Modification of Simha–Somcynsky equation of state for small and large molecules

The Simha–Somcynsky equation of state (SS EOS) represents the PVT behavior of polymers quite satisfactorily, but cannot be applied to gases at low pressures. This work proposes a modification of the free volume contribution of the SS EOS to allow representation of gaseous state of low molecular-weight substances by introducing the perturbed hard-chain theory of Beret and Prausnitz into the EOS. In addition to this modification, two universal constants are introduced to the free volume term for better representation of properties of low molecular-weight substances. Characteristic parameters in the modified SS EOS were determined for 44 low molecular-weight substances and 64 polymers. The absolute average deviations (AADs) for critical temperature, critical pressure and vapor pressures were 0.86, 2.38 and 2.01%, respectively, while AAD for critical density and saturated liquid density at normal boiling point were somewhat larger, being 20.46 and 5.30%, respectively. The high performance of the original SS EOS for polymer PVT behavior was maintained in the modified EOS with grand AAD of 0.050% for densities.     

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.     

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.     

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.     

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.     

Vapor-liquid equilibria simulation and an equation of state contribution for dipole-quadrupole interactions

A systematic investigation on vapor-liquid equilibria (VLEs) of dipolar and quadrupolar fluids is carried out by molecular simulation to develop a new Helmholtz energy contribution for equations of state (EOSs). Twelve two-center Lennard-Jones plus point dipole and point quadrupole model fluids (2CLJDQ) are studied for different reduced dipolar moments micro*2=6 or 12, reduced quadrupolar moments Q*2=2 or 4 and reduced elongations L*=0, 0.505, or 1. Temperatures cover a wide range from about 55% to 95% of the critical temperature of each fluid. The NpT+test particle method is used for the calculation of vapor pressure, saturated densities, and saturated enthalpies. Critical data and the acentric factor are obtained from fits to the simulation data. On the basis of this data, an EOS contribution for the dipole-quadrupole cross-interactions of nonspherical molecules is developed. The expression is based on a third-order perturbation theory, and the model constants are adjusted to the present 2CLJDQ simulation results. When applied to mixtures, the model is found to be in excellent agreement with results from simulation and experiment. The new EOS contribution is also compatible with segment-based EOS, such as the various forms of the statistical associating fluid theory EOS.     

A new equation of state for metal alloys

A perturbed hard-trimer (PHT) equation of state (EOS) has been employed to model volumetric properties of molten metals and their alloys considering a trimer expression obtained from the statistical associating fluid theory. The van der Waals dispersion forces were applied as perturbation term. Two parameters appeared in the PHT EOS, reflecting the dispersive energy among trimers, ε and the hard-core diameter σ were determined based on the molecular scaling parameters. The performance of the proposed PHT EOS has been evaluated by predicting the saturated and isobaric densities of 16 molten metals including alkali metals, alkali earth and refractory metals over the temperature range within 234–7400 K and pressures up to 436 MPa. From 677 data points examined, the average absolute deviation (AAD) of the predicted densities from the experimental ones was found to be 1.60%. Furthermore, the estimated uncertainties of predicted densities of alloys were ±3.00%.     

Volumetric profile of polymer melts from the ISM equation of state

Knowledge of the volumetric or pressure–volume–temperature (PVT) profile of molten polymers is important for both engineering and polymer physics. Ihm–Song–Mason (ISM) equation of state (EOS) has been employed to predict the volumetric properties of 12 molten polymers. The significance of the present paper is three temperature-dependent parameters of the ISM EOS to be determined using corresponding states correlations based on the molecular scaling constants, dispersive energy parameters between segments/monomers (ε) and segment diameter (σ) rather than bulk properties, e.g. the liquid density and temperature both at normal boiling point. The ability of the ISM EOS has been evaluated by comparing the results with 1390 literature datapoints for the specific volumes over the temperature range from 293 to 603.5 K and pressure range from 0.1 to 200 MPa. The average absolute deviation (AAD) of the calculated specific volumes from literature data was found to be 0.52%. The isothermal compressibility coefficients, κ_T values of molten polymers have also been predicted using the ISM EOS. From 684 datapoints examined, the AAD of estimated κ_T was equal to 7.55%. Our calculations on the volumetric and thermodynamic properties of studied polymers reproduce the literature data with reasonably good accuracy.     

