Simplified Perturbed-chain Statistical Associating Fluid Theory Research Articles

Solubility of digitoxin in supercritical CO2: Experimental study and modeling

In this communication, the solubility of digitoxin drug in supercritical CO2 was studied at different operating conditions (311 < T (K) < 343, 120 < P (bar) < 300). The results revealed digitoxin drug solubility (in mole fraction) was between 0.095 × 10−5 to 1.12 × 10−5. In the case of thermodynamic solubility modeling, cubic and non-cubic equation of states i.e. SAFT (statistical associating fluid theory), SRK (Soave-Redlich-Kwong) and sPC-SAFT (simplified perturbed chain SAFT) EoSs and six density-based correlations (Chrastil, Kumar-Johnston (KJ), Mendez-Santiago-Teja (MST), Garlapati and Madras (GM), Bartle et al. and Sung-Shim models) were considered. All used equations indicated reasonable behavior with appropriate accuracy for the solubility of the digitoxin drug. Meanwhile, sPC-SAFT EoS and Kumar-Johnston correlation with AARD% set to 8.96 % and 6.25 %, respectively exhibited greater accuracy in fitting the solubility data. Moreover, total, solvation and vaporization enthalpies of the digitoxin/supercritical carbon dioxide binary mixture were calculated based on KJ, Chrastil and Bartle et al. models.

Measurement and Modeling the Excess Molar Volumes and Refractive Index Deviations of Binary Mixtures of 2-Propanol, 2-Butanol and 2-Pentanol with N-Propylamine

The densities, ρ, and refractive indices, n D, of 2-alkanols (C3–C5) with N-propylamine have been measured for the whole range of composition at temperatures from (298.15–328.15) K at 10 K intervals and ambient pressure of 81.5 kPa, using an Anton Paar DMA 4500 oscillating tube densimeter and an Anton Paar Abbemat 500 automatic refractometer. From the experimental data, excess molar volumes \( V_{\text{m}}^{\text{E}} \) partial molar volumes \( \bar{V}_{i} \) apparent molar volumes V ϕi and refractive index deviations Δn D the binary systems consisting of N-propylamine + 2-alkanols (2-propanol, 2-butanol, 2-pentanol) were calculated and \( V_{\text{m}}^{\text{E}} \) and Δn D values were correlated with the Redlich–Kister polynomial. The effect of temperature and the chain length of the alcohol on the excess molar volumes and refractive index deviations are discussed in terms of molecular interaction between unlike molecules. The excess molar volumes are negative and refractive index deviations are positive over the entire composition range, which indicates strong hydrogen bonding between molecules of the mixtures. A comparative study has been made of the refractive indices obtained experimentally and those calculated by means of the Lorentz–Lorenz, Weiner and Arago–Biot relations. The perturbed chain statistical associating fluid theory (PC-SAFT), simplified PC-SAFT and Prigogine–Flory–Patterson theory were also applied to correlate and predict the density and excess molar volumes of the mixtures.

Modeling the solubility and volumetric properties of H2 and heavy hydrocarbons using the simplified PC-SAFT

The solubility and volumetric properties of H2 and heavy hydrocarbons are important to the design of many chemical processes. In this paper, a simplified Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) is chosen to model the solubility and volumetric properties of H2/heavy alkanes and H2/bitumen mixtures. The number of reduced density roots given by the simplified PC-SAFT is discussed and a robust procedure is employed to solve for the root with the lowest Gibbs free energy. The development of new H2 parameters and the kij correlation of H2-heavy alkane pairs for the simplified PC-SAFT is completed using extensive experimental data. The new parameters are applied with a developed bitumen characterization method to predict H2 solubility in Athabasca Bitumen. The average absolute deviations (AADs) between the measured solubility data and the modeling results are within 0.57% for the five H2/heavy alkane systems and 0.69% for the H2/Athabasca bitumen systems. Finally, the density, thermal expansion coefficient, and compressibility of the systems are predicted over wide ranges of temperature and pressure.

