value (i.e., 0.009). Tale 2 shs the results f F statistical test f the ietic parameters. The multiple crrelati idex is greater tha 0.9 ad the F-statistic is mre tha te times f the critical F-statistic i the cfidece regi f 99%. The fial ietic parameters fr the five site mdel are listed i Tale 3. Figure 2 GPC decvluti results fr a represetative HDPE sample frm the parallel reactr cfigurati plat data; distriuti fr differet sites; regressed curve Figure 3 Effect f the umer f catalyst active sites the regressed D Tale 2 F statistical test f the ietic parameters Numer f parameters Numer f degrees f freedm ultiple crrelati idex F-statistic 10 F F Tale 3 Numerical values f the ietic rate cstats (at 85 C) fr a five-site Ziegler-Natta catalyst Site 1 Site 2 Site 3 Site 4 Site 5 iitial fracti f active sites μ 0 (0) iitiati 0i /L ml 1 s prpagati p11 /L ml 1 s p12 /L ml 1 s p21 /L ml 1 s p22 /L ml 1 s chai trasfer th /L ml 1 s tm11 /L ml 1 s tm12 /L ml 1 s tm21 /L ml 1 s tm22 /L ml 1 s ts /s deactivati d /s

4 Chi. J. Chem. Eg., Vl. 21, N. 8, August CSTR mdel The mass fracti f Ti i the catalyst is 4.8%, the ttal mlar fracti f Ti availale as active sites is equal t 40%. The rate f csumpti f each mmer ca e calculated y N N xtiti R = ( μ ) [ ] site m (1) pi pji 0, j i s, i = 1 j= 1,Ti The ccetrati f sites f type havig a chai edig i mmer f type 1 r 2, respectively, (i.e. a cplymer system) is give y μ μ 0,1 = μ0 0,2 = μ0 p21[ 1] s p21[ 1] s + p12[ 2] s p12[ 2 ] s p12[ 2] s + p21[ 1] s (2) (3) The ccetrati f active sites f type ca e fud y 0 dμ = dμ0 (4) dt Fr a CSTR the residece-time distriuti is 1 Et () = exp ( t/ τ ) (5) τ The mea catalyst residece time is calculated as a fucti f the desired slids ctet i the reactr, reactr vlume, ad catalyst feed rate accrdig t [15] V τ = Y q + ρp ρ1 R s,r s,r 1 s,r (1 + ) cat Yield f plymer is calculated y N m Y R dt i= 1 t 0 pi (6) = (7) The mea yield f hmplymer i the first reactr is calculated y a a a a ( )d 0 Y = Y E t t (8) The prperties f the cplymer phase ca e calculated i a similar fashi as the hmplymer phase. Hever, there are several additial ccepts that must e icluded. Sice the prperties f the cplymer phase deped the time the catalyst speds i the hmplymer reactr, a additial itegral ver hmplymer residece time, t a, is ecessary. Secdly, the ietic rates f plymerizati i the secd reactr deped the umer ad distriuti f catalyst active sites availale after the catalyst leaves the hmplymer stage. Thus, the fial umer f sites the catalyst pssesses after the first stage (hmplymer reactr) must e the iitial umer f sites fr the secd stage (cplymer reactr). Therefre, the mea yield f cplymer i the secd reactr is calculated y a dule itegral: ( ) a a ( ) ( )d d 0 0 Y E t Y E t t t = (9) Uder the cditis f liear additi f lg plymer chais, live plymer termiati y chai trasfer r catalyst deactivati uder cstat reacti cditis (temperature ad ccetrati), the istataeus plymer chai legth distriuti at each site f a multisite catalyst is ell descried y the lg-chai expetial apprximati t the Schulz- Flry mst-prale distriuti [16]: ( ) ( ) 2 ( ) exp / E = (10) If the istataeus chai legth distriuti is idepedet f residece-time, the utlet chai legth distriuti fr a ctiuus reactr at steady-state is give y N 1 = i Y = 1 sites i, ( ) (,, i i) E Y E ( i = a r ) (11) i hich refers t the utlet. The utlet verall chai legth distriuti fr a system cmpsed f t reactrs ca e calculated as sites 1 E (,) = Y E + Y E Y Y = 1 a ( + ) N ( ) ( ),a,a,, (12) The verall mlecular-mass distriuti fr a system cmpsed f t reactrs ca e calculated as ( ) E ( ) E, =, l(10) (13) If the average chai legths ad cmpsitis at each site are idepedet f residece-time ad catalyst size, the umer-average mlecular mass f the plymer frmed i each reactr ca e calculated y site, 1 1 N Y i i i i, i, = 1,m = ( i = a r ) (14) Y Ad the umer-average mlecular mass f the cmpsite prduct after t reactrs i series is Nsites,a, 1 1 Y Y = + a,a,a,, ( Y ) 1 + Y =,m,m (15) If the mass-average chai legth ad cmpsitis at each catalyst site is idepedet f residece time ad catalyst size, the average mass mlecular mass f the plymer frmed i each reactr ca e calculated accrdig t the fllig equatis:

5 854 Chi. J. Chem. Eg., Vl. 21, N. 8, August 2013 sites 1 N i, i, i, i,m i Y = 1 = Y ( i = a r ) (16) Ad the mass-average mlecular mass f the cmpsite prduct after t reactrs i series is = a ( + ) N sites 1,a,a,a,,, Y,m Y +,m Y 1 Y = (17) The plydispersity idex is the calculated y [13] I PD = (18) Fr lg plymer chais the istataeus cplymer cmpsiti is very arr ad distriuted arud its mea value. Therefre, fr all itets ad purpses, e may characterize the distriuti y its mea value ithut sigificat lss f ifrmati. I this r e fcus the calculati f the average cplymer cmpsiti i plymer particles. Fr a multisite Ziegler-Natta catalyst, e expect the cmpsiti f the cplymer frmed at each plymerizati site t remai ivariat. The average cplymer cmpsiti ( v 2 = average cmmer mle fracti i the cplymer) i the secd stage f a multistage prcess is calculated frm the itegrated yields f each mmer y v 2 2 Y = Y Y ( / ) (19) Ad the average cmmer mle fracti (v 2 ) i the cmpsite prduct after t reactrs i series is v 2 = Y 2 ( )( / ) a Y Y Y (20) The melt idex (I ) f plyethylee ca e crrelated t the mass-average mlecular mass ith a simple per-la fucti such as [7] I i ( ) ( x i ) = α ( i = a r ) (21) here α ad x are empirical cstats. Fr imdal plyethylee prcesses, the rage f I is very large the rder f g (10 mi) 1. It is impssile t cver the hle rage f I values ith a sigle expressi [17]. Thus, e use the same frmula ith differet cefficiets fr calculatig the I f the prduct prduced i each reactr. The cefficiets ere acquired y multi-liear regressi f steady-state plat data. The α ad x values are ad 1.21 i the first reactr, hile they are ad 2.31 i the secd reactr, respectively. I f multimdal prducts ca e taied usig a typical mixig rule ith plymer mass fracti ad idividual melt idexes fr the plymer prduced i each reactr as iputs [18]: 1/ p p [ I ] [ I ] [ I ] 1/ 1/ p a a = + (22) here the expet, p, is 3.5. I the plat, aalysis t measure the desity is typically carried ut ly fr pellets. Fr imdal plyethylee prcesses, I f the plymer prduced i each reactr as t high r t l fr desity measuremets. S e ly predict the desity f the cmpsite prduct after t reactrs i series. The plymer desity is calculated usig the fllig equati [7], ρ = ( xb ) l ( ) (23) here x B is the 1-utee mle fracti ad is the mass-average mlecular mass f the fial plymer material. 3 RESULTS AND DISCUSSION 3.1 del predictis vs. plat data Durig the reacti, reacti rates are ctrlled y the ccetrati f reactats disslved i the plymer surrudig the sites. Gaseus sustaces are sred ly it the amrphus regis f the plymer [14]. Fr the preset simulatis, it is assumed that the amrphus plymer phase is i equilirium ith the liquid phase ad that diffusial effects ithi the amrphus phase are egligile. Hery s la as used t calculate the ccetrati f mmer, cmmer ad hydrge i the liquid phase, hile Rault s la as applied t the slvet. The srpti factr η i (slid-liquid iterface) as assumed t e uity. Base case peratig cditis fr prducti