Molecular-based Equation Of State Research Articles

Thermodynamic characterisation of aqueous alkanolamine and amine solutions for acid gas processing by transferable molecular models

The development of new alkanolamines/amines is a topic which has attracted a great deal research interest, particularly as absorbents for the removal of acid gases from industrial sources and CO2 capture applications. One of the major challenges when evaluating the techno-economic performance of selected new single amines or blends is the lack of experimental data on the thermophysical properties required for a reliable process design and simulation. In this contribution, a robust theoretical framework for the description of key thermophysical properties of aqueous solutions of single and mixed alkanolamines/amines at relevant gas separation process conditions is proposed. The approach is based on the coupling of the Free-Volume Theory and the Density Gradient Theory with a molecular-based equation of state (soft-SAFT) for the integrated modelling of phase behaviour, enthalpies, densities, viscosities and interfacial tensions. The alkanolamines and amines investigated differ in their family and structure, and included primary (monoethanolamine), secondary (diethanolamine), tertiary (methyldiethanolamine), sterically hindered (2-amino-2-methyl-1-propanol) and cyclic amines (piperazine). The study was performed in a systematic manner, starting from the development of the models for the pure amines, the description of their thermophysical properties, and the properties of the aqueous mixtures. Compared to other models described in literature, the present modelling approach preserves the effects due the chemical structure and key intermolecular interactions of the examined alkanolamines/amines through a set of molecular parameters obtained from pure substance data, whenever available, or transferred from substances of different chemical families. This enabled the development of a consistent modelling framework which can provide reliable thermodynamic property predictions of both single and blended amine solutions over a broad range of temperatures (298–373 K) and compositions (0–50 wt% amine). The proposed approach is well-suited for implementation and extension to other alkanolamines and amines, making it a valuable tool for having reliable process simulations as well as for the screening and discovery of new amine systems, which will be required for the deployment of more economical acid gas removal processes.

Predicting the phase behavior of fluorinated organic molecules using the GC-SAFT-VR equation of state

Fluorinated molecules such as perfluoroalkanes (PFA), perfluoroalkylalkanes (PFAA), fluoroalkanes, and hydrofluoroethers (HFE) possess attractive physical properties that have resulted in their use in a wide range of applications. However, while there is an abundance of thermophysical data for hydrocarbons in the literature, only limited studies have been performed that report the properties of the corresponding fluorinated species. Predictive approaches are therefore needed to accurately and reliably determine the physical properties of these molecules. The statistical associating fluid theory (SAFT) is a commonly used molecular-based equation of state that in its various forms has been applied to study a wide range of fluid systems. In recent work, several group contribution (GC) SAFT equations of state have been proposed, such as the GC-SAFT-VR equation that combines the SAFT equation for potentials of variable range (VR) with a group contribution approach that uniquely allows for the description of hetero-segmented chains. The GC-SAFT-VR equation has been shown to provide an excellent description of the phase behavior of pure associating and non-associating fluids and their mixtures, with a minimal reliance on fitting the model parameters to experimental data. Specifically, parameters for key functional groups (such as CH3, CH2, CH, CH2=CH, C=O, C6H5, ether and ester, OH, NH2, CH=O, COOH) have been obtained by fitting to experimental vapor pressure and saturated liquid density data for selected low molecular weight fluids and then used to predict the phase behavior of pure fluids and their mixtures without further adjusting the group parameters. To expand upon this effort, here we report parameters for the CF3, CF2, CF, CH2F, CHF2, and CHF functional groups and their cross interactions. The theoretical predictions are compared with experimental data for pure PFAs, PFAAs, and HFEs, as well as binary mixtures of alkanes, alkenes, PFAs, PFAAs, and CO2 in order to test the transferability of the new group parameters. The GC-SAFT-VR approach is found to accurately predict the phase behavior of the systems studied.

Determination of Perturbed-Chain Statistical Association Fluid Theory Parameters for Pure Substances, Single Carbon Number Groups, and Petroleum Fractions Using Cubic Equations of State Parameters

A new-generation equation of state, perturbed-chain statistical association fluid theory (PC-SAFT), has attracted much attention to modeling the phase behavior of fluids using molecular-based equations of state. A set of three pure component parameters is needed for non-associative compounds, conventionally determined by fitting vapor pressure and liquid density data simultaneously. Unfortunately, experimental data are scarce, and the number of pure substances is too large. Thus, it is indispensable for developing predictive methods to determine the pure component parameters. In the present paper, a new model has been developed to estimate PC-SAFT parameters for different pure components, single carbon number (SCN) groups, and petroleum fractions through the connection established between classical and molecular corresponding states theories and creating a relationship between cubic equation-of-state parameters (critical pressure, critical temperature, and acentric factor) and PC-SAFT parameters. Accordin...

