A crossover lattice fluid equation of state for pure fluids

A lattice fluid model is one of the most versatile, molecular-based engineering equations of state (EOS) but, in common with all analytic equations of state, the lattice fluid (LF) EOS exhibits classical behaviour in the critical region rather than the non-analytical, singular behaviour seen in real fluids. In this research, we use the LF EOS and develop a crossover lattice fluid (xLF) equation of state near to and far from the critical region which incorporates the scaling laws valid asymptotically close to the critical point while reducing to the original classical LF EOS far from the critical point. We show that, over a wide range of states, the xLF EOS yields the saturated vapour pressure data and the density data with much better accuracy than the classical LF EOS.     

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.     

Estimation of 2nd-order derivative thermodynamic properties using the crossover lattice equation of state

We apply the crossover lattice equation of state (xLF EOS) [M.S. Shin, Y. Lee, H. Kim, J. Chem. Thermodyn. 40 (2007) 174–179] to the calculations of thermodynamic 2nd-order derivative properties (isochoric heat capacity, isobaric heat capacity, isothermal compressibility, thermal expansion coefficient, Joule–Thompson coefficient, and sound speed). This equation of state is used to calculate the same properties of pure systems (carbon dioxide, normal alkanes from methane to propane). We show that, over a wide range of states, the equation of state yields properties with better accuracy than the lattice equation of state (LF EOS), and near the critical region, represents singular behavior well.     

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.     

Empirical correction to the Peng–Robinson equation of state for the saturated region

This work presents an empirical correction to improve the Peng–Robinson equation of state (PR EOS) for representing the densities of pure liquids and liquid mixtures in the saturated region using the volume translation method. A temperature-dependent volume correction is employed to improve the original PR EOS so that it can match the true critical point of pure fluids. The volume correction is generalized as a function of the critical parameters and the reduced temperature. The volume translation PR (VTPR) EOS with the generalized volume correction accurately represents the saturated liquid densities for different polar and non-polar fluids, including alkanes, cycloparaffins, halogenated hydrocarbons, olefins, cyclic olefins, aromatics and inorganic molecules. The average relative deviations for 91 pure compounds was 1.37%. The generalized VTPR EOS was also used to predict the saturated liquid density of 53 binary mixtures with a relative deviation of 0.98%. The generalized VTPR EOS can also be extended to other materials. The accuracy of the generalized VTPR EOS compares well with other methods and equations of state.     

A novel equation of state for the prediction of thermodynamic properties of fluids

This work proposes a new equation of state (EOS) based on molecular theory for the prediction of thermodynamic properties of real fluids. The new EOS uses a novel repulsive term, which gives the correct hard sphere close packed limit and yields accurate values for hard sphere and hard chain virial coefficients. The pressure obtained from this repulsive term is corrected by a combination of van der Waals and Dieterici potentials. No empirical temperature functionality of the parameters has been introduced at this stage. The novel EOS predicts the experimental volumetric data of different compounds and their mixtures better than the successful EOS of Peng and Robinson. The prediction of vapor pressures is only slightly less accurate than the results obtained with the Peng-Robinson equation that is designed for these purposes. The theoretically based parameters of the new EOS make its predictions more reliable than those obtained from purely empirical forms.     

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.     

Equation of state for square-well chain molecules with variable range II. Extension to mixtures

An equation of state (EOS) developed in our previous work for square-well chain molecules with variable range is further extended to the mixtures of non-associating fluids. The volumetric properties of binary mixtures for small molecules as well as polymer blends can well be predicted without using adjustable parameter. With one temperature-independent binary interaction parameter, satisfactory correlations for experimental vapor–liquid equilibria (VLE) data of binary normal fluid mixtures at low and elevated pressures are obtained. In addition, VLE of n-alkane mixtures and nitrogen + n-alkane mixtures at high pressures are well predicted using this EOS. The phase behavior calculations on polymer mixture solutions are also investigated using one-fluid mixing rule. The equilibrium pressure and solubility of gas in polymer are evaluated with a single adjustable parameter and good results are obtained. The calculated results for gas + polymer systems are compared with those from other equations of state.     

