Polymers
The inclusion of the PC-SAFT equation of state in Multiflash extended Multiflash applications to the calculation of the phase behaviour of polymers, solvents and gases. PC-SAFT is a complex equation and to be able to develop a robust implementation capable of predicting multiple phases is unusual. Owing to the high molecular weight, and correspondingly low mole fractions, of polymers in solution considerable effort has gone into improving the phase algorithms in Multiflash, but we are aware that further improvements may be necessary.
Data input
It will not be apparent to the user, but we have re-structured the pure component databanks to provide a more flexible structure. This will allow storage of the data required for new models, such as PC-SAFT. Although we made these changes in Multiflash 3.3 we have not yet included any data for polymer components. At present these need to be created using the Multiflash User Defined component route (Select/Components) and either saved as part of a complete .mfl file or a partial file containing the polymer data only.
The required input data are:
- Critical temperature (TCRIT),
- critical pressure (PCRIT),
- acentric factor (ACENTRICFACTOR),
- PC-SAFT parameters (SAFTEK, SAFTSIGMA, SAFTM, SAFTKAPPA, SAFTEPSILON, SAFTFF)
- Ideal gas Cp (CPIDEAL).
Users should note that TCRIT, PCRIT and ACENTRICFACTOR are necessary to generate starting values for flash calculations but do not affect the computed results from PC-SAFT. Also SAFTKAPPA, SAFTEPSILON and SAFTFF are only needed for associating components.
If your system is polydisperse, i.e. has the same polymer but with a range of molecularweight, then you can enter several polymers with varying properties, each called by a different name. This is analogous to setting up different petroleum fractions, although we do not yet have a facility to help the user set up the data for polymers.
Polymers are not well defined chemical compounds but rather a distribution of chain molecules of varying molecular weight. In Multiflash, polymers must be represented by one or more pseudocomponents which must be set up as user-defined components.
Using PC-SAFT, every pseudocomponent for a given polymer must be assigned the same values of the pure-compound parameters SAFTSIGMA (in metres, not Ångstrom units) and SAFTEK. In addition, the SAFTM parameter must be specified. This is normally quoted as a ratio to the molecular weight, so it has to be calculated for each polymer pseudocomponent knowing the molecular weight. For polystyrene, for example, Gross and Sadowski give the ratio as 0.019, so for a polystyrene pseudocomponent of molecular weight 100000, the SAFTM parameter should be set to 100000´0.019=1900, etc.
Our example polymer.mfl describes a simple binary of polystyrene plus butane. The required properties of polystyrene are included in the input file, as are the pure component SAFT parameters for butane. Load the input file in the normal way and carry out a P,T flash at the input conditions supplied. The results show a liquid-liquid split as expected.
Flash at fixed P and T:
T (degC) = 100.000 P (bar ) = 16.5000
NO. PHASES = 2 CONVERGED STABLE
COMPONENT OVERALL PHASE1 PHASE2
LIQUID1 LIQUID2
fractions fractions fractions
POLYSTYRENE 5.811926E-05 1.929234E-04 0.00000
BUTANE 0.999942 0.999807 1.00000
Total(mole ) 13.7648 4.14672 9.61808
Z (Fug. Model) 7.169292E-02 8.439547E-02 6.621636E-02
Av.Mol.Wt. 72.6486 106.342 58.1222
Den/V(m3/mol ) 1.348054E-04 1.586902E-04 1.245077E-04
H ( J/mol ) -13263.9 -21431.2 -9742.64
S ( J/mol/K ) -49.0432 -59.5252 -44.5240
U ( J/mol ) -13486.3 -21693.0 -9948.07
G ( J/mol ) 5036.61 780.678 6871.50
