Perturbed-Chain SAFT Equation Of State Research Articles

Equation-Oriented Approach for Handling the Perturbed-Chain SAFT Equation of State in Simulation and Optimization of Polymerization Processes

The perturbed-chain SAFT (PC-SAFT) equation of state (EOS) is a very popular and promising model for fluids. Resolution of the PC-SAFT EOS is generally conducted by subroutine-based calculations that involve logical conditions. This approach can lead to nonsmoothness and convergence issues when used with gradient-based solvers in an equation-oriented (EO) framework. In this paper, we propose a novel EO approach for the PC-SAFT EOS embedded in large flowsheet optimization. First, the mathematical structure of the PC-SAFT EOS is analyzed through a digraph. It reveals that for polymerization systems, resolution of the PC-SAFT EOS is coupled not only by phase equilibrium but also by the polymerization kinetics. This feature strongly motivates implementation of both EOS resolution and process optimization in a complete EO framework. A novel EO approach is proposed for selecting the appropriate root of the PC-SAFT EOS by incorporating thermal stability criteria to eliminate the undesirable roots. Numerical exam...

Modeling natural gas-carbon dioxide system for solid-liquid-vapor phase behavior

With the shale gas boom, natural gas has become one of the main energy sources in the United States. But in the cryogenic processes of this natural gas, the formation of solid carbon dioxide remains a concern because it can cause the blockage of equipment. Accurately modeling the rich phase behavior of carbon dioxide in methane is helpful for optimizing the industrial processes, especially where experimental data are lacking at the operation conditions. In this work, the Perturbed Chain-SAFT (PC-SAFT) equation of state is applied to model the phase behavior of hydrocarbon (i.e., methane, ethane, butane) + carbon dioxide systems over a wide range of temperatures and pressures. It is observed that the PC-SAFT equation of state can accurately predict the vapor-liquid equilibria (VLE), solid-vapor equilibria (SVE), and solid-liquid equilibria (SLE) of hydrocarbon + carbon dioxide systems using a single set of temperature and pressure independent binary interaction parameters. In the end, the effect of addition of ethane and butane on SLE of methane + carbon dioxide is also investigated which has applications in reducing the carbon dioxide solidification conditions.

Vapor–liquid equilibrium of copolymer + solvent mixtures: Thermodynamic modeling by two theoretical equations of state

Copolymers are increasing their importance from the commercial point of view, mainly due to their tuned physical properties for specific applications in the polymer manufacturing. Copolymers allow tailoring new materials with desirable features by blending specific copolymers, which contribute for the physical properties of the final material. The description of the fluid-phase equilibrium of copolymer + solvent mixtures by thermodynamic models is essential for the design of new manufacture processes. In this work, vapor–liquid equilibrium data for several copolymer + solvent mixtures were modeled using two theoretical equations of state: one based on the lattice gas theory (LGT) and another one based on the statistical association fluid theory, called perturbed chain-SAFT (PC-SAFT). The results show that the PC-SAFT equation of state provides a better representation of the experimental data in terms of pressure deviations.

Modeling the thermodynamic behavior of poly(lactide-co-glycolide) + supercritical fluid mixtures with equations of state

In this work, the thermodynamic behavior of binary systems composed by one commercial biodegradable copolymer [poly( d, l-lactide-co-glycolide)] and supercritical fluids, SCF, (dimethyl ether, carbon dioxide, chlorodifluoromethane and trifluoromethane) was studied. The perturbed chain-SAFT (PC-SAFT) and the Sanchez–Lacombe (SL) non-cubic equations of state (EoS) were used to model the fluid–liquid equilibrium (FLE) for these binary systems, by fitting one temperature-dependent binary interaction parameter. For comparison, the same data were also modeled by using the traditional Peng–Robinson (PR) cubic EoS. The three PC-SAFT and SL pure-component parameters and two PR pure-component parameters were regressed by fitting pure-component data (liquid pressure–volume–temperature, PVT, data for copolymer and saturated liquid vapor pressure and molar volume for SCF). Liquid PVT data of PLAG copolymers were estimated by using a group contribution method, taken from literature. The estimation of pure-component and binary interaction parameters was performed by using the modified maximum likelihood method with an objective function that includes the cloud point pressure. An excellent agreement was obtained with the PC-SAFT EoS, while the performance of the SL and PR EoS were less satisfactory.