Totally inclusive cubic equation of state with five parameters for pure fluids

A totally inclusive cubic equation of state (cubic EOS) is proposed. Although, its form is fairly simple as compared with the present cubic equations, it can include all of them as special cases. The EOS has five parameters. By fitting the experimental critical isothermal for six typical substances combining the critical conditions, the generalized expressions for the five parameters at critical temperature are established. The temperature coefficients of the five parameters for 43 substances are determined by fitting the experimental data of vapor pressure and saturated liquid density. These coefficients are correlated with the critical compressibility factor and acentric factor to obtain the generalized expressions. The predicted saturated vapor pressure, saturated liquid density, critical isothermal and coexistence curve near the critical point show that the equation gives the best results when compared with the Redlich–Kwong–Soave (RKS) and Peng–Robinson (PR) EOS.     

由L-J流体的FMSA状态方程计算流体的PVT性质

运用Tang等提出的Lennard-Jones (L-J)流体两参数的一阶平均球形近似(FMSA)状态方程, 计算了流体的汽液共存相图和饱和蒸汽压曲线, 以及非饱和区的PVT性质, 并与文献数据进行比较. L-J参数由Tr＜0.95的汽液相共存数据回归得到. 计算结果表明, 对于分子较接近球形的流体, 除临界点附近外, 该方程可以在较大的温度和压力范围内计算真实流体的PVT性质, 结果满意. 对于球形分子, 该方程的精确度随分子尺寸的变大基本保持稳定. 该方程不适用于强极性物质. 在高密度区, 该方程的计算结果明显优于P-R方程. 对于分子偏离球形较远的流体, 该方程的适用性变差, 此时要考虑分子形状的影响, 可采用三参数的FMSA状态方程进行计算.     

Predicting the dew point pressure for gas condensate reservoirs: empirical models and equations of state

This paper presents a new empirical model to estimate dew point pressure (DPP) for gas condensate reservoirs as a function of routinely measured gas analysis and reservoir temperature. The proposed model was developed using experimentally measured and collected data of 340 gas condensate samples covering a wide range of gas properties and reservoir temperatures. The new model has an average relative deviation (ARD) of 0.44% and average absolute deviation (AAD) of 7.68% or 346 psia (1 psia=6.894757E−3 mPa). The accuracy of the model has been compared to SRK-EOS, PR-EOS and other correlations. Gas condensate samples from this study as well as from literature have been used to check the validity of the proposed model against EOS simulation. These examples have shown that the model successfully captures the physical trend and that the model is reliable. This model is useful to provide an estimate of the DPP when experimentally measured ones are not available.The current study also shows that predicting the DPP for gas condensates depends on the EOS(s), the number of pseudo-components and the characterization of the plus fraction. For most of the gas condensates used in this study, a 10–12 pseudo-components of the heptane plus (C₇₊) fraction resulted in minimum error in calculation of DPP using PR-EOS with Pedersen et al. characterization of the plus fraction.     

Application of GC-PPC-SAFT EoS to amine mixtures with a predictive approach

The GC-PPC-SAFT equation of state (EoS) is a combination of a group contribution method [S. Tamouza et al., Fluid Phase Equilib. 222-223 (2004) 67-76; S. Tamouza et al., Fluid Phase Equilib. 228-229 (2005) 409-419] and the PC-SAFT EoS [J. Gross, G. Sadowski, Ind. Eng. Chem. Res. 40 (2001) 1244-1260] which was adapted to the polar molecules [D. Nguyen-Huynh et al., Fluid Phase Equilib. 264 (2008) 62-75]. It is here applied to the vapour pressure and liquid molar volume of primary, secondary and tertiary amines and their mixtures with n-alkanes, primary and secondary alcohols, using previously published group parameters. The mixing enthalpy is also evaluated for the binary systems. Binary interaction parameters k_ij are computed using a group-contribution pseudo-ionization energy, as proposed by Nguyen-Huynh [D. Nguyen-Huynh et al., Ind. Eng. Chem. Res. 47 (2008) 8847-8858]. A unique corrective parameter for the cross-association energy between amines and alcohols is used.The agreement with experimental data in correlation and prediction were found rather encouraging. The mean absolute average deviation (AAD) on bubble pressure is about 3.5% for pure amines. The mean AAD on the vapour-liquid equilibria (VLE) are respectively 2.2% and 5.5% for the amine mixtures with n-alkanes and alcohols. The AADs on saturated liquid volume are about 0.7% for the pure compounds and 0.9% for the mixtures. Prediction results are qualitatively and quantitatively accurate and they are comparable to those obtained with GC-PPC-SAFT on previously investigated systems.     

