Predicting thermophysical properties of biodiesel fuel blends using the SAFT-VR approach

Modeling of thermophysical properties and phase equilibria of long-chain methylesters mixtures are presented, using the SAFT-VR approach for mixtures. Molecules are represented as chains of spherical segments that can associate due to the presence of short-ranged attractive sites, using previous molecular parameters obtained for pure fatty acid methyl esters. These attractive sites as well as the intermolecular interactions between monomers segments are modeled via variable-ranged square-well potentials. The cross-energy binary-interaction parameter of the extended Berthelot combining rule was fitted to liquid densities and speed of sound. Very good predictions are obtained for isochoric heat capacities and for binary and ternary phase diagrams.     

Modelling of phase equilibria for associating mixtures using an equation of state

In the present work, the group contribution with association equation of state (GCA-EoS) is extended to represent phase equilibria in mixtures containing acids, esters, and ketones, with water, alcohols, and any number of inert components. Association effects are represented by a group-contribution approach. Self- and cross-association between the associating groups present in these mixtures are considered. The GCA-EoS model is compared to the group-contribution method MHV2, which does not take into account explicitly association effects. The results obtained with the GCA-EoS model are, in general, more accurate when compared to the ones achieved by the MHV2 equation with less number of parameters. Model predictions are presented for binary self- and cross-associating mixtures.     

Modelling the VLE properties using van der Waals-type equation of state

The vapour–liquid equilibrium (VLE) properties of polar and non-polar fluids have been modelled by the use of two modified van der Waals (vdW)-type equations of state (EOSs). In this article, a revised method is applied to the above-mentioned EOSs to improve the representation of VLE properties of different class of fluids. In this respect, the repulsion parameter b is considered to be temperature dependent and also a temperature-dependent revision factor α(T) is introduced to the liquid fugacity coefficient expression derived from traditional isothermal integration to reproduce the vapour pressure (P^s) of pure liquids. The present method is also extended to represent the VLE properties of binary mixtures containing noble gases, refrigerants and hydrocarbons. This method outperforms the original vdW-type EOSs in predicting the VLE and pressure-volume-temperature (PVT) properties of 22 pure substances and 7 binary mixtures.     

Modeling of phase equilibria with CPA using the homomorph approach

For association models, like CPA and SAFT, a classical approach is often used for estimating pure-compound and mixture parameters. According to this approach, the pure-compound parameters are estimated from vapor pressure and liquid density data. Then, the binary interaction parameters, k_ij, are estimated from binary systems; one binary interaction parameter per system. No additional mixing rules are needed for cross-associating systems, but combining rules are required, e.g. the Elliott rule or the so-called CR-1 rule. There is a very large class of mixtures, e.g. water or glycols with aromatic hydrocarbons, chloroform-acetone, esters-water, CO₂-water, etc., which are classified as “solvating” or “induced associating”. The classical approach cannot be used and the cross-association interactions are difficult to be estimated a priori since usually no appropriate experimental data exist, while the aforementioned combining rules cannot capture the physical meaning of such interactions (as at least one of the compounds is non-self-associating). Consequently, very often one or more of the interaction parameters are optimized to experimental mixture data. For example, in the case of the CPA EoS, two interaction parameters are often used for solvating systems; one for the physical part (k_ij) and one for the association part (β^cross). This limits the predictive capabilities and possibilities of generalization of the model. In this work we present an approach to reduce the number of adjustable parameters in CPA for solvating systems. The so-called homomorph approach will be used, according to which the k_ij parameter can be obtained from a corresponding system (homomorph) which has similar physical interactions as the solvating system studied. This leaves only one adjustable parameter for solvating mixtures, the cross-association volume (β^cross). It is shown that the homomorph approach can be used with success for mixtures of water and glycols with aromatic hydrocarbons as well as for mixtures of acid gases (CO₂, H₂S) with alcohols and water. The homomorph approach is less satisfactory for mixtures with fluorocarbons as well as for aqueous mixtures with ethers and esters. In these cases, CPA can correlate liquid-liquid equilibria for solvating systems using two adjustable parameters. The capabilities and limitations of the homomorph approach are discussed.     

