Shape factors in equations of state. Part II. Repulsion phenomena in multicomponent chain fluids

An equation of state for the multicomponent fluid phase of nonattracting rigid particles of arbitrary shape is presented. The equation is a generalization of a previously presented equation of state for pure fluids of rigid particles; the approach describes the volumetric properties of a pure fluid in terms of a shape factor, zeta, which can be back calculated by scaling the volumetric properties of pure fluids to that of a hard sphere. The performance of the proposed equation is tested against mixtures of chain fluids immersed in a "monomeric" solvent of hard spheres of equal and different sizes. Extensive new Monte Carlo simulation data are presented for 19 binary mixtures of hard homonuclear tangent freely-jointed hard sphere chains (pearl-necklace) of various lengths (three to five segments), with spheres of several size ratios and at various compositions. The performance of the proposed equation is compared to the hard-sphere SAFT approach and found to be of comparable accuracy. The equation proposed is further tested for mixtures of spheres with spherocylinders. In all cases, the equation proved to be accurate and simple to use.     

Application of a new simplified SAFT to VLE study of associating and non-associating fluids

A new equation of state based on the Statistical Associating Fluid Theory (SAFT) is presented to study the phase behavior of associating and non-associating fluids. In the new equation of state, the hard sphere contribution to compressibility factor of the simplified version of the SAFT (SSAFT) is replaced with that proposed by Ghotbi and Vera. The Ghotbi–Vera SSAFT (GV-SSAFT) was also extended to study the phase behavior of associating and non-associating mixtures. The GV-SSAFT like the SSAFT equation of state has three adjustable segment parameters for non-associating fluids and five parameters for associating fluids. The experimental data of liquid densities and vapor pressures for pure fluids studied in this work were used to obtain the best values for the parameters of the GV-SSAFT. The results obtained from the GV-SSAFT for liquid densities and vapor pressures of pure associating and non-associating fluids were compared with those obtained from the SSAFT equation of state. The results showed that the GV-SSAFT similar to the SSAFT can accurately correlate the experimental data of liquid density and vapor pressure for systems studied. On the other hand the results obtained from two SAFT-based equations of state are almost identical. In order to show capability of the GV-SSAFT and SSAFT equations of state, they were used to directly calculate heat of vaporization for a number of pure associating and non-associating fluids. Slightly better results for heat of vaporization comparing to the experimental data were obtained from the GV-SSAFT EOS than those obtained from the SSAFT. The GV-SSAFT was also used to study the VLE phase behavior for a number of binary associating and non-associating mixtures. The results also showed that the GV-SSAFT can be successfully used to study the phase behavior of mixtures studied in this work.     

Prediction of thermodynamic, transport and vapor-liquid equilibrium properties of binary mixtures of ethylene glycol and water

Equilibrium and non-equilibrium molecular dynamics and Monte Carlo simulation techniques were applied to predict various thermodynamic, transport and vapor-liquid equilibrium properties of binary mixtures of ethylene glycol and water (EG-W) based on OPLS-AA and SPC/E force fields. The properties predicted include density, vaporization enthalpy, enthalpy of mixing, heat capacities, diffusion coefficients, shear viscosities, thermal conductivities, vapor-liquid coexistence isotherms and isobaric curves, and saturation vapor pressures. Good agreements with experimental data were obtained for most of these properties. Errors are mostly related to inaccuracy found in predictions of pure fluids; a correction to prediction of pure substance can systematically improve prediction for the mixture. This work suggests that OPLS-AA and SPC/E force fields using the common combining rules are transferable for predicting multiple physical properties of EG-W mixtures.     

A New Association Term for SAFT Equation of State

This work is devoted to present a new expression for association part of SAFT equation of state. This expression is obtained by calculating the mole fraction of not bonded molecules through a general chemical theory of association. The new equation of state is named CSAFT and has one adjustable parameter less than original SAFT for pure associating fluids. The performance of CSAFT is investigated by PVT calculations for pure fluids and LLE calculations for binary and ternary mixtures. Results show that CSAFT correlates vapor pressure and liquid density data of pure associating components more accurate than SAFT. Also the accuracy of CSAFT model is much better than SAFT for LLE prediction of binary and ternary mixtures, considering SAFT has one pure component parameter more than CSAFT.     

Application of the crossover lattice equation of state for fluid mixtures

In previous work, we developed the crossover lattice equation of state (xLF EOS) for pure fluids and the xLF EOS yielded the saturated vapour pressure and the density values with a much better accuracy than the classical LF EOS over a wide range. In this work, we extended xLF EOS to fluid mixtures. Classical composition-dependent mixing rules with only adjustable two binary interaction parameters same as the LF EOS are used. A comparison is made upon experimental data for fluids mixtures in the one- and two-phase regions. The xLF EOS shows more improved representations than the LF EOS, especially in the critical region.     