f imdal plyethylee pipe resi ad film resi H i a series f reactrs ere tae frm plat ad sh i Tale 4. The verall mlecular mass distriuti f the simulated prducts is cmpared t the data f plat i Figs. 4 ad 5. Gd agreemet etee ur five-site mdel ad the idustrially prduced imdal plyethylee GPC curve is evidet. The ther prperties f the simulated prducts are cmpared t the data f plat i Tales 5 ad 6. Frm a cmparis f the mdel predictis ad the idustrial prducti rate,,, I ad desity data, it is apparet that the ul prperties f the plymer prduced i the idustrial reactr ca largely e explaied y the mdel. 3.2 Effect f the catalyst fl rate (residece time) As the catalyst particle passes thrugh the reactr

6 Chi. J. Chem. Eg., Vl. 21, N. 8, August Tale 4 Simulati cditis used fr the ase case imdal plyethylee Variale Pipe resi Film resi H First reactr Secd reactr First reactr Secd reactr temperature/ C pressure/pa reactr vlume/m slids fracti/% (y mass) / H2 C2 / C4 C2 catalyst fl rate/g s diameter f catalyst particle/μm ethylee feed fl/g h hydrge feed fl/g h slvet feed fl/g h cmmer feed fl/g h umer-average chai legth-site umer-average chai legth-site umer-average chai legth-site umer-average chai legth-site umer-average chai legth-site Figure 4 Base case GPC curve fit f imdal plyethylee pipe resi fr 2 CSTRs i series plat data (pipe resi ); mdel predicti Figure 5 Base case GPC curve fit f imdal plyethylee film resi H fr 2 CSTRs i series plat data (film resi H); mdel predicti Item Tale 5 Cmparis f predicti results ad plat data fr pipe resi First reactr Secd reactr After t reactrs Plat data Simulated value Plat data Simulated value Plat data Simulated value mea residece time/h prducti/t h I PD cmmer ctet/% (y mle) I /g (10 mi) desity/g cm

7 856 Chi. J. Chem. Eg., Vl. 21, N. 8, August 2013 Item Tale 6 Cmparis f predicti results ad plat data fr film resi H First reactr Secd reactr After t reactrs Plat data Simulated value Plat data Simulated value Plat data Simulated value mea residece time/h prducti/t h I PD cmmer ctet/% (y mle) I /g (10 mi) desity/g cm Tale 7 Summary f simulati fr the effect f catalyst fl rate q /g s 1 ea residece time/h ea yield (plyethylee)/g (g cat.) 1 cat First reactr Secd reactr First reactr Secd reactr I PD system, mmer plymerizes causig plymer t ecapsulate the catalyst hich expads ad grs it the resultat plymer particle. I this secti, the t stage reactrs ere simulated at catalyst fl rate frm 0.01 t 1.0 g s 1. The ther peratig cditis i Tale 4 fr prducti f imdal plyethylee pipe resi ere ept the same i each stage, that is, e assume the mass fracti f slids i the slvet, plymerizati temperature, pressure, hydrge/ ethylee mle rati ad cmmer/ethylee mle rati t e cstat. As the catalyst fl rate icreases, the fl rates f ethylee, hydrge, cmmer ad slvet have t icrease i rder t maitai the reactr pressure ad mass fracti f slids i the slvet. This leads t the reducti f the residece time. Tale 7 shs the chages f catalyst mea residece time, catalyst mea yield, mass average mlecular mass ( ), umer average mlecular mass ( ) ad plydispersity ith icreasig the fl rate f catalyst. The effect f catalyst fl rate the GPC curves as sh i Fig. 6. It ca e see that he q cat >0.05 g s 1, the plydispersity,, ad D f imdal plyethylee chaged little. O the ther had, icreased catalyst fl rate results i ler catalyst mea residece time ad catalyst mea yields. Figure 6 Effect f catalyst fl rate the GPC curves f imdal plyethylee prduced i 2 CSTR series catalyst fl rate/g s 1 : ; ; 3 0.1; ; ; 6 0.5; The reacti rate f plymerizati is depedet several parameters such as mmer ccetrati, temperature ad active site ccetrati. It is apparet that as the catalyst fl rate icreases, active site ccetrati icreases ad s des the plymerizati rate. Sice the ietic rates f plymerizati i the secd reactr deped the umer ad distriuti f catalyst active sites availale after the catalyst leaves the hmplymer stage, the prperties f the cplymer phase deped the time the catalyst speds i the hmplymer reactr. The catalyst mea