Calculations of vapor–liquid equilibria of the H2O-N2 and H2O-H2 systems with improved SAFT-LJ EOS

The SAFT-LJ equation of state (EOS) improved by our previous study, which introduces a multi-polar term to explicitly account for the contribution of multi-polar interactions (including the dipole–dipole, dipole–quadrupole and quadrupole–quadrupole interactions), is applied to the H2O-N2 and H2O-H2 systems. N2 and H2 are modeled as chain molecules with evenly distributing quadrupole moments. The van der Waals one-fluid mixing rule was used to calculate parameters for mixtures and two binary parameters for the interactions of H2O-N2 and H2O-H2 pairs were evaluated from mutual solubility data of binary water–gas systems. Comparison with the experimental data shows that this molecular-based EOS can well represent vapor–liquid equilibria of H2O-N2 and H2O-H2 systems over a wide P–T range (273–623K and 0–1000bar). In addition, the effect of the dipole moment of H2O and quadrupole moments of N2, H2 and CO2 on VLE of the CO2-N2, H2O-N2 and H2O-H2 systems was checked. It was found that the SAFT-LJ model without any polar term gives good prediction (without any binary parameters) for vapor compositions of the CO2-N2, H2O-N2 and H2O-H2 systems except in the critical region and taking account of the contribution of multi-polar interactions does not improve the prediction of this EOS any more. However, taking account of multi-polar interactions indeed significantly improves the prediction of this EOS for compositions of liquid phase. We argue that it is the reason why this EOS can quantitatively represent VLE of highly non-ideal water–gas systems. Comparison of calculations of this EOS with experimental VLE data of the ternary CO2-N2-H2O system confirms the prediction capability of this EOS for thermodynamic properties of multi-component systems.

SAFT-γ Force Field for the Simulation of Molecular Fluids: 2. Coarse-Grained Models of Greenhouse Gases, Refrigerants, and Long Alkanes

In the first paper of this series [C. Avendaño, T. Lafitte, A. Galindo, C. S. Adjiman, G. Jackson, and E. A. Müller, J. Phys. Chem. B2011, 115, 11154] we introduced the SAFT-γ force field for molecular simulation of fluids. In our approach, a molecular-based equation of state (EoS) is used to obtain coarse-grained (CG) intermolecular potentials that can then be employed in molecular simulation over a wide range of thermodynamic conditions of the fluid. The macroscopic experimental data for the vapor-liquid equilibria (saturated liquid density and vapor pressure) of a given system are represented with the SAFT-VR Mie EoS and used to estimate effective intermolecular parameters that provide a good description of the thermodynamic properties by exploring a wide parameter space for models based on the Mie (generalized Lennard-Jones) potential. This methodology was first used to develop a simple single-segment CG Mie model of carbon dioxide (CO2) which allows for a reliable representation of the fluid-phase equilibria (for which the model was parametrized), as well as an accurate prediction of other properties such as the enthalpy of vaporization, interfacial tension, supercritical density, and second-derivative thermodynamic properties (thermal expansivity, isothermal compressibility, heat capacity, Joule-Thomson coefficient, and speed of sound). In our current paper, the methodology is further applied and extended to develop effective SAFT-γ CG Mie force fields for some important greenhouse gases including carbon tetrafluoride (CF4) and sulfur hexafluoride (SF6), modeled as simple spherical molecules, and for long linear alkanes including n-decane (n-C10H22) and n-eicosane (n-C20H42), modeled as homonuclear chains of spherical Mie segments. We also apply the SAFT-γ methodology to obtain a CG homonuclear two-segment Mie intermolecular potential for the more challenging polar and asymmetric compound 2,3,3,3-tetrafluoro-1-propene (HFO-1234yf), a novel replacement refrigerant with promising properties. The description of the fluid-phase behavior and the prediction of the other thermophysical properties obtained by molecular simulation using our SAFT-γ CG Mie force fields are found to be of comparable quality (and sometimes superior) to that obtained using the more sophisticated all-atom (AA) and united-atom (UA) models commonly employed in the field. We should emphasize that though the focus of our current work is on simple homonuclear models, the SAFT-γ methodology is based on a group contribution methodology which is naturally suited to the development of more sophisticated heteronuclear models.