Calculation of isentropic compressibility and sound velocity in two-phase fluids

Derivative properties from equations of state (EoS) are well defined for homogeneous fluid systems. However, some of these properties, such as isothermal and isentropic (or adiabatic) compressibilities and sound velocity need to be calculated at conditions for which a homogeneous fluid splits into two (or more) phases, liquid or vapor. The isentropic compressibility and sound velocity of thermodynamically equilibrated fluids exhibit important discontinuities at phase boundaries, as noticed long ago by Landau and Lifschitz in the case of pure fluids. In this work, the two-phase isentropic compressibility (or inverse bulk modulus) is expressed in terms of the two-phase isothermal compressibility, two-phase thermal expansivity and an apparent heat capacity, defined as the partial derivative of total enthalpy with respect to temperature at constant pressure and composition. The proposed method is simple (simpler than previous approaches), easy to implement and versatile; it is not EoS-dependent and it requires only a flash routine and the expression of total enthalpy at given pressure, temperature and composition. Our approach is applied to a variety of fluid systems representative of reservoir applications and geophysical situations, including petroleum fluids (oil and gas condensate) and mixtures of water and gas (methane or CO₂). For low gas content in the two-phase fluid, i.e., near bubble point conditions, we obtain significantly lower bulk moduli and sound velocities than predicted within Wood's conventional approach, in which the liquid and gas phases are considered to be “frozen” at the passage of the acoustic wave.     

Computer-aided product design of alternative solvents based on phase equilibrium synergism in mixtures

A systematic methodology is proposed to find binary azeotropic mixtures as new alternative solvents for the extraction process of volatile aroma molecules widely used in perfume and cosmetic industries. We investigated the use of the reverse engineering approach with computer-aided product design (CAPD) instead of the traditional “trial and error” approach. First, the design problem is defined from the real functionalities of the classical solvents. The latter are translated into physicochemical properties and the corresponding boundary values for each property are defined. The reverse engineering method coupled with CAPD consists in using optimization techniques for building molecular structures that match as best as possible the complete set of target physicochemical properties, thus defining for each candidate a performance index. Property values are evaluated by using group contribution methods for each molecular structure generated by a CAPD tool or by using database values. Acknowledging the contradictory relationship between two selected physicochemical properties, that is, low boiling temperature and high flash point, which is rarely found in pure components, binary azeotropic mixtures were studied to enhance the global performance of solvent candidates. Dimethyl carbonate used as a solvent for the extraction of aroma molecules from plants exhibits between the boiling temperature and the flash point. It was selected as the key component for designing binary azeotropic mixtures. The global performance of the binary azeotropic mixtures was verified by means of calculations of the vapor–liquid and liquid–liquid equilibrium using modified universal functional activity coefficient (UNIFAC) method as a thermodynamic method.     

Second-order thermodynamic derivative properties of selected mixtures by the soft-SAFT equation of state

We have discussed the capability of the soft-SAFT equation of state (EoS) to predict second order thermodynamic derivative properties of pure fluids in a recent paper [F. Llovell, L.F. Vega, J. Phys. Chem. B 110 (2006) 11427–11437]. The goal of this work is to extend these calculations to selected binary mixtures. The equation was applied in a semi-predictive manner: the pure component molecular parameters needed to apply soft-SAFT to experimental systems were obtained by fitting vapor–liquid equilibrium data and used, without further fitting, to calculate isochoric and isobaric heat capacities of selected alkane + n-alkane and n-alkane + 1-alkanol binary mixtures; isentropic compressibility coefficients and the speed of sound of selected n-alkane + 1-alkanol mixtures were calculated following the same procedure. We have used the crossover soft-SAFT equation which explicitly incorporates a renormalization group term in order to take into account the long range fluctuations appearing in the near critical region. Soft-SAFT was able to capture the qualitative behavior of the mixture properties studied, for a wide range of conditions, showing quantitative agreement with experimental data in some of the cases. As a further test to the equation, we have also calculated excess properties. The equation was able to capture the non-ideal behavior upon mixing experienced by these properties. This work shows the robustness of the molecular parameters and the equation to calculate properties not included in the fitting procedure, in a predictive manner.     