Cp (J/mol/K ) 179.968 171.105 183.790
Cv (J/mol/K ) 122.249 128.749 119.446
Sp.Sound (m/s) 529.028 726.610 495.635
You can also carry other flashes, such as a bubble point calculation
Bubble point at fixed T:
T (degC) = 100.000 P (bar ) = 15.3038
NO. PHASES = 3 CONVERGED STABLE
COMPONENT OVERALL PHASE1 PHASE2 PHASE3
GAS LIQUID1 LIQUID2
fractions fractions fractions fractions
POLYSTYRENE 5.811926E-05 0.00000 1.952548E-04 0.00000
BUTANE 0.999942 1.00000 0.999805 1.00000
Total(mole ) 13.7648 0.00000 4.09721 9.66759
Z (Fug. Model) 6.658870E-02 0.747584 7.855970E-02 6.151529E-02
Av.Mol.Wt. 72.6486 58.1222 106.925 58.1222
Den/V(m3/mol ) 1.349946E-04 1.515568E-03 1.592632E-04 1.247093E-04
H ( J/mol ) -13257.1 5731.67 -21571.6 -9733.42
S ( J/mol/K ) -48.9820 -3.01468 -59.6532 -44.4594
U ( J/mol ) -13463.7 3412.28 -21815.3 -9924.28
G ( J/mol ) 5020.47 6856.60 688.030 6856.60
Cp (J/mol/K ) 180.470 134.436 171.258 184.374
Cv (J/mol/K ) 122.227 110.641 128.841 119.424
Sp.Sound (m/s) 525.896 183.460 726.936 492.955
PC-SAFT has two interaction parameters. No interaction parameters for PC-SAFT are stored, both are set to zero by default. As with all Multiflash models it is possible for the user to enter BIPs through the Tools/BIP command or as part of the input file. As with CPA, in most cases it is the parameter, SAFTBIP, that is adjusted. As the polymer is involatile, changing the BIP may affect the phase distribution and phase compositions more than the bubble point prediction. The result of altering the SAFTBIP from 0.0 to .05 for our sample system is shown below
Bubble point at fixed T:
T (degC) = 100.000 P (bar ) = 15.3038
NO. PHASES = 3 CONVERGED STABLE
COMPONENT OVERALL PHASE1 PHASE2 PHASE3
GAS LIQUID1 LIQUID2
fractions fractions fractions fractions
POLYSTYRENE 5.811926E-05 0.00000 0.00000 1.866587E-03
BUTANE 0.999942 1.00000 1.00000 0.998133
Total(mole ) 13.7648 0.00000 13.3362 0.428590
Z (Fug. Model) 6.804944E-02 0.747584 6.151529E-02 0.271370
A slightly more complex system, polymer2.mfl, shows the unusual ability of Multiflash to deal with complex systems. In this example pentane replaces Butane as a solvent and we introduce the styrene monomer as a fourth component. In this case a bubble point calculation predicts the presence of four phases.
Bubble point at fixed T:
T (degC) = 100.000 P (bar ) = 6.97611
NO. PHASES = 4 CONVERGED STABLE
COMPONENT OVERALL PHASE1 PHASE2 PHASE3 PHASE4
GAS LIQUID1 LIQUID2 WATER
fractions fractions fractions fractions fractions
POLYSTYRENE 0.125346 0.00000 0.311710 0.00000 0.00000
PENTANE 0.622376 0.705195 0.512945 0.751494 1.449821E-03
STYRENE 0.195825 0.257754 0.163480 0.234856 1.446265E-03
WATER 5.645317E-02 3.705082E-02 1.186577E-02 1.364953E-02 0.997104
Total(g ) 1595.59 0.00000 641.622 883.356 70.6098
Z (Fug. Model) 2.604256E-02 0.867031 3.468028E-02 2.874048E-02 4.622900E-03
The series of papers by Sadowski et al, detailed in the "Models and Physical Properties Guide”, are a useful source of input parameters for PC-SAFT for several polymers.
N.B. Occasionally the phase labels, LIQUID1 and LIQUID2 may be interchanged. If this causes confusion they can be forced to stay the same by defining a key components for one of the liquid phases. A useful options is to set
Key liquid2 heaviest;
Until the advent of PC-SAFT, Flory-Huggins was sometimes used for polymer calculations. This is still possible but not recommended. To apply the Flory Huggins model, in addition to the critical parameters required by the Multiflash algorithms the additional data needed are: vapour pressure (PSAT), saturated liquid density (LDENS), solubility parameter (SOLUPAR) and molar volume at 25°C (V25).