Optimized Binary Interaction Parameters for VLE Calculations of Natural Gas Mixtures via Cubic and Molecular-Based Equations of State

The objective of this study is to analyze the performance of a selected collection of equations of state (EOS) for the prediction of vapor–liquid equilibrium of the components of a typical natural gas mixture. In this work, 13 biparametric, triparametric, and tetraparametric, widely used simple-cubic-type EOS and three complex, but state-of-the-art, molecular-based EOS are used. A simple, one-fluid-based mixing rule was applied for the extension to mixtures of the models. Binary interaction parameters for the different equations were calculated by correlation of available binary vapor–liquid equilibria data in the experimental literature, in wide temperature–pressure ranges, for the key binary systems relevant to natural gases. The results allow one to infer the performance of the different EOS commonly used for phase equilibria analysis in the natural gas industry, and to study how the different complexity of the studied EOS does (or does not) lead to an improvement in the quality of the predictions.

Correlation and prediction of fluid–fluid equilibria of carbon dioxide–aromatics and carbon dioxide–dichlorobenzoates binary mixtures

In this work, the capabilities and usefulness of several cubic equations of state (PR, SRK, SOF-PR, SOF-RK) as well as a molecular-based equation of state, PC-SAFT were explored. Specifically, the two phase fluid–fluid regions (VLE, LLE) of several demanding binary mixtures of aromatics as well as dichlorobenzoates (alkyl and semi-fluorinated) with supercritical CO 2 were evaluated. Group contribution approaches were used to estimate the pure fluid parameters for the alkyl and semi-fluorinated dichlorobenzoates needed for each equation of state. We show that these models can capture many important features of the complex phase behavior of highly asymmetric systems composed of supercritical CO 2 and alkyl (nonfluorinated or semi-fluorinated) 2,5-dichlorobenzoates.

SAFT-γ Force Field for the Simulation of Molecular Fluids. 1. A Single-Site Coarse Grained Model of Carbon Dioxide

An application of the "top-down" concept for the development of accurate coarse-grained intermolecular potentials of complex fluids is presented. With the more common "bottom-up" procedure, coarse-grained models are constructed from a suitable simplification of a detailed atomistic representation, and small adjustments to the intermolecular parameters are made by comparison with limited experimental data where necessary. In contrast, in the top-down approach, a molecular-based equation of state is used to obtain an effective coarse-grained intermolecular potential that reproduces the macroscopic experimental thermophysical properties over a wide range of conditions. These coarse-grained intermolecular potentials can then be used in conventional molecular simulation to obtain properties (such as structure or dynamics) that are not directly accessible from the equation of state or at extreme conditions where the theory is expected to fail. To demonstrate our procedure, a coarse-grained model for carbon dioxide (CO(2)) is obtained from a recent implementation of the statistical associating fluid theory of variable range (SAFT-VR) employing a Mie (generalized Lennard-Jones) potential; the parameters of this single-site Mie model of CO(2) are estimated by optimizing the equation of state's description of the experimental vapor-pressure and saturated liquid density data. This approach is only viable because of the excellent agreement of the SAFT-VR Mie EoS with simulation data. Our single-site SAFT-γ coarse-grained model for CO(2) is used in Monte Carlo molecular simulation to assess the adequacy of the description of the fluid-phase behavior and properties that were not used to develop the potential model such as the enthalpy of vaporization, interfacial tension, density profiles, supercritical densities, and second-derivative thermodynamic properties (thermal expansivity, isothermal compressibility, heat capacity, Joule-Thompson coefficient, and speed of sound). The accuracy of the description with the single-site SAFT-γ model of CO(2) is found to be of similar quality to that of more sophisticated intermolecular potentials such as a six-site (three LJ centers and three charged sites) all-atom model. The SAFT-γ top-down approach to coarse-graining resolves a key challenge with coarse-graining techniques: the provision of a direct robust link between the microscopic and macroscopic scales.