Predicting the multiphase equilibrium and density of bitumen with C2H6, C3H8 and CO2 using the simplified PC-SAFT Equation of State

Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) shows promising prediction results for the vapor–liquid equilibrium and density of many hydrocarbon systems. In this work, a simplified version of PC-SAFT is applied to predict the multiphase equilibrium of bitumen with C2H6, C3H8 and CO2. More specifically, the simplified PC-SAFT and a previously proposed bitumen characterization for vapor–liquid equilibrium (VL2E) modeling are adopted to predict the multiphase boundaries of Athabasca Bitumen and Peace River Bitumen systems. The multiphase boundaries indicate good agreement with the phase boundary data over a wide range of temperature and pressure. In addition, the simplified PC-SAFT and Peng–Robinson Equation of State are applied to predict the mutual solubility and density under liquid–liquid equilibrium (L1L2E) and are tested against the measured data of bitumen and C2H6 system. It has been found that the prediction results by the simplified PC-SAFT are more reliable. The simplified PC-SAFT gives an average absolute relative deviation (AARD) of 13.1% for solubility and an AARD of 3.7% for density, whereas Peng–Robinson Equation of State gives an AARD of 15.7% for solubility and an AARD of 4.2% for density.

Modeling the density, solubility and viscosity of bitumen/solvent systems using PC-SAFT

Abstract Stemming from statistical thermodynamics, Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) shows promising results for predicting phase equilibrium and density for light and heavy oil. In this work, the simplified version of PC-SAFT was applied to model the density and solubility of bitumen/solvent systems and was integrated with the Expanded Fluid Viscosity Theory to predict and match the viscosity of such systems. A simple new eight-pseudo-component characterization method was developed for different Alberta Bitumens using distillation and molar mass data. The proposed characterization method for the simplified PC-SAFT was applied to match the density and solubility data of Athabasca Bitumen with gas alkanes and CO2 and was used to predict the density of Athabasca Bitumen and Peace River Bitumen with liquid solvents (alkanes and aromatics), without further adjustment. Finally, the viscosity of the bitumen and solvent mixtures was predicted and matched using PC-SAFT coupled with the Expanded Fluid Viscosity Model. The overall average absolute relative deviations were within 2.3% for the density of the 13 bitumen/solvent systems, within 6.6% for the solubility of three systems, and 14.6% for the viscosity of eight systems.

Modeling the liquid–liquid equilibrium of petroleum fluid and polar compounds containing systems with the PC-SAFT equation of state

A critical test for the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EOS) is the modeling of systems containing petroleum fluid and polar compounds. In this work, two approaches are proposed for the simplified PC-SAFT EOS to obtain the necessary pure component parameters for the characterized non-associating pseudo-components of petroleum fluids. New pure component parameters of mono-ethylene glycol (MEG) are obtained by considering the liquid–liquid equilibrium (LLE) data of MEG with normal hydrocarbons in the estimation process and a simple binary interaction scheme of MEG with pseudo-components is proposed. These new parameters are applied to model LLE of the systems of petroleum fluid+MEG with or without water. The results show that the simplified PC-SAFT EOS yields promising predictions of the key mutual solubility of these systems: 15–18% overall deviations for the systems of petroleum fluid+MEG and 23–25% overall deviations for the systems of petroleum fluid+MEG+water. The two approaches are further studied in a more theoretical manner to show the relationship between the solubility of petroleum fluid in the polar phase and the PC-SAFT parameter segment diameter.

