Thermodynamics & Properties Lab. 1

Equation of State Modeling of Phase Equilibriumin the Low-Density Polyethylene Process

Yong Soo KimThermodynamics & Properties Lab.

Chemical and Biological Engineering, Korea Univ.

H. Orbey, C. P. Bokis, and C. C. ChenInd. Eng. Chem. Res. 1998, 37, 4481-4491

Thermodynamics & Properties Lab. 2

Contents

Introduction LDPE process Modeling by Equation of State

Application of the Equation of state(EOS)• Sanchez-Lacombe Lattice model(SL model)• Statistical Associating Fluid Theory (SAFT)• Polymer-SRK Equation of State

Determination of pure component parameters Correlation of Binary VLE of ethylene-LDPE mixture

Simulation of Flash Operations in the LDPE process Conclusion

Thermodynamics & Properties Lab. 3

LDPE Process

Bernard et al., ”Phase Equilibrium in High-Pressure Polyethylene technology”, I&EC, 1995, 34, 1501-1516

Thermodynamics & Properties Lab. 4

Modeling by Equation of State

Characteristics of LDPE process Highly non-ideal at high pressure Difference in size between polymer and solvent Broad molecular weight distribution Existence of variable multi-phase

Advantage on using equation of state Application to the region between low pressure to supercritical

condition Unified method to predict the behavior of multi-phase equilibria Ability of describing volumetric, calorimetric and phase

equilibrium properties at the same time

Thermodynamics & Properties Lab. 5

Sanchez-Lacombe Lattice Model (SL model)

Pressure

Parameters and mixing rule

0~11~1ln(~~~ 2 =

−+−++ ρρρ

rTP

***~~~

ρρρ ===

PPP

TTT with

**

*

**

**

rvM

vP

kT === ρεε

===i i

i

mixi jijijji

mixmix

i jijjimix rr

vv

vvφεφφεφφ 11 **

****

=

j jj

j

ii

ii v

w

vw

**** ρρφ ( )( ) 21***

ijjjiiij lvvv −+= ( )ijjjiiij k−= 1*** εεε

Thermodynamics & Properties Lab. 6

Statistical Associating Fluid Theory (SAFT)

Compressibility factorassocchaindisphs ZZZZ

RTPvZ ++++== 1

−−+

−+

−= 3

3

323

23

21

3

30

)1()3(

)1(3

16

ξξξ

ξξξ

ξξξ

ρπ Ahs N

Z

( ) ( ) =n m

mcp

nnmdisp kTumDrZ 33 // ξξ

−=i iiichain dLrxZ )()1(

( )( )[ ] ∂∂−= ρρ /2/1/1 ii SSiassoc XXxZ

( ) 11

−

+=j Y ij

YjA

S

j

ji WXxNX ρ

Thermodynamics & Properties Lab. 7

Statistical Associating Fluid Theory (SAFT)

Parameters

074048.0 mvρη =30

000 3exp1

−−=kT

uCvv

+=

kTeuu 10

Mixing rule

( )3

3/103/100 )()(21

+= jiij vvv ( ) 2/1)1( jjiiijij uuku −=

=

i jijjiji

i jij

ijjiji

vmmxx

vkTu

mmxx

kTu

)(

)(

0

0

=i j

ijji mxxm

)1(2

)(ij

jiij l

mmm −

+=

Thermodynamics & Properties Lab. 8

Polymer-SRK Equation of State

Pressure

For polymer

)()(bVV

TabV

RTP+

−−

= withc

c

PRT

b 08664.0=

235.03

25.02

5.01 ])1()1()1(1[ RRR TCTCTC −+−+−+=α

αc

c

PTR

a22

42748.0=and

25.01

13001300

Pm

c

Pc

DTT

=−−

T in Kelvin P

mc

Pc

DPP 1

55

=−− P in bar and

Parameters and mixing rulemonomer

nP M

MD =

=i

iibxb

+−=

i i ii

ex

i

ii b

bxRTG

RTba

xbRT

a ln546.1

Thermodynamics & Properties Lab. 9

Determination of Pure Component Parameters

Ethylene Using the vapor pressure and saturated liquid and vapor density All models should represent the behavior of supercritical region.

Thermodynamics & Properties Lab. 10

Determination of Pure Component Parameters

Polyethylene All models should represent properties for a different number-

average molecular weight

Thermodynamics & Properties Lab. 11

Determination of Pure Component Parameters

Thermodynamics & Properties Lab. 12

Correlation of Binary VLE of ethylene-LDPE mixture

SAFT model The difference between using

two binary parameters versus one binary parameter is not very noticeable.

Thermodynamics & Properties Lab. 13

Correlation of Binary VLE of ethylene-LDPE mixture

SL model For using two binary parametes the model is capable of

representing the high-pressure region better.

Thermodynamics & Properties Lab. 14

Correlation of Binary VLE of ethylene-LDPE mixture

Polymer –SRK model Using one binary parameter

the model represents the VLE behavior quite accurately

Thermodynamics & Properties Lab. 15

Simulation of Flash Operations in the LDPE process

The estimation of the amount of monomer left in the final product

Polymer residues in vapor phase => Flugging in recycle

Thermodynamics & Properties Lab. 16

Simulation results

Thermodynamics & Properties Lab. 17

Conclusion

SAFT model is the most convenient from the point of availability of segment-based pure component parameters.

For polymer-SRK we had to devise a method for the model parameters as a function of molecular size.

For SL model a general method of estimation of pure component parameters is necessary for which no data exists.

In general, for the polymeric molecules EOSs are very capable of prediciting the behavior of phase equilibria, yet they have some shortcomings in important areas such as the critical region.