Equation of State Modeling of Phase Equilibrium in the Low-Density Polyethylene Process

Transcription

1 Equaton of State Modelng of Phase Equlbrum n the Low-Densty Polyethylene Process H. Orbey, C. P. Boks, and C. C. Chen Ind. Eng. Chem. Res. 1998, 37, Yong Soo Km Thermodynamcs & Propertes Lab. Chemcal and Bologcal Engneerng, Korea Unv. Thermodynamcs & Propertes Lab. 1

2 Contents Introducton LDPE process Modelng by Equaton of State Applcaton of the Equaton of state(eos) Sanchez-Lacombe Lattce model(sl model) Statstcal Assocatng Flud Theory (SAFT) Polymer-SRK Equaton of State Determnaton of pure component parameters Correlaton of Bnary VLE of ethylene-ldpe mxture Smulaton of Flash Operatons n the LDPE process Concluson Thermodynamcs & Propertes Lab. 2

3 LDPE Process Bernard et al., Phase Equlbrum n Hgh-Pressure Polyethylene technology, I&EC, 1995, 34, Thermodynamcs & Propertes Lab. 3

4 Modelng by Equaton of State Characterstcs of LDPE process Hghly non-deal at hgh pressure Dfference n sze between polymer and solvent Broad molecular weght dstrbuton Exstence of varable mult-phase Advantage on usng equaton of state Applcaton to the regon between low pressure to supercrtcal condton Unfed method to predct the behavor of mult-phase equlbra Ablty of descrbng volumetrc, calormetrc and phase equlbrum propertes at the same tme Thermodynamcs & Propertes Lab. 4

5 Sanchez-Lacombe Lattce Model (SL model) Pressure ~ 2 ~ ~ ~ 1 ln(1 1 ~ ρ + P + T ρ + ρ = 0 r ~ T ~ P ~ ρ T = P = ρ = wth T P ρ Parameters and mxng rule v mx = ε ε T = P = ρ = k v φφ v ε mx = φφ ε v = v 1 mx r 1 mx φ r M rv ρ v w φ = ( v = v + v )( 1 l ) 2 ε = ε ε ( 1 k ) w ρ v Thermodynamcs & Propertes Lab. 5

6 Statstcal Assocatng Flud Theory (SAFT) Compressblty factor Pv Z = = 1+ Z hs + Z dsp + Zchan + Z assoc RT 3 6 ξ 0ξ 3 3ξ 1ξ 2 (3 ξ3) ξ2 Zhs = πn A ρ 1 ξ3 (1 ξ3) (1 ξ3) n ( u / kt ) ( ξ ξ ) Z = r md 3 / 3 dsp n m nm Z = x (1 r ) L( d ) Z chan assoc cp ( 1/ X 1/ 2)( ) S S X [ ] x = ρ / ρ m X S = ( ) Y 1+ N x ρx W 1 A Y Thermodynamcs & Propertes Lab. 6

7 Statstcal Assocatng Flud Theory (SAFT) Parameters η = ρmv Mxng rule 0 v 1 C exp = v u kt 0 3 = 0 e u u 1 + kt ) 3 0 1/ 3 0 1/ 3 ( v ) + ( v ) v ( ) 1/ 2 u kt = = x x x m m x m m u kt ( v u = ( 1 k ) uu ( v 0 ) 0 ) m = m x ( m = x m + m 2 ) (1 l ) Thermodynamcs & Propertes Lab. 7

8 Polymer-SRK Equaton of State Pressure P RT a( T) V b V ( V + b) = wth For polymer T T P c m c 1300 = 1300 D P α = T n Kelvn Parameters and mxng rule b = a brt = x b a b = RT P c c and R T a = P [ 1+ C1 (1 TR ) + C2 (1 TR ) + C3(1 TR ) ] G P c m c P 5 = 1 P 5 D x x ln RTb RT b ex P b P n bar and D = Thermodynamcs & Propertes Lab. 8 P M 2 M c n 2 c monomer α

9 Determnaton of Pure Component Parameters Ethylene Usng the vapor pressure and saturated lqud and vapor densty All models should represent the behavor of supercrtcal regon. Thermodynamcs & Propertes Lab. 9

10 Determnaton of Pure Component Parameters Polyethylene All models should represent propertes for a dfferent numberaverage molecular weght Thermodynamcs & Propertes Lab. 10

11 Determnaton of Pure Component Parameters Thermodynamcs & Propertes Lab. 11

12 Correlaton of Bnary VLE of ethylene-ldpe mxture SAFT model The dfference between usng two bnary parameters versus one bnary parameter s not very notceable. Thermodynamcs & Propertes Lab. 12

13 Correlaton of Bnary VLE of ethylene-ldpe mxture SL model For usng two bnary parametes the model s capable of representng the hgh-pressure regon better. Thermodynamcs & Propertes Lab. 13

14 Correlaton of Bnary VLE of ethylene-ldpe mxture Polymer SRK model Usng one bnary parameter the model represents the VLE behavor qute accurately Thermodynamcs & Propertes Lab. 14

15 Smulaton of Flash Operatons n the LDPE process The estmaton of the amount of monomer left n the fnal product Polymer resdues n vapor phase => Fluggng n recycle Thermodynamcs & Propertes Lab. 15

16 Smulaton results Thermodynamcs & Propertes Lab. 16

17 Concluson SAFT model s the most convenent from the pont of avalablty of segment-based pure component parameters. For polymer-srk we had to devse a method for the model parameters as a functon of molecular sze. For SL model a general method of estmaton of pure component parameters s necessary for whch no data exsts. In general, for the polymerc molecules EOSs are very capable of predctng the behavor of phase equlbra, yet they have some shortcomngs n mportant areas such as the crtcal regon. Thermodynamcs & Propertes Lab. 17