Binary interaction coefficients of asymmetric CH4, C2H6, and CO2 with high n-alkanes for the simplified PC-SAFT correlation and prediction

The phase equilibrium, density, and viscosity of CH4, C2H6, and CO2 with high n-alkane systems are of particular importance in various industrial processes and design. The binary interaction coefficients (kij) of these systems for the simplified Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) modeling were studied systematically. A new kij correlation on temperature and molecular weight was proposed to compensate the deviations as the simplified PC-SAFT averages the temperature- and molecular weight-dependent segment diameters of the original PC-SAFT. The average absolute relative deviations in pressure by the new correlation was only 3.6% for more than 2000 vapor–liquid equilibrium data, covering 49 binary systems of CH4, C2H6, and CO2 with n-alkanes up to n-C44H90. In addition, the prediction ability of the new correlation was verified by predicting the phase equilibrium and saturated density and viscosity of various high asymmetric systems. The new correlation has increased the prediction accuracy of the simplified PC-SAFT.

Modeling Water Containing Systems with the Simplified PC-SAFT and CPA Equations of State

Numerous studies have been presented for modeling of water containing systems with the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EOS), and more than 20 water parameter sets have been published with emphasis on different applications. In this work, eight of these sets and new estimated parameters with different association schemes are systematically compared on describing properties of pure water, the liquid–liquid equilibria (LLE) of water with hydrocarbons, and the vapor–liquid (VLE) and/or vapor–liquid–liquid equilibria (VLLE) of water with 1-alcohols. An interactive procedure is further proposed for including the LLE of water with hydrocarbons into the pure fluid parameter estimation. The results show that it is possible for PC-SAFT to give an accurate description of the LLE of water and hydrocarbons while retaining satisfactory accuracy for both vapor pressure and saturated liquid density of water. For the aforementioned aqueous systems, the PC-SAFT correlations...

Group Contribution Prediction of Vapor Pressure with Statistical Associating Fluid Theory, Perturbed-Chain Statistical Associating Fluid Theory, and Elliott−Suresh−Donohue Equations of State

The group contribution methodology developed by Elliott and Natarajan has been extended to the statistical associating fluid theory (SAFT) and perturbed-chain statistical associating fluid theory (PC-SAFT) equations of state (EOS). Thermodynamic properties were correlated and predicted for a database of 878 compounds, including associating compounds. Association contributions were treated with Wertheim’s theory. The database covers 19 chemical families including hydrocarbons, cyclic hydrocarbons, aromatic hydrocarbons, alcohols, amines, nitriles, thiols, sulfides, aldehydes, ketones, esters, ethers, halocarbons, and silicones. The present group contribution (GC) method was developed in two stages. Initially, pure component parameters of each EOS were obtained by matching their boiling temperatures at 10 or 760 mmHg and available GC estimates of solubility parameter and liquid density, while applying standard hydrogen-bonding parameters. Then, group contributions were regressed for the shape factor parameters of each EOS. Group contributions are presented for 84 first-order functional groups (FOG). Given the GC shape factors, the same GC estimates of solubility parameter and liquid density can be applied to estimate all EOS parameters on a GC basis. The resulting correlation enables three-parameter corresponding states predictions without any experimental data. A byproduct of the correlation for equation of state parameters is the capability to predict vapor pressure only on the basis of chemical structure. This capability was evaluated by computing the vapor pressures at 10, 100, and 760 mmHg. On the basis of the present work, vapor pressure average absolute percent deviations (P AAD%) were 36% for Elliott−Suresh−Donohue (ESD) EOS, 65% for SAFT, 32% PC-SAFT. For comparison, the first- and second-order groups (FOG and SOG) provided by Tihic et al. (for simplified PC-SAFT) have been applied to ∼650 nonassociating compounds. The resulting P AAD% were 53% for Tihic FOG and 42% for Tihic SOG. An alternative characterization of accuracy is the average absolute deviation (|ΔT|) between experimental and calculated saturated temperature. These were 8, 12, 8, 10, and 9 K for ESD, SAFT, PC-SAFT, Tihic FOG, and Tihic SOG equations, respectively.