The extension of coordination number model by using the local composition theory: mixtures

The extension of a new coordination number model to mixture is presented in this work. Extended model agrees well with the Monte Carlo (MC) simulation results for square-well (SW) mixture fluids and shows better results compared with other models. To test our model, we compare the compressibility factors from various models for SW fluids at different λ values and for SW fluid mixtures at λ=1.5. Although our model is obtained by fitting simulation data at λ=1.5, it shows better results for the different λ values than other coordination number model. Compared with the compressibility factors of various binary mixtures of SW fluids calculated from other models, this model presents better results. Because our model considers the temperature dependency importantly by using the total site number, it predicts coordination number and compressibility factor well in the wide temperature range and enables one to derive an equation of state (EOS) through integration of the coordination number equation.     

Simple modification of the temperature dependence of the Sanchez–Lacombe equation of state

In this work, the interaction energy term of the Sanchez–Lacombe equation of state (SL EOS) was modified to take into account the temperature dependence of hydrogen bonding and ionic interactions. A simple function was used in the form of the Langmuir equation that reduces to the original SL EOS at high temperature. Comparisons are shown between the ?*-modified SL EOS and the original SL EOS. The ?*-modified SL EOS could represent volumetric data for the group of non-polar fluids, polar fluids and ionic liquids to within an absolute average deviation (AAD) of 0.85%, 0.51%, and 0.054%, respectively whereas, the original Sanchez–Lacombe EOS gave AAD values of 0.99%, 1.2%, and 0.21%, respectively. The ?*-modified SL EOS provides remarkably better PVT representation and can be readily applied to mixtures.     

Generalized Flory-Huggins theory-based equation of state for ring and chain fluids

By modeling the ring-like molecule as a pearl necklace of freely jointed hard sphere, we develop a new equation of state (EOS) for the ring-like fluids on the basis of generalized Flory-Huggins (GFH) theory. Before proposing the new EOS of the ring-like fluids, we first modify the generalized Flory-Huggins theory for the chain fluids by incorporating a function related to the packing fraction into the insertion probability. The results indicate that the modified GFH EOS can predict the compressibility factors more accurately than the GFH EOS, especially for the intermediate and high packing fractions (η ≥ 0.157). Subsequently, the modified GFH theory-based EOS for the ring-like fluids is proposed. Compared to the Monte Carlo data of 3-mer, 4-mer, 5-mer, 6-mer, 16-mer, and 32-mer ring-like fluids, our EOS exhibits the best prediction among four EOSs for the compressibility factors at intermediate and high packing fractions (η ≥ 0.157), although our EOS also shows a slight underestimation for the compressibility factors at low packing fractions. In summary, this is the first report on the generalized Flory-Huggins theory-based EOS for the ring-like fluids. It is expected that the same strategy can be applied to these fluids with more complex architectures.     

Application of a volume-translated Peng-Robinson equation of state on vapor-liquid equilibrium calculations

A volume-translated Peng-Robinson (VTPR) equation of state (EOS) is developed in this study. Besides the two parameters in the original Peng-Robinson equation of state, a volume correction term is employed in the VTPR EOS. In this equation, the temperature dependence of the EOS energy parameter was regressed by an improved expression which yields better correlation of pure-fluid vapor pressures. The volume correction parameter is also correlated as a function of the reduced temperature. The VTPR EOS includes two optimally fitted parameters for each pure fluid. These parameters are reported for over 100 nonpolar and polar components. The VTPR EOS shows satisfactory results in calculating the vapor pressures and both the saturated vapor and liquid molar volumes. In comparison with other commonly used cubic EOS, the VTPR EOS presents better results, especially for the saturated liquid molar volumes of polar systems. VLE calculations on fluid mixtures were also studied in this work. Traditional van der Waals one-fluid mixing rules and other mixing models using excess free energy equations were employed in the new EOS. The VTPR EOS is comparable to other EOS in VLE calculations with various mixing rules, but yields better predictions on the molar volumes of liquid mixtures.     