Estimated properties have been included in the file polymer3.mfl for polystyrene and the predicted bubble point for the polystyrene-butane binary shown below.
Bubble point at fixed T:
T (degC) = 100.000 P (bar ) = 13.3448
NO. PHASES = 2 CONVERGED STABLE
COMPONENT OVERALL PHASE1 PHASE2
GAS LIQUID1
fractions fractions fractions
POLYSTYRENE 0.800000 0.00000 0.800000
BUTANE 0.200000 1.00000 0.200000
Total(kg ) 1.00000 0.00000 1.00000
Z (Fug. Model) 0.146040 1.00000 0.146040
Co-Polymers
PC-SAFT can also be applied to co-polymers. Multiflash allows the user to define up to four polymer segments which can be used to define any number of homopolymers or copolymers. If the polymer is formed from only one type of segment, it is a homopolymer of that segment; if it is formed of two or more types of segment, it is a copolymer.
We will look at an example where the constituent segments are ethylene and propylene (PE and PP). The appropriate PC-SAFT parameters were taken from papers by Sadowski et al as are the BIPs A co-polymer structure (PEP1) has to be defined. The physical properties of the co-polymer must also be defined. The MW, Tc, Pc and acentric factor are required although the latter three are only used as starting values and arbitrary numbers may be assigned as long as Tc is high and Pc very low in line with the low volatility of polymers.. Next a “template” has to be created to indicate the structure of the co-polymer. In this example there are regular alternating ethylene and propylene segments.
The bond structure is generated through Tools/Pure component/SAFT bond fractions.
The names of the constituent segments are entered as shown. The pattern of bond fractions is that for an alternating co-polymer. A random co-polymer would have a bond fraction pattern
| Bond Fracs | |
| 0.25 | |
| 0.5 | 0.25 |
Our input file, copol.mfl, has a co-polymer with a MW of 96400 g/mol. It is present at 15 wt% in a solvent, 1-butene, at 85 wt%. Calculation of the polymer cloud point is a difficult calculation. You can calculate this using a series of P,T flashes to see, for a given temperature, the pressure at which a second liquid phase appears or disappears. Another useful technique is to set the temperature of interest and calculate a bubble point. If you only have a gas and one liquid phase then changing the pressure will not result in a liquid liquid separation. If at the bubble point you have gas and two liquid phases
Bubble point at fixed T:
T (degC) = 100.000 P (bar ) = 17.9719
NO. PHASES = 3 CONVERGED STABLE
COMPONENT OVERALL PHASE1 PHASE2 PHASE3
GAS LIQUID1 LIQUID2
fractions fractions fractions fractions
1-BUTENE 0.850000 1.00000 1.00000 0.647845
PE 0.00000 0.00000 0.00000 0.00000
PP 0.00000 0.00000 0.00000 0.00000
PEP1 0.150000 0.00000 0.00000 0.352155
Total(g ) 1.00000 0.00000 0.574052 0.425948
then you can calculate the cloud point, the point at which a second liquid phase appears, using the fixedphase fraction flash at specified T. The solution type should be set to “unspecified” and it may sometimes be necessary to use starting values.
Fixed Phase Fraction Flash - at specified T (Mole Fraction):
T (degC) = 100.000 P (bar ) = 82.8188
NO. PHASES = 2 CONVERGED STABLE
COMPONENT OVERALL PHASE1 PHASE2
LIQUID1 LIQUID2
fractions fractions fractions
1-BUTENE 0.850000 0.850000 0.999245
PE 0.00000 0.00000 0.00000
PP 0.00000 0.00000 0.00000
PEP1 0.150000 0.150000 7.552029E-04
Total(g ) 1.00000 1.00000 0.00000
A complex picture of the phase behaviour of co-polymers of the same type but differing molecular weight can be built up as shown in the following figure.
To specify the co-polymers of differing MW you need only change the MW using Tools/Pure Component properties, all other SAFT properties remain the same. In MF3.4 changing the co-polymer MW also changed the overall composition. From MF3.5, provided the overall composition is specified in mass, this will remain the same even if the co-polymer MW is varied.