A Predictive Group-Contribution Simplified PC-SAFT Equation of State: Application to Polymer Systems

A group-contribution (GC) method is coupled with the molecular-based perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EoS) to predict its characteristic pure compound parameters. The estimation of group contributions for the parameters is based on a parameter database of 400 low-molecular-weight compounds estimated by fitting experimental vapor pressures and liquid densities. The method has been successfully used for estimating the PC-SAFT parameters for common polymers. Specifically, using the new polymer parameters as calculated from the proposed GC scheme, the simplified PC-SAFT yields rather good predictions of polymer densities and gives promising modeling results of various binary polymer mixtures exhibiting both vapor—liquid and liquid—liquid phase equilibria. In summary, the data required for calculating polymer phase equilibria with the proposed method are the molecular structure of the polymer of interest in terms of functional groups and a single binary interaction parameter for accurate mixture calculations.

Applications of the simplified perturbed-chain SAFT equation of state using an extended parameter table

An equation of state based on perturbation theory, the simplified perturbed-chain statistical associating fluid theory (PC-SAFT) is applied to binary systems that include an extensive number of non-associating compounds. Pure-component parameters of different compounds that are not available in the literature are estimated by correlating vapour-pressure and liquid-density data and by using an interpolation method. PC-SAFT parameters for 200 new compounds are estimated for different families of nonassociating compounds (alkanes, alkenes, alkynes, cycloalkenes, nitroalkanes, polynuclear aromatics, ketones, esters, sulphides, siloxanes, plasticizers, cyclo- and fluorinated-hydrocarbons, etc.). For many different families of compounds, the segment diameter and interaction energy are found to be constant with increasing molar mass, while the segment number increases linearly with molar mass. Using these parameters, simplified PC-SAFT is shown to predict vapour–liquid equilibria successfully for many nonassociating systems and also correlates liquid–liquid equilibria for perfluorohexane- n-alkane systems. In a few cases, a small binary interaction parameter k ij is needed for the satisfactory correlation of the experimental data.

Capabilities, limitations and challenges of a simplified PC-SAFT equation of state

PC-SAFT (perturbed-chain statistical associating fluid theory) is a novel equation of state, proposed by Gross and Sadowski in 2001 [J. Gross, G. Sadowski, Perturbed-chain SAFT: an equation of state based on a perturbation theory for chain molecules, Ind. Eng. Chem. Res. 40 (2001) 1244]. It is a variant of the SAFT family and has already found several successful applications, especially for polymer and co-polymer solutions at both low and high pressures. Recently, a simplified version of PC-SAFT proposed by von Solms et al. [N. von Solms, M.L. Michelsen, G.M. Kontogeorgis, Computational and physical performance of a modified PC-SAFT equation of state for highly asymmetric and associating mixtures, Ind. Eng. Chem. Res. 42 (2003) 1098.] has been applied to several complex polymer–solvent systems, including vapor–liquid equilibria, liquid–liquid equilibria and gas solubilities for both single-solvent and mixed-solvents (ternary) systems. This manuscript briefly reviews previous successful applications of PC-SAFT, illustrates the capabilities of the model and indicates some problems and limitations in specific areas, especially aqueous systems and blends, as well as challenges that need to be addressed in the future for describing various systems of practical significance.

Application of the perturbed chain SAFT equation of state to complex polymer systems using simplified mixing rules

A simplified perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state is applied to polymer systems that include a variety of non-associating (esters, cyclic hydrocarbons), polar (ketones) as well as associating (amines, alcohols) solvents. The solvent pure-component parameters that are not available in the literature are estimated by correlating vapor-pressure and liquid-density data. The performance of the simplified PC-SAFT is compared to the original PC-SAFT equation of state for polymer systems of varying complexity. It is shown that the applied simplification is not at the expense of the accuracy of equation of state, while the computational time and complexity are significantly reduced, especially for associating systems. With no binary interaction parameter, simplified PC-SAFT is successfully able to predict vapor–liquid equilibria of polymers with non-associating solvents. In the case of associating solvents, a small binary interaction parameter k ij is usually needed for the satisfactory correlation of the experimental data.