A new cubic simplified perturbed hard-body equation of state

A new cubic equation of state (EOS) was developed in this study for vapor-liquid equilibrium (VLE) calculations of nonpolar fluids. The repulsive term of this EOS reexpressed the results of Walsh and Gubbins (1990) from their modified thermodynamic perturbation theory of polymerization into a simple form in which a non-spherical parameter was employed to account for the different shapes of molecules. The repulsive compressibility factors calculated from this EOS agree well with the molecular simulation data for various kinds of hard bodies ranging from a single hard sphere to tangent or fused long chain molecules. A simple attractive term was then coupled with the repulsive to complete the EOS in a cubic form. Equation parameters were determined for a diversity of nonpolar real fluids. These parameters were expressed in generalized forms for engineering computations. Satisfactory results from this EOS on the saturated properties of pure nonpolar fluids were obtained. This EOS was also extended to calculate the VLE of nonpolar fluid mixtures. The results are again satisfactory over wide ranges of temperature and pressure.     

Joule–Thomson inversion curves of mixtures by molecular simulation in comparison to advanced equations of state: Natural gas as an example

Molecular modelling and simulation as well as four equations of state (EOS) are applied to natural gas mixtures regarding Joule–Thomson (JT) inversion. JT inversion curves are determined by molecular simulation for six different natural gas mixtures consisting of methane, nitrogen, carbon dioxide and ethane. These components are also regarded as pure fluids, leading to a total of 10 studied systems. The results are compared to four advanced mixture EOS: DDMIX, SUPERTRAPP, BACKONE and the recent GERG-2004 Wide-Range Reference EOS. It is found that molecular simulation is competitive with state-of-the-art EOS in predicting JT inversion curves. The molecular based approaches (simulation and BACKONE) are superior to DDMIX and SUPERTRAPP.     

Description of self-diffusion coefficients of gases,liquids and fluids at high pressure based on molecular simulation data

The purpose of this work is to evaluate the potential of modeling the self-diffusion coefficient (SDC) of real fluids in all fluid states based on Lennard–Jones analytical relationships involving the SDC, the temperature, the density and the pressure. For that, we generated an equation of state (EOS) that interrelates the self-diffusion coefficient, the temperature and the density of the Lennard–Jones (LJ) fluid. We fit the parameters of such LJ–SDC–EOS using recent wide ranging molecular simulation data for the LJ fluid. We also used in this work a LJ pressure–density–temperature EOS that we combined with the LJ–SDC–EOS to make possible the calculation of LJ–SDC values from given temperature and pressure. Both EOSs are written in terms of LJ dimensionless variables, which are defined in terms of the LJ parameters ɛ and σ. These parameters are meaningful at molecular level. By combining both EOSs, we generated LJ corresponding states charts which make possible to conclude that the LJ fluid captures the observed behavioral patterns of the self-diffusion coefficient of real fluids over a wide range of conditions. In this work, we also performed predictions of the SDC of real fluids in all fluid states. For that, we assumed that a given real fluid behaves as a Lennard–Jones fluid which exactly matches the experimental critical temperature T_c and the experimental critical pressure P_c of the real fluid. Such an assumption implies average true prediction errors of the order of 10% for vapors, light supercritical fluids, some dense supercritical fluids and some liquids. These results make possible to conclude that it is worthwhile to use the LJ fluid reference as a basis to model the self-diffusion coefficient of real fluids, over a wide range of conditions, without resorting to non-LJ correlations for the density–temperature–pressure relationship. The database considered here contains more than 1000 experimental data points. The database practical reduced temperature range is from 0.53 to 2.4, and the practical reduced pressure range is from 0 to 68.4.     

Group contribution multifluid lattice theory for simultaneous predictions of thermodynamic properties of pure fluids and mixtures

A unified group contribution (GC) lattice equation of state (EOS) was formulated based on the multifluid approximation of the nonrandom lattice fluid theory. The GC-EOS requires segment size and interaction energy parameter from functional group characteristics. The unique feature of the approach is that a single set of group parameters are used for both pure fluids and mixtures. The approach was found to be quantitatively applicable for predicting thermodynamic properties of real pure fluids and mixtures. Its potential utility was demonstrated for vapor pressures, vapor–liquid coexistence densities of pure fluids and phase equilibrium properties of mixtures including polymeric solutions.     