8 Chi. J. Chem. Eg., Vl. 21, N. 8, August Tale 8 Effect f hydrge t ethylee mlar rati the mlecular mass, I PD ad I f plyethylee prduced after t reactrs i series Numer Hydrge/ethylee (mlar rati) First reactr Secd reactr I PD I residece time i the first reactr fr catalyst fl rate f 0.01 g s 1 is 3 times as lg as that fr catalyst fl rate f 0.05 g s 1, the effects f catalyst deactivati may e imprtat, hich ca cause the chage f umer ad distriuti f catalyst active site. As the mea residece-time is prgressively decreased (ttal fl rate icreases), catalyst deactivati ecmes less imprtat ad the plydispersity chages little. Hever, he catalyst feed rate is chaged frm 0.01 t 1.0 g s 1, the catalyst mea yield rati f the first reactr t the secd reactr decreases frm 1.63 t It meas that the mass fracti f the l mlecular mass hmplymer ithi the fial prduct after t reactrs i series decreases, hile the mass fracti f the high mlecular mass cplymer icreases. This causes the sl icrease f ad chage f GPC curves f the fial prduct. 3.3 Effect f the hydrge ifl rate It is ell that, i Z-N catalytic lefi plymerizati, the hydrge ccetrati is emplyed t ctrl the melt idex f plylefi, hich is related t its mlecular mass [19]. I this secti, the t stage reactrs ere simulated at hydrge/ethylee mlar rati i the first ad secd reactrs f the series chaged frm 4.0 t 10 ad frm 0.15 t 0.25, respectively. The ther peratig cditis i Tale 4 fr prducti f imdal plyethylee pipe resi ere ept the same i each stage, that is, e assume the mass fracti f slids i the slvet, plymerizati temperature, pressure, catalyst fl rate ad cmmer/ ethylee mlar rati t e cstat. We als assume that the mea yield f hmplymer i the first reactr is equal t that f cplymer i the secd reactr. The effect f hydrge t ethylee mlar fl rate rati the mlecular mass, I PD, I ad D f plyethylee prduced after t reactrs as sh i Tale 8 ad Fig. 7. As hydrge is the chai trasfer aget, the average mlecular mass decreases ith the icrease f hydrge ccetrati. Hever, he hydrge/ ethylee mlar flrate rati icreases i the first reactr ad decreases i the secd reactr at the same Figure 7 Effect f hydrge t ethylee ml fl rate rati imdal plyethylee prduced i 2 CSTR series 1st reactr, H 2 /C 2 H 4 = 4; 2d reactr, H 2 /C 2 H 4 = 0.25; 1st reactr, H 2 /C 2 H 4 = 6; 2d reactr, H 2 /C 2 H 4 = 0.25; 1st reactr, H 2 /C 2 H 4 = 8; 2d reactr, H 2 /C 2 H 4 = 0.20; 1st reactr, H 2 /C 2 H 4 = 10; 2d reactr, H 2 /C 2 H 4 = 0.15 time, f imdal plyethylee icreases, hile ad I f imdal plyethylee decrease. It demstrates that the mass average mlecular mass ad melt idex f cplymer prduced i the secd reactr plays a sigificat rle the mass average mlecular mass ad melt idex f imdal plyethylee ad the umer average mlecular mass f hmplymer prduced i the first reactr maes ctriuti t the umer average mlecular mass f imdal plyethylee. Additially, he hydrge/ethylee mlar flrate rati icreases i the first reactr ad remais uchaged i the secd reactr, ad f imdal plyethylee decrease, ad I f imdal plyethylee icreases due t a itesificati f hydrge chai trasfer. The higher the hydrge/ethylee ml rati f the first reactr t the secd reactr is, the rader is the D f imdal plyethylee. 3.3 Effect f the cmmer ifl rate Ather simulati is carried ut varyig the