Evaluation of the parameters of the Bender equation of state for low acentric factor fluids and carbon dioxide

Volumetric properties of several low acentric factor fluids (Ar, CH₄, C₂H₆, Kr, N₂, Ne, O₂, Xe) as well as CO₂ are modeled using the Bender equation of state. This equation is a linear function of 19 adjustable parameters, which are evaluated from properties data, using a linear numerical procedure. The validity of the EOS is tested by calculating the Joule-Thomson inversion curve. A simple model is in particular used to correlate the inversion properties predicted by the Bender equation, expressed in term of reduced pressure as a function of reduced temperatures ranging from 0.8 to 6. The simple correlation reproduces accurately the used data. We employ data on state behaviour ρ(P,T) of homogeneous fluid phases, vapour-liquid equilibrium, second virial coefficient and the coordinates of the critical point.     

An analytical perturbed equation of state for hard chain fluids: Application to n-alkanes and n-perfluoroalkanes

A completely analytical equation of state for pure hard chain fluids, derived on the basis of perturbation theory and reported in our previous work, is applied for the calculation of pVT properties and the prediction of vapour–liquid equilibria of n-alkanes and n-perfluoroalkanes. The molecules are treated as a chain formed from freely joined spheres which interact via an extended site-site square-well potential. The molecular parameters of compounds are obtained from the experimental compressibility factor data above the critical temperature. These parameters are capable of relatively satisfactory prediction of the vapour–liquid equilibrium coexistence curves of compounds. Linear relationships have been found between the potential parameters of fluids and their molecular weight, which make it possible to predict the pVT data and vapour–liquid phase equilibria of heavier compounds.     

A simplified approach to vapor–liquid equilibria calculations with the group-contribution lattice-fluid equation of state

Equations of state that are based on the lattice-statistics approach use Guggenheim's quasi-chemical approximation to describe the non-randomness in the mixture due to the energetic interactions between the molecules. For ternary and higher-component systems the non-randomness expression is complex and requires an iterative calculation procedure. We have shown that the non-randomness parameters play a negligible role in the application of the GCLF-EoS model (based on the Panayiotou–Vera EoS) for predicting vapor–liquid equilibria. Omission of the non-randomness parameters from such calculations can significantly improve the computation efficiency. Binary, ternary, and quaternary vapor–liquid equilibria predictions were made including polystyrene, polyvinyl acetate, polyethylene, and polypropylene in polar and non-polar solvents to test the theory.     

Solid–liquid equilibrium and hydrogen solubility of trans-decahydronaphthalene + naphthalene and cis-decahydronaphthalene + naphthalene for a new hydrogen storage medium in fuel cell system

Solid–liquid equilibrium was measured for benzene + cyclohexane, trans-decahydronaphthalene + naphthalene and cis-decahydronaphthalene + naphthalene under the atmospheric pressure in the temperature range from 226.69 to 353.14 K. The apparatus was specially designed in this study, and it was based on a cooling method. The phase diagram with the complete immiscible solids was observed for the three systems, and the eutectic point was found at x₂ = 0.2709 and T_eu = 232.11 K for benzene + cyclohexane, x₂ = 0.9816 and T_eu = 241.98 K for trans-decahydronaphthalene + naphthalene, and x₃ = 0.9822 and T_eu = 225.74 K for cis-decahydronaphthalene + naphthalene, respectively. Hydrogen solubility was also measured for the two pure substances, trans-decahydronaphthalene and cis-decahydronaphthalene, and the three mixtures, trans-decahydronaphthalene + cis-decahydronaphthalene, trans-decahydronaphthalene + naphthalene, and cis-decahydronaphthalene + naphthalene, in the pressure range from 1.702 to 4.473 MPa at 303.15 K. Considering the solid–liquid equilibrium data, mole ratio of trans-decahydronaphthalene:cis-decahydronaphthalene was set to 50:50, and those of trans-decahydronaphthalene + naphthalene, and cis-decahydronaphthalene + naphthalene to 85:15. The hydrogen solubility increased linearly with the pressure following the Henry's law for all systems. The experimental solubility data were correlated or predicted with the Peng–Robinson equation of state [D.Y. Peng, D.B. Robinson, Ind. Eng. Chem. Fundam. 15 (1976) 59–64; R. Stryjek, J.H. Vera, Can. J. Chem. Eng. 64 (1986) 323–333].     

