Modeling of solid–liquid equilibria for polyethylene and polypropylene solutions with equations of state

Abstract

ABSTRACT:We modeled solid-liquid equilibria (SLEs) in polyethylene and polypropylene solutions with a Soave-Redlich-Kwong (SRK) cubic equation of state (EOS) and a perturbed-chain statistical associating fluid theory (PC-SAFT) EOS. Two types of mixing rules were used with SRK EOS: The Wong-Sandler mixing rule and the linear combination of the Vidal and Michelsen mixing rules (LCVM), both of which incorporated the Bogdanic and Vidal activity coefficient model. The performance of these models was evaluated with atmospheric-pressure and high-pressure experimental SLE data obtained from literature. The basic SLE equation was solved for the equilibrium melting temperature instead of for the composition. The binary interaction parameters of SRK and PC-SAFT EOS were estimated to best describe the experimental equilibrium behavior of 20 different polymer-solvent systems at atmospheric pressure and 31 other polymer-solvent systems at high pressure. A comparison with experimental data showed that SRK-LCVM agreed very well with the atmospheric SLE data and that PC-SAFT EOS was more efficient in highpressure conditions.

Investigating the effect of co-catalyst on the final product properties and the yield of ziegler–natta catalyst in propylene polymerization in optimum temperature reaction in absence of hydrogen via mathematical model

“…In this study, the assumptions for modeling are: (1) It was supposed that propylene polymerization was carried out in the amorphous phase (2) the amorphous phase concentrations during polypropylene polymerization were at the thermodynamic equilibrium condition that obeys the one from Sanchez and Lacombe equation (SLE) [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. 2It was assumed that γ1 = γ2 = ••• = γNC, where γ is equilibrium constant and NC are several solvents in slurry phase components [2].…”

Determination of optimal reaction temperature and hydrogen amount for propylene polymerization by a mathematical model

“…The following modelling assumptions were considered: (1) Propylene polymerization is carried out in the amorphous phase, and amorphous phase concentration during polypropylene polymerization is at thermodynamic equilibrium condition that obeys that from Sanchez and Lacombe equation (SLE) for calculating the amount of the hydrogen molar ratio (x = CH/C m ). 14 (2) γ1 = γ2 =.....= γNC, where γ is equilibrium constant, and NC is the number of solvent in slurry phase components. 2 (3) The reaction temperature, pressure, and monomer concentration is kept constant during the polymerization process.…”

Hydrogen effect modeling on Ziegler-Natta catalyst and final product properties in propylene polymerization

“…The following modeling assumptions are considered: (1) It was supposed that propylene polymerization was carried out in the amorphous phase and amorphous phase concentrations during the polypropylene polymerization are at the thermodynamic equilibrium condition that obeys from Sanchez and Lacombe Equation(SLE) [24] for calculating the amount of X = C H / C m , the hydrogen molar ratio. (2) It was assumed that γ 1 = γ 2 = ..... = γ NC .…”