Modeling of Polar Systems with the Perturbed-Chain SAFT Equation of State. Investigation of the Performance of Two Polar Terms

The Perturbed-Chain SAFT (PC-SAFT) equation of state is applied to model phase equilibria and the thermodynamic properties of ethers and esters. A systematic study of these two homologous series is conducted, and the performance of two different approaches for including the dipolar interactions in the equation of state is evaluated. Although both Polar PC−SAFT [dipolar contribution due to Jog and Chapman, Mol. Phys. 1999, 97, 307−319] and PC−SAFT + Fischer [dipolar contribution by Saager and Fischer, Mol. Simul. 1991, 6, 27−49] yield similar results for the considered systems, the parameters of Polar PC−SAFT are more physically meaningful than those of PC−SAFT + Fischer. Consequently, Polar PC−SAFT is considered to be more suitable for extrapolations, and for application to components that have multiple polar groups in the chain.

Vapor–liquid equilibria of nitrogen–hydrocarbon systems using the PC-SAFT equation of state

Enhanced oil recovery by nitrogen injection is a tertiary oil recovery method that is actually used in certain Mexican fields. In order to describe or predict the process of nitrogen flooding by reservoir simulation, the phase behavior of nitrogen–oil systems has to be known. In this work, the perturbed-chain SAFT (PC-SAFT) equation of state was applied to the calculation of the vapor–liquid equilibria of nitrogen–hydrocarbon systems by using conventional one-fluid mixing rules. The binary interaction parameters, introduced in this equation to correct the segment–segment interactions of unlike chains, were estimated by minimizing the sum of squared relative deviations of bubble point pressures and the sum of squared deviations in mole fraction of phase equilibrium compositions. The calculation of the phase equilibria was carried out by minimization of the Gibbs free energy using stability tests to find the most stable state of the system. On the whole, the results show that the quality of the fit with the experimental data is good for most systems studied. Satisfactory predictions of the vapor–liquid equilibria of nitrogen-containing ternary and quaternary systems were obtained by using a generalized N 2- n-alkane binary interaction parameter for normal paraffins between methane and n-hexatriacontane.

Application of the Perturbed-Chain SAFT equation of state to polar systems

The Perturbed-Chain SAFT (PC-SAFT) equation of state is applied to pure polar substances as well as to vapor–liquid and liquid–liquid equilibria of binary mixtures containing polar low-molecular substances and polar co-polymers. For these components, the polar version of the PC-SAFT model requires four pure-component parameters as well as the functional-group dipole moment. For each binary system, only one temperature-independent binary interaction k ij is needed. Simple mixing and combining rules are adopted for mixtures with more than one polar component without using an additional binary interaction parameter. The ability of the model to accurately describe azeotropic and non-azeotropic vapor–liquid equilibria at low and at high pressures, as well as liquid–liquid equilibria is demonstrated for various systems containing polar components. Solvent systems like acetone–alkane mixtures and co-polymer systems like poly(ethylene-co-vinyl acetate)/solvent are discussed. The results for the low-molecular systems also show the predictive capabilities of the extended PC-SAFT model.

Modeling Copolymer Systems Using the Perturbed-Chain SAFT Equation of State

The perturbed-chain SAFT equation of state is extended to heterosegmented molecules and is applied to copolymers with a well-defined (alternating) repeat-unit sequence as well as to systems with a statistical sequence of the monomers in the backbone. Copolymers with a statistical sequence of the constituting repeat units usually require an assumption on the sequence of neighboring repeat units within the chain. A simple approach for defining such repeat-unit arrangements is proposed. Systems containing polyolefine copolymers (poly(ethylene-co-propylene) and poly(ethylene-co-1-butene)) covering the complete range of copolymer composition (including both of the appropriate homopolymers) were modeled in a mixture with solvents. Good results were found for mixtures of copolymer/solvent systems using constant interaction parameters. Copolymers comprising both nonpolar and polar repeat units, for example, poly(ethylene-co-vinyl acetate) and poly(ethylene-co-methyl acrylate), require an interaction parameter cor...

Application of the Perturbed-Chain SAFT Equation of State to Associating Systems

The perturbed-chain SAFT (PC−SAFT) equation of state is applied to pure associating components as well as to vapor−liquid and liquid−liquid equilibria of binary mixtures of associating substances. For these substances, the PC−SAFT equation of state requires five pure-component parameters, two of which characterize the association. The pure-component parameters were identified for 18 associating substances by correlating vapor pressure and liquid density data. A comparison to an earlier version of SAFT confirms the good results for pure substances. When only one associating compound is present in a mixture, the PC−SAFT equation of state does not require mixing rules for the association term. Using one binary interaction parameter kij for the dispersion term only, the model was applied to azeotropic and nonazeotropic vapor−liquid equilibria at low and at high pressures, as well as to liquid−liquid equilibria. Simple mixing and combining rules were adopted for mixtures with more than one associating compound, introducing no additional binary interaction parameter. The simultaneous description of liquid−liquid and vapor−liquid equilibrium was also possible with a single kij parameter.