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.     

Mixing rules for van-der-Waals type equation of state based on thermodynamic perturbation theory

A concept based on the thermodynamic perturbation theory for a `simple fluid' has been applied to the attractive term of a van-der-Waals type equation of state (EOS) to derive a simple mixing rule for the a parameter. The new mixing rule is a small correction to the original one-fluid approximation to account for the influence of particles of j-type on the correlation function of ii-type in a mixture consisting of particles of i and j types. The importance of the correction has been shown by comparison of the calculated results for binary mixtures of Lennard–Jones fluids with the data obtained by numerical method (Monte-Carlo simulation). The new mixing rules can be considered as a flexible generalization of the conventional mixing rules and can be reduced to the original v-d-W mixing rules by defaulting the extra binary parameters to zero. In this way the binary parameters already available in the literature for many systems can be used without any additional regression work. Extension of the new mixing rules to a multicomponent system do not suffer from `Michelsen–Kistenmacher syndrome' and provide the correct limit for the composition dependence of second virial coefficients. Their applicability has been illustrated by various examples of vapor–liquid and liquid–liquid equilibria using a modified Patel–Teja EOS. The new mixing rules can be applied to any EOS of van-der-Waals type, i.e., EOS containing two terms which reflect the contributions of repulsive and attractive intermolecular forces.     

Prediction of gas condensate properties by Esmaeilzadeh–Roshanfekr equation of state

The Esmaeilzadeh–Roshanfekr (ER) equation of state (EOS) is used to predict the PVT properties of gas condensate reservoir fluids. Three gas condensate fluid samples taken from three wells in a real field in Iran, referred here as SA1, SA4 and SA8, as well as five samples from literature have been used to check the validity of the ER EOS in calculating the PVT properties of gas condensate mixtures. Some experiments such as constant composition expansion (CCE), constant volume depletion (CVD) and dew point pressures are carried out on these samples. In order to have an unbiased comparison between the ER and the Peng–Robinson (PR) equation of state, van der Waals mixing rules are used without using any adjustable parameters (k_ij = 0). Also, no pure component parameters are adjusted. The critical properties and acentric factor for plus-fraction are estimated by the Kesler–Lee, Pedersen et al. and Riazi–Daubert characterization methods. The results of dew point pressure calculations show that the ER EOS has smaller error than the PR EOS. For some mixtures, relative volume, gas compressibility factor and condensate drop-out in CVD and CCE test were also predicted. Comparison results between experimental and calculated data indicate that the ER EOS has smaller error than the PR EOS. The total average absolute deviation was found to be 0.82% and 2.97% for calculating gas compressibility factor and gas specific gravity in CVD test. Also, the total average absolute deviation was found to be 2.06% and 3.42% for calculating gas compressibility factor and relative volume in CCE test.     

Semi-empirical insertion probability for hard-spheres and hard-sphere chains

In spite of its simplicity and a well-defined theoretical basis, the Flory–Guggenheim approach is conventionally regarded as inapplicable to off-lattice system since the insertion probability of the approach does not account for the excluded region, existing in the off-lattice system. In this work, we propose the insertion probability accounting for the excluded region of off-lattice fluids and derive a new version of equation of state (EOS) for hard-sphere chains basing on the Flory–Guggenheim approach. To investigate the behavior of the excluded regions, a Monte Carlo sampling was performed for hard disks and the various excluded regions were found to have different density dependence. On the basis of the simulation result, we formulated the insertion probability for hard-sphere and that of hard-sphere chain which accounts for the effect of chain-connectivity on the monomer insertion. The proposed insertion probability was found to correctly predict the simulation data for monomer and correctly correlate the simulation data for chain fluids. The resulting EOS was found to meet closed-packed limit and predict the simulation data of compressibility factor for monomer and chains with a reasonable degree of accuracy. When compared with other off-lattice based EOS, it shows a comparable or better result. For second virial coefficient of chain molecules, the model was found to reasonably predict the simulation data.