Extending the GC-SAFT-VR approach to associating functional groups: Alcohols, aldehydes, amines and carboxylic acids

The statistical associating fluid theory is a widely used molecular-based equation of state that has been successfully applied to study a broad range of fluid systems. It provides a framework in which the effects of molecular shape and interactions on the thermodynamics and phase behavior of fluids can be separated and quantified. In the original approach, molecules were modeled as chains composed of identical segments; the heterogeneity of molecules in terms of structure and functional groups was described implicitly through effective parameters. To overcome this limitation, in recent works [Peng et al. Fluid Phase Equilib. 227(2), 131 (2009); Ind. Eng. Chem. Res. 49(3), 1378 (2010)] the GC-SAFT-VR approach has been developed to extend the theory to model chains composed of segments of different size and/or energy of interaction and enable the development of a group-contribution approach within the SAFT-VR framework in which molecular heterogeneity and connectivity is explicitly accounted for. The parameters for several key functional groups (CH 3, CH 2, CH, CH 2 CH, C O, C 6H 5, esters, ethers, cis-alkenes and trans-alkenes groups) were determined by fitting to experimental vapor pressure and saturated liquid density data for a number of small molecules containing the functional groups of interest and transferability of the parameters tested by comparing the theoretical predictions with experimental data for pure fluids not included in the fitting process and binary mixtures of both simple fluids and the VLE and LLE of small molecules in polymer systems. In this work, we further extend the applicability of the GC-SAFT-VR approach through the study of the vapor–liquid phase behavior of associating systems, such as linear and branched alcohols, primary and secondary amines, aldehydes, and carboxylic acids, and their mixtures. In the study of these new molecules several new functional groups (OH (linear and branched), HC O, NH 2, NH and C OOH) are defined and their molecular parameters characterized. The transferability of the parameters is again tested by comparing the theoretical predictions with experimental data for pure fluids and binary mixtures not included in the fitting process. The GC-SAFT-VR approach is found to predict the phase behavior of the systems studied in most cases in good agreement with experimental data and accurately captures the effects of changes in structure and molecular composition on phase behavior.

On the isobaric thermal expansivity of liquids

The temperature and pressure dependence of isobaric thermal expansivity, α(p), in liquids is discussed in this paper. Reported literature data allow general trends in this property that are consistent with experimental evidence to be established. Thus, a negative pressure dependence is to be expected except around the critical point. On the other hand, α(p) exhibits broad regions of negative and positive temperature dependence in the (T, p) plane depending on the nature of the particular liquid. These trends are rationalized here in terms of various molecular-based equations of state. The analysis of the Lennard-Jones, hard sphere square well and restricted primitive model equations allows understanding the differences in the α(p) behavior between liquids of diverse chemical nature (polar, nonpolar, and ionic): broader regions of negative temperature and positive pressure dependencies are obtained for liquids characterized by larger ranges of the interparticle potential. Also, using the statistical associating fluid theory (SAFT) allowed the behavior of more complex systems (basically, those potentially involving chain and association effects) to be described. The effect of chain length is rather simple: increasing it is apparently equivalent to raise the interaction range. By contrast, association presents a quite complex effect on α(p), which comes from a balance between the dispersive and associative parts of the interaction potential. Thus, if SAFT parameters are adjusted to obtain low association ability, α(p) is affected by each mechanism at clearly separate regions, one at low temperature, due to association, and the other to dispersive forces, which has its origin in fluctuations related with vapor-liquid transition.

Direct calculation of interfacial properties of fluids close to the critical region by a molecular-based equation of state

The crossover soft-SAFT equation coupled with the Density Gradient Theory is applied here to the prediction of interfacial tensions of pure fluids and mixtures, including non-polar and polar compounds, far from and near to the critical region. The approach is able to accurately describe the interfacial tensions of pure systems and mixtures as compared with available experimental data, in the whole range of thermodynamic conditions, with the same degree of accuracy of vapor–liquid equilibria previously reported. A correlation for the influence parameter as a function of the molecular weight is obtained for the n-alkanes and 1-alkanol families, empowering the equation with predictive capabilities for interfacial tensions of compounds of the family for which experimental data is unavailable or difficult to obtain, such as heavy n-alkanes. It is shown how the equation is able to capture the S-shape of the interfacial tension of water, succeeding a stringent test to any equation applied to water. For mixtures, the theory is able to quantitatively predict the mixture behavior of heavy alkanes, with calculations made from pure component parameters and no fitting; good results are also obtained for other mixtures considered, including nitriles systems, while two binary parameters, close to the ideal values, were needed for the description of CO 2–butane mixtures. The results presented here show the robustness of using an accurate and versatile equation of state for the bulk combined with a simple and elegant method for calculating interfacial properties, with very modest computational effort.