Critical points of hydrocarbon mixtures with the Peng–Robinson,SAFT, and PC-SAFT equations of state

The phase behavior of fluids at high pressures can be rather complex, even for mixtures of relatively simple molecules, such as hydrocarbons. In this work, we use the Hicks and Young algorithm to calculate mixture critical points, comparing five modeling options: Peng–Robinson EOS: (1) original and (2) with parameters fitted from molar volume and vapor pressure data; (3) SAFT EOS; and PC-SAFT EOS: (4) original and (5) with refitted parameters to match pure component critical data. Calculations were carried out for binary hydrocarbon mixtures and 29 multicomponent mixtures. The SAFT EOS provided the worst representation of the systems tested and, interestingly, the conventional cubic EOS provided, in general, the best representation.     

Phase behavior of binary mixtures of water,carbon dioxide and decane predicted with a lattice-gas model

The Kleintjens—Koningsveld lattice-gas model is used to predict the phase behavior of pure CO₂, water and decane, and of binary mixtures of CO₂ with water and decane. The model, with parameters fitted to experimental data, predicts very accurate vapor pressures and liquid—vapor coexistence densities for the pure fluids. For the binary mixtures, the model correctly predicts the qualitative patterns of phase behavior using two temperature-dependent mixture parameters fitted to simple polynomials over a small range of temperature. For quantitative predictions over wide temperature ranges, however, the temperature dependence of the mixture parameters must be fitted carefully over the same ranges of temperatures. The performance of the Kleintjens—Koningsveld model is compared to that of the Peng—Robinson model.     

A new cubic equation of state for simple fluids: pure and mixture

A two-parameter cubic equation of state is developed. Both parameters are taken temperature dependent. Methods are also suggested to calculate the attraction parameter and the co-volume parameter of this new equation of state. For calculating the thermodynamic properties of a pure compound, this equation of state requires the critical temperature, the critical pressure and the Pitzer’s acentric factor of the component. Using this equation of state, the vapor pressure of pure compounds, especially near the critical point, and the bubble point pressure of binary mixtures are calculated accurately. The saturated liquid density of pure compounds and binary mixtures are also calculated quite accurately. The average of absolute deviations of the predicted vapor pressure, vapor volume and saturated liquid density of pure compounds are 1.18, 1.77 and 2.42%, respectively. Comparisons with other cubic equations of state for predicting some thermodynamic properties including second virial coefficients and thermal properties are given. Moreover, the capability of this equation of state for predicting the molar heat capacity of gases at constant pressure and the sound velocity in gases are also illustrated.     

Studies on fluids and their mixtures using the Born-Green-Yvon integral equation technique

We have developed the Born-Green-Yvon (BGY) integral equation theory for investigating the equilibrium properties of fluids and their mixtures both on the lattice and in the continuum. Using the continuum theory we have studied hard sphere fluids over a range in density having chain lengths between one and fifty sites. We have also investigated the collapse transition of a square well chain and a square well ring, each having up to four hundred sites, and have predicted the theta temperature for these systems. Turning to the case of a dilute (hard-sphere) solution we have been able to show the effect of solvation on a hard sphere chain, and captured the dependence of this effect on the ratio of hard sphere diameters of the solvent and chain segments. In all the continuum studies we have found good to excellent agreement with simulation results. We have also derived a lattice BGY theory which, while less sophisticated than the continuum version, has the advantage of producing simple closed-form expressions for thermodynamic properties of interest. This theory is capable of exhibiting the full range of miscibility behaviour observed experimentally, including upper and lower critical solution temperatures and closed-loop phase diagrams. We find that the theory does an excellent job of fitting to different kinds of experimental data and, making use of the parameters derived from fits to pure component data alone, we have been able to predict properties ranging from pure fluid vapour pressures and critical temperatures to changes in the volume and enthalpy on mixing as well as coexistence curves for solutions.     

Activity coefficients of associating mixtures by group contribution

A group contribution model is presented for the prediction of activity coefficients in associating mixtures. An association term has been added to the traditional UNIFAC residual and combinatorial contributions to the activity coefficients. The association term is based on Wertheim's theory for fluids with highly directed attractive forces, as applied in the SAFT equation, and it follows the group contribution approach proposed by Gros et al. in the GCA-EOS model. Good predictions of both vapor–liquid and liquid–liquid equilibria are achieved, with a set of group interaction parameters determined from infinite dilution activity coefficients.     

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.     