Predictive use of a SAFT EOS for phase equilibria of some hydrocarbons and their binary mixtures

A systematic study of several hydrocarbons with a SAFT equation of state (EOS) is presented. First, it is shown that the phase behavior of the whole family of n-alkanes may be represented with the use of only three parameters. The approach is then extended to moderately branched alkanes, alkenes and ring compounds using one additional property, namely normal boiling point. Binary mixtures are also investigated and reasonable results are obtained with no additional binary parameters.     

Solid-liquid equilibrium using the SAFT-VR equation of state: Solubility of naphthalene and acetic acid in binary mixtures and calculation of phase diagrams

A solid-liquid equilibrium (SLE) thermodynamic model based on the SAFT-VR equation of state (EOS) is presented. The model allows for the calculation of solid-liquid phase equilibria in binary mixtures at atmospheric pressure. The fluid (liquid) phase is treated with the SAFT-VR approach, where molecules are modelled as associating chains of tangentially bonded spherical segments interacting via square-well potentials of variable range. The equilibrium between the liquid and solid phase is treated following a standard thermodynamic method that requires the experimental temperature and enthalpy of fusion of the solute. The model is used to calculate the solubilities of naphthalene and acetic acid in common associating and non-associating organic solvents and to determine the solid-liquid phase behaviour of binary mixtures with simple eutectics. The SAFT-VR pure component model parameters are determined by comparison to experimental vapour pressure and saturated liquid density data with the choice of association models according to the nature of the molecule; in addition, an unlike adjustable parameter (k_ij) is used to model the solutions. The solubility data of naphthalene and acetic acid in both associating and non-associating solvents are reproduced essentially within the accuracy of the experimental measurements. The phase boundaries and the position of the eutectic points in the binary mixtures considered are, in most cases, reproduced with the accuracy commensurate with the industrial applications. Overall, the results presented show that the SAFT-VR EOS can be used with confidence for the prediction of the SLE of binary systems at atmospheric pressure.     

Mutual solubilities of hydrocarbons and water with the CPA EoS

The knowledge of hydrocarbon/water phase equilibria is important in the design and operation of equipment for petroleum transport and refining and petrochemical plants. The presence of water in a hydrocarbon mixture can affect the product quality and damage the operation equipment due to corrosion and formation of gas hydrates. Tracing the concentration of hydrocarbons in aqueous media is also important for technical purposes like preventing oil spills and for ecological concerns such as predicting the fate of these organic pollutants in the environment.     

Crossover Peng-Robinson equation of state with introduction of a new expression for the crossover function

In this research, we use the original Peng-Robinson (PR) equation of state (EOS) for pure fluids and develop a crossover cubic equation of state which incorporates the scaling laws asymptotically close to the critical point and it is transformed into the original cubic equation of state far away from the critical point. The modified EOS is transformed to ideal gas EOS in the limit of zero density. A new formulation for the crossover function is introduced in this work. The new crossover function ensures more accurate change from the singular behavior of fluids inside the regular classical behavior outside the critical region. The crossover PR (CPR) EOS is applied to describe thermodynamic properties of pure fluids (normal alkanes from methane to n-hexane, carbon dioxide, hydrogen sulfide and R125). It is shown that over wide ranges of state, the CPR EOS yields the thermodynamic properties of fluids with much more accuracy than the original PR EOS. The CPR EOS is then used for mixtures by introducing mixing rules for the pure component parameters. Higher accuracy is observed in comparison with the classical PR EOS in the mixture critical region.     

Solubility of hydrocarbons in water: Experimental measurements and modeling using a group contribution with association equation of state (GCA-EoS)

In this communication, new experimental data on the solubility of n-hexane, cyclo-hexane and iso-octane in pure water are reported. The data have been measured using a static-analytic technique that takes advantage of a Rolsi™ sampling device in the temperature range of 298–353 K and at pressures up to 0.5 MPa. The experimental data measured in this work at 298 K have been compared with some selected data from the literature and good agreement is found. A group contribution plus association equation of state, namely the GCA-EoS, is used to model the phase equilibrium of water + hydrocarbon (C₂ to n-C₆, cy-C₆, i-C₄ and i-C₈) system. The predictions of the model are found in good agreement with the experimental data measured in this work and some selected data from the literature.     