A duality-based optimisation approach for the reliable solution of ( P, T) phase equilibrium in volume-composition space

Abstract A reliable algorithm for the solution of fluid phase equilibrium at constant pressure and temperature ( P, T flash) is presented. The approach is applicable to multi-component mixtures described with general equations of state and is based on a formulation of P, T phase equilibrium as a dual optimisation problem in volume-composition space, translated away from the Gibbs free energy to the Helmholtz free energy. This formulation facilitates the use of guaranteed solution algorithms, particularly in the case of sophisticated equations of state (EOSs) such as SAFT (statistical associating fluid theory), because such representations are higher-than-cubic functions in volume and are formulated in the Helmholtz free energy. With the proposed algorithm (which is based on a combination of local and global optimisation, where the number of subproblems to be solved globally is kept at a minimum) one is guaranteed to identify the number of stable phases present at equilibrium, along with their properties, without any need for initial guesses, or indeed any a priori knowledge about the behaviour of the system. The method is applicable to the calculation of any kind of fluid phase behaviour (e.g., vapour–liquid (VLE), liquid–liquid (LLE), vapour–liquid–liquid (VLLE), etc.). Several algorithmic options are investigated and their computational performance compared. A prototype implementation is used to determine the fluid phase equilibria of a number of binary and ternary systems, where the thermodynamic properties are calculated through a molecular-based EOS. Examples are shown for the VLE and VLLE for mixtures modelled with an augmented van der Waals EOS, a non-cubic EOS that incorporates the Carnahan and Starling representation of the repulsive interactions. Further examples are presented for VLE and VLLE in polymer systems, modelled with an EOS of the generic SAFT form. Fluid phase equilibrium calculations for polymer systems are notoriously difficult, and convergence problems are often encountered, even with good initial guesses. The proposed method is found to be reliable in all cases examined.

Prediction of vapor–liquid equilibrium and PVTx properties of geological fluid system with SAFT-LJ EOS including multi-polar contribution. Part I: Application to H 2O–CO 2 system

Molecular based equations of state (EOS) are attractive because they can take into account the energetic contribution of the main types of molecular interactions. This study models vapor–liquid equilibrium (VLE) and PVTx properties of the H 2O–CO 2 binary system using a Lennard-Jones (LJ) referenced SAFT (Statistical Associating Fluid Theory) EOS. The improved SAFT-LJ EOS is defined in terms of the residual molar Helmholtz energy, which is a sum of four terms representing the contributions from LJ segment–segment interactions, chain-forming among the LJ segments, short-range associations and long-range multi-polar interactions. CO 2 is modeled as a linear chain molecule with a constant quadrupole moment, and H 2O is modeled as a spherical molecule with four association sites and a dipole moment. The multi-polar contribution to Helmholtz energy, including the dipole–dipole, dipole–quadrupole, and quadrupole–quadrupole contribution for H 2O–CO 2 system, is calculated using the theory of Gubbins and Twu (1978). Six parameters for pure H 2O and four parameters for pure CO 2 are needed in our model. The Van der Waals one-fluid mixing rule is used to calculate the Lennard-Jones energy parameter and volume parameter for the mixture. Two or three binary parameters are needed for CO 2–H 2O mixtures, which are evaluated from phase equilibrium data of the binary system. Comparison with the experimental data shows that our model represents the PVT properties of CO 2 better than other SAFT EOS without a quadrupole contribution. For the CO 2–H 2O system, our model agrees well with the vapor–liquid equilibrium data from 323–623 K. The average relative deviation for CO 2 solubility (expressed in mole fraction) in water is within 6%. Our model can also predict the PVTx properties of CO 2–H 2O mixtures up to 1073 K and 3000 bar. The good performance of this model indicates that: (1) taking account of the multi-polar contribution explicitly improves the agreement of calculated properties with experimental data at high temperatures and high pressures, (2) the molecular-based EOS with just a few parameters fit to data in the sub-critical region can predict the thermodynamic properties of fluids over a wide range of P– T conditions.

A note on scenarios of metastable water

A recently developed molecular-based equations of state for water are analyzed with respect to the behavior of the liquid spinodal curve. It is shown that all of them yield the spinodal exhibiting a minimum in accordance with Speedy’s stability-limit conjecture and with the behavior predicted by the accurate (but purely empirical) IAPWS-95 equation. It means that the considered equations of state give consistent results but qualitatively different from those resulting from available computer simulations, which yield a monotonic spinodal line.