9 858 Chi. J. Chem. Eg., Vl. 21, N. 8, August 2013 Tale 9 Summary f simulati fr the effect f cmmer fl rate 1-utee/ethylee (mlar rati) I PD v /% (y mle) 2 v 2/% (y mle) ρ/g cm utee ilet ccetrati. The results are depicted i Tale 9. It as served that the average 1-utee mle fracti i the cplymer prduced i the secd reactr ad i the cmpsite prduct icreased ith higher 1-utee t ethylee mlar rati (i.e., the cmmer ccetrati icreases). As expected, plyethylee desity decreases ith the additi f 1-utee. I idustrial practice, this is the mai variale maipulated t ctrl plymer desity. Icreasig 1-utee ccetrati i the secd reactr gives higher 1-utee icrprati i the cplymer. Als the cplymer mlecular mass is see t e decreased y icreasig 1-utee ccetrati. The cmmer ehaces trasfer reacti rate. The small effect f the cmmer ccetrati the plydispersity idex ca e attriuted t the simultaeus reducti i th mass-average mlecular mass ad umer-average mlecular mass. 4 CONCLUSIONS A five-site cmprehesive mathematical simulati mdel fr the plymerizati f ethylee ith multiple site crdiati catalysts at steady state i a prcess ith t CSTRs peratig i series has ee develped. The predictis fr mlecular mass ad plydispersity, melt idex, desity ad average cmmer icrprati are i gd agreemet ith plat data. O this asis, the effects f catalyst fl rate, ethylee ad hydrge ml rati ad cmmer ifl rate the mlecular mass, plydispersity ad plymer prperties such as melt idex ad desity ere simulated usig this mdel. (1) As the catalyst fl rate icreases, catalyst mea residece time ad catalyst mea yield decrease, ad icrease, the mass fracti f the l mlecular mass hmplymer decreases, hile the mass fracti f the high mlecular mass cplymer icreases. (2) Whe hydrge/ethylee mlar fl rate rati icreases i the first reactr ad decreases i the secd reactr at the same time, f imdal plyethylee icreases, hile ad I f imdal plyethylee decrease. Whe hydrge/ethylee mlar fl rate rati icreases i the first reactr ad des t chage i the secd reactr, ad f imdal plyethylee decrease, ad I f imdal plyethylee icreases. The higher the hydrge/ethylee mlar rati f the first reactr t the secd reactr is, the rader is the WD f imdal plyethylee. (3) The cplymer mlecular mass is decreased ith icreasig 1-utee ccetrati. The additi f 1-utee results i the decrease f plyethylee desity. NOENCLATURE C d D rmalized ccetrati f dead sites rmalized ccetrati f dead chais f legth at site E geeric distriuti represetati I melt idex, g (10 mi) 1 1 rate cstat, L ml - 1 s [ i ] s sred ccetrati f mmer i at the catalyst sites, ml L 1 mlecular mass, g ml 1 average mlecular mass, g ml 1 N site umer f sites N m umer f mmers chai legth umer-average chai legth at site mass-average chai legth at site P 0 rmalized ccetrati f vacat sites f type P i, rmalized ccetrati f sites f type ad chai legth edig i mmer i q cat catalyst mass fl rate t reactr, g s 1 R Pi 1 ietic rate f mass csumpti f mmer i, g (g cat.) 1 s t chrlgical time, s V R reactr vlume, m 3 f mass fracti f plymer ith differet mlecular mass Ti mass fracti f titaium i the catalyst s,r slids mass fracti i reactr i plymer mass fracti prduced i reactr i x Ti fracti f titaium atms that are catalyst sites, dimesiless Y plymer plyethylee yield, g (g cat.) 1 Y mea yield f plymer plyethylee, g (g cat.) 1 Y 1, Y 2 yield f mmer 1,2 i plymer μ 0 rmalized zerth mmet f all plymer chais at site average cmmer ctet i plymer (mlar fracti) v 2

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