The special features of molecular transport in nanosized channels

The molecular theory of the transport of pure substances and mixtures of molecules of different shapes in narrow slit-like pores, in which the potential of surface forces creates a strongly anisotropic distribution of molecules across pores and thereby makes the hydrodynamics equation inapplicable, is considered. The new microhydrodynamic approach is based on the lattice gas model, which takes into account the intrinsic volume of molecules and intermolecular interactions in the quasi-chemical approximation. Self-consistent calculations of dissipative coefficients taking nonlocal fluid properties into account were performed on the basis of the transition state model including information about equilibrium adsorbate distribution. Changes in fluid concentrations from the gaseous to liquid state and a broad temperature range, including the critical region, are analyzed. This allows vapor, liquid, and vapor-liquid fluid flows to be considered in the presence of capillary condensation. An increase in the size of pores transforms the equations of the theory into hydrodynamic transfer equations for gas or liquid flows, while preserving the relation of transfer coefficients to intermolecular potentials. The use of microhydrodynamic approach equations in numerical calculations and the possibility of applying this approach are discussed.     

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.     

Theoretical prediction of the coordination number, local composition, and pressure-volume-temperature properties of square-well and square-shoulder fluids

By assuming a Boltzmann distribution for the molecular equilibrium between local and bulk environments, a general model is derived for the prediction of coordination numbers and local compositions of square-well and square-shoulder fluids. The model has no empirical parameter fitted from the data of square-well and square-shoulder fluids, but is valid from the low-density limit to the high-density limit. The applicable width of well or shoulder covers the commonly used range varying from 1.0 to 2.0. The model can accurately predict the coordination numbers of pure square-well and square-shoulder fluids, so the equation of state derived from it is superior to other equations of state based on the existing coordination number models. The model also accurately predicts the local compositions of mixtures in wide ranges of density and size ratio (1.0-8.0), as well as the configuration energy of lattice gases and highly nonideal lattice mixtures. It is remarkable that the model correctly predicts temperature-dependent coordination numbers and local compositions for both equal- and unequal-sized mixtures at close packing, which cannot be predicted by the existing coordination number models. Our derivation demonstrates that the energy parameters in local composition models should represent the potential difference of a molecule between the local and bulk environments, not the pair-interaction potential, and depend on the system conditions and different kinds of pair-interaction parameters. This result is very useful for the development of local composition and activity coefficient models and the mixing rules of equations of state.     

A Helmholtz energy equation of state for calculating the thermodynamic properties of fluid mixtures

A new approach has been developed for calculating the properties of mixtures based on an equation of state explicit in reduced Helmholtz energy. This approach allows for the representation of the thermodynamic properties over a wide range of fluid states and is based on highly accurate equations of state for the pure components combined at the reduced temperature and density of the mixture. The reducing parameters used for temperature and density depend on composition. For simple mixtures (those that closely follow Raoult's law), a very accurate representation of all thermodynamic properties has been achieved with relatively simple functions. For nonideal mixtures, the reducing functions for density and temperature were modified, and a departure function was added to the equation of state. Generally, the model is able to represent liquid and vapor states with uncertainties of 0.1% in density, 1% in heat capacities and 1% in bubble point pressures if experimental data of comparable uncertainties exist. Two applications of the mixture model concepts were developed independently by the authors in the United States and Germany over the same time period. These applications include the development of individual equations for each binary system and a generalization of the model which is valid for a wide variety of mixtures. The individual approaches are presented with an explanation of the similarities and differences. Although the paper focuses mainly on binary systems, some results for ternary mixtures are also presented.     

Dependence of the critical temperature on molecular parameters

At the critical temperature the surface tension between coexisting liquid and vapor phases must be zero, and the repulsive contributions associated with cavity formation must exactly counterbalance those from interactions of a molecule in the cavity and the bulk. An expression for the critical temperature of pure fluids in terms of the parameters of scaled particle theory (SPT) has been obtained, and the calculated critical temperatures are compared with experimental data for a range of pure fluids. These include noble and diatomic gases, short and medium length hydrocarbons, aromatic compounds, halogenated compounds, oxygen-containing compounds, and water. Considering the simplicity of this approach, a remarkably good correlation between calculated and experimental values is found for most of these fluids.     

A three-parameter cubic equation of state for prediction of thermodynamic properties of fluids

A new cubic three-parameter equation of state has been proposed for PVT and VLE calculations of simple, high polar and associating fluids. The parameters are temperature dependent in sub-critical region, but temperature independent in super-critical region. The results for 42 simple and 14 associative pure compounds indicate that the calculated saturation properties and volumetric properties over the whole temperature range, up to high pressures, by the proposed equation of state (EOS), were in better agreement with the experimental data, compared with those obtained by the five well-known EOSs (P–R, P–T, Adachi et al., Yu–Lu, and M4). Two derivative properties, molar enthalpy and heat capacity of water and ammonia have been calculated, and demonstrated the thermodynamic consistency of the EOS parameters. Also VLE calculations have been performed for 41 binary mixtures of different type of fluids, including those of interest in petroleum industry. The results indicated the high capability of the proposed EOS for calculating the thermodynamic properties of pure and fluid mixtures.