Phase equilibria modeling by the quasilattice equation of state for binary and ternary systems composed of carbon dioxide, water and some organic components

The hole lattice quasichemical group-contribution model (HM) has been applied to described liquid-liquid, liquid-liquid-vapour and vapour-liquid equilibria at elevated and high pressures in binary and ternary mixtures containing CO₂, water, alkanols, paraffinic and aromatic hydrocarbons. An estimation of the concentration of alkanol monomers in the binaries with CO₂ has been performed. The results of modeling by the HM EOS and the Associated Perturbed Anisotropic Chain Theory (APACT) are compared. In most cases both EOS give satisfactory agreement with experimental data.     

Modeling phase equilibria of alkanols with the simplified PC-SAFT equation of state and generalized pure compound parameters

The simplified PC-SAFT equation of state has been applied to liquid–liquid, vapor–liquid and solid–liquid equilibria for mixtures containing 1- or 2-alkanols with alkanes, aromatic hydrocarbons, CO₂ and water. For the alkanols we use generalized pure compound parameters. This means that two of the physical pure compound parameters, m (segment number) and σ (segment diameter), are obtained from linear extrapolations, since m and mσ³, increase linearly with respect to the molar mass, and moreover, the two association parameters (association energy and association volume) were assumed to be constant for all alkanols. Only the dispersion energy is fitted to experimental data. Thus it is possible to estimate parameters for several 1- and 2-alkanols. The final aim is to develop a group contribution approach for PC-SAFT which is suitable for complex compounds, considering that the motivation of this project is to obtain a thermodynamic model which can be used in the development of sophisticated products such as pharmaceuticals, polymers, detergents or food ingredients. One of the severe limitations in applying SAFT-type equations of state to these compounds is that the procedure for obtaining the pure compound parameters is usually based on fitting to saturated vapor pressure and liquid density data over an extended temperature range. However, such data are rarely available for complex compounds. To verify the new pure compound parameters, comparisons to ordinary optimized alkanol parameters, where all five pure compound parameters were fitted to experimental liquid density and vapor pressure data, were made. The results show that the new generalized alkanol parameters from this work perform at least as well as other alkanol parameter sets.     

Measurement and correlation of solubility of carbon dioxide in 1-alkyl-3-methylimidazolium hexafluorophosphate ionic liquids

The solubility of carbon dioxide in the ionic liquids 1-butyl-3-methylimidazolium hexafluorophosphate and 1-nonyl-3-methylimidazolium hexafluorophosphate was measured at temperatures of 293.15 and 298.15 K and pressure up to 4 MPa using a stoichiometric phase equilibrium apparatus. The measured data for 1-butyl-3-methylimidazolium hexafluorophosphate were in good agreement with existing literature data and new solubility data were reported for 1-nonyl-3-methylimidazolium hexafluorophosphate. The measured data were correlated using the group contribution non-random lattice fluid equation of state (GC-NLF EoS) proposed by Lee and co-workers. The group parameters for CG-NLF EoS were slightly modified at limited range to accommodate recent experimental data and better prediction at high pressure and long alkyl chains.     

Application of the CPA equation of state to reservoir fluids in presence of water and polar chemicals

The complex phase equilibrium between reservoir fluids and associating compounds like water, methanol and glycols has become more and more important as the increasing global energy demand pushes the oil industry to target reservoirs with extreme or complicated conditions, such as deep or offshore reservoirs. Conventional equation of state (EoS) with classical mixing rules cannot satisfactorily predict or even correlate the phase equilibrium of those systems. A promising model for such systems is the Cubic-Plus-Association (CPA) EoS, which has been successfully applied to well-defined systems containing associating compounds. In this work, a set of correlations was proposed to calculate the CPA model parameters for the narrow cuts in ill-defined C₇₊ fractions. The correlations were then combined with either the characterization method of Pedersen et al. or that of Whitson et al. to extend CPA to reservoir fluids in presence of water and polar chemical such as methanol and monoethylene glycol. With a minimum number of adjustable parameters from binary pairs, satisfactory results have been obtained for different types of phase equilibria in reservoir fluid systems and several relevant model multicomponent systems. In addition, modeling of mutual solubility between light hydrocarbons and water is also addressed.