A new algorithm for estimating association parameters in molecular-based equations of state by quantum chemistry

This note presents a new algorithm for estimating association parameters within molecular-based equations of state that allows the user to incorporate results from quantum chemistry. Using the simplified SAFT equation as an example, we show that the traditional parameter estimation approach (i.e., fitting parameters to vapor pressure and liquid density data) provides results that run counter to quantum chemistry findings on association strengths. Numerical results show that the parameter estimation approach proposed in this work provides a much more appropriate match to quantum chemistry results and gives markedly different amounts of site–site bonding.

Phase equilibria in perfluoroalkane + alkane binary systems from PC-SAFT equation of state

Phase equilibria of perfluoroalkane + alkane binary mixtures have been studied according to the perturbed chain-statistical associated fluid theory (PC-SAFT) molecular-based equation of state together with a simple monoparametric mixing rule. These systems, for a fixed perfluoroalkane, show transitions from type II phase behaviour, according to the van Konynenburg classification, for the short members of each homologous series, to type III for the largest ones which are properly predicted by the model. These transitions are described by the model via a type IV zone which is studied according to a quasi-binary approach inferring a double critical endpoint (DCEP) and a tricritical point (TCP) in the intermediate transitional zone. The barotropic inversion phenomena for the type III mixtures are also analyzed with the studied equation of state. The general shape of the global phase diagrams of these mixtures is correctly predicted in a qualitative way by the model with a binary interaction parameter temperature independent of the whole temperature range, but the simultaneous correlation of critical loci, three-phase equilibria and equilibrium compositions is not possible with just a single parameter in a quantitative way. The accurate correlation of the complex phase behaviour of these mixtures would require temperature-dependent binary interaction parameters or more complex mixing rules that should take account of the complex weak intermolecular forces rising in these mixtures.

Liquid–liquid equilibria of lactam containing binary systems

In this work, we report a study on the liquid–liquid phase equilibria for N-methyl-2-pyrrolidone (NMP) + hydrocarbon ( n-hexane, n-octane, n-decane, cyclohexane, cyclooctane, 2-methylpentane, 3-methylpentane, isooctane, 2,2-dimethylbutane and 2,3-dimethylbutane) and N-cyclohexyl-2-pyrrolidone (NCP) + water binary mixtures at ambient pressure. The studied systems, except NCP + water, present miscibility curves with upper critical solutions temperatures (UCSTs). The results for NMP + hydrocarbon mixtures are correlated using two different approaches: (i) NRTL and UNIQUAC semiempirical models and (ii) molecular-based equations of state (statistical associating fluid theory (SAFT) and perturbed-chain statistical associating fluid theory (PC-SAFT)). Accurate correlations are inferred for NRTL and UNIQUAC models whereas for SAFT and PC-SAFT EOS complex mixing rules are required to obtain accurate results.

Phase Equilibria of Ethylene Glycol Oligomers and Their Mixtures

We present and discuss the influence of the molecular architecture on the phase equilibria behavior of ethylene glycol oligomers and their mixtures based on predictions from a molecular-based equation of state (EoS). The soft statistical associating fluid theory (SAFT) EoS is used to fit the molecular parameters from the available vapor liquid experimental data, providing a correlation of the molecular parameters with the molecular weight of the compounds, which can be used to predict the behavior of heavy members of the series. The same equation is used to describe the ethylene glycol oligomer mixtures with several compounds, including carbon dioxide, benzene, methane, and n-hexane. The performance of the soft-SAFT equation is compared with some Gibbs excess free energy models and the Peng−Robinson EoS, where soft-SAFT is superior in most of the cases. Once the performance of the equation and the molecular model are established, soft-SAFT is used as a predictive tool to systematically study the influence...

Tricritical phenomena in chain-like mixtures from a molecular-based equation of state

A molecular-based equation, the Soft-SAFT (from Statistical Associating Fluid Theory) equation of state, is applied to study the three-phase region of binary mixtures of chain-like molecules. Two sets of mixtures are investigated: model binary mixtures of Lennard–Jones chains and model binary mixtures of hydrocarbons. The molecular parameters of the equation but one are kept constant and the phase diagrams are obtained as a function of chain length or molecular weight. The equation is used to locate the tricritical point of these mixtures as well as to investigate the approach to the tricritical point. We report the temperatures and pressures corresponding to the lower and upper critical end points of various mixtures. The tricritical points of the mixtures are obtained as the point where the two critical end-point lines of the mixture merge.