A new cubic equation of state for reservoir fluids

A new three-parameter cubic equation of state is developed with special attention to the application for reservoir fluids. One parameter is taken temperature dependent and others are held constant. The EOS parameters were evaluated by minimizing saturated liquid density deviation from experimental values and satisfying the equilibrium condition of equality of fugacities simultaneously. Then, these parameters were fitted against reduced temperature and Pitzer acentric factor. For calculating the thermodynamic properties of a pure component, this equation of state requires the critical temperature, the critical pressure, the acentric factor and the experimental critical compressibility of the substance. Using this equation of state, saturated liquid density, saturated vapor density and vapor pressure of pure components, especially near the critical point, are calculated accurately. The average absolute deviations of the predicted saturated liquid density, saturated vapor density and vapor pressure of pure components are 1.4%, 1.19% and 2.11%, respectively. Some thermodynamic properties of substances have also been predicted in this work.     

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.     

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 three-parameter cubic equation of state for calculation physical properties and vapor–liquid equilibria

A new three-parameter cubic equation of state is presented by combination of a modified attractive term and van der Waals repulsive expression. Also a new alpha function for the attractive parameter of the new EOS is proposed. The new coefficients of alpha function and the other parameters of the attractive term are adjusted using the data of the saturated vapor pressure and liquid density of almost 60 pure compounds including heavy hydrocarbons. The new EOS is adopted for prediction of the various thermophysical properties of pure compounds such as saturated and supercritical volume, enthalpy of vaporization, compressibility factor, heat capacity and sound velocity. Following successful application of the new EOS for the pure components, using vdW one-fluid mixing rules, the new EOSs are applied to prediction of the bubble pressure and vapor mole fraction of the several binary and ternary mixtures. The accuracy of the new EOS for phase equilibrium calculation is demonstrated by comparison of the results of the present EOSs with the PT, PR, GPR and SRK cubic EOSs.     

Thermodynamic properties of synthetic natural gases: Part 4. Dew point curves of synthetic natural gases and their mixtures with water: measurement and correlation

Experimental measurements of dew points for five synthetic natural gases (SNG)+water mixtures were carried out between 2.1×10⁵ and 73.2×10⁵ Pa in the temperature range from 224.3 to 270.2 K. The experimental results were analysed in terms of both an equation of state (EOS) model and an excess function–EOS method, which reproduced the experimental data with an AAD from 2.1 to 3.4 K and from 1.9 to 3.0 K, respectively.     

Liquid densities at high pressures

Aalto et al. recently proposed a model for compressed liquid densities. The model was found more accurate than the Hankinson–Brobst–Thomson (HBT) and Chang–Zhao models. However, the pressure region of the data studied was limited to 200 bar maximum. In this work, the recently developed liquid density model is extended to high pressures. The equation describing the pressure dependence of liquid density is reformulated and the required parameters are optimized using a database containing 7478 data points for 31 pure hydrocarbons; maximum pressure in this data set is 8000 bar. The average absolute deviation (AAD) between these data and the recommended model is 0.4636%. A comparison to the results obtained with the HBT and Chang–Zhao models for the same data set shows that the new model is clearly more accurate in the extended pressure range, as well. The revised model is also tested in predicting liquid densities for mixtures; 84 different combinations of mixing rules are studied. The evaluation of the mixing rules is carried out using two compilations of experimental data: the first one contains 6712 points for 47 binary and two ternary mixtures, and the second 3582 points for 11 methane+alkane mixtures. In addition, the predictions are tested with a data set of 1119 points for other miscellaneous mixtures. No binary interaction parameters are used. With the recommended mixing rules, the AAD percentage is 0.5824% for the first set of data. If one simply adopts the mixing rules recommended for the HBT model, the AAD value for the same data set becomes 0.7482%.     

Measurements and predictions of density and carbon dioxide solubility in binary mixtures of ethanol and n-decane

The solubility of carbon dioxide (CO₂) in binary mixtures of ethanol and n-decane has been measured using an in-house developed pressure-volume-temperature (PVT) apparatus at pressures up to 6 MPa and two different temperatures (303.2 and 323.2 K). Three different binary mixtures of ethanol and n-decane were prepared, and the densities of the prepared mixtures were measured over the studied pressure and temperature ranges. The experimental data of CO₂ solubility in the prepared mixtures and their saturated liquid densities were then reported at each temperature and pressure. The solubility data indicated that the gas solubility reduced as the ethanol mole fraction in the liquid mixture increased. The dissolution of CO₂ in the liquid mixtures resulted in the increase in the saturated liquid densities. The impact of gas dissolution on the saturated liquid densities was more pronounced at the lower temperature and lower ethanol compositions. The experimental solubility and density data were compared with the results of two cubic equations of state (EOSs), Soave–Redlich–Kwong (SRK) and Peng–Robinson (PR). The modeling results demonstrated that both EOSs could predict the solubility data well, while the saturated liquid densities calculated with the PR EOS were much better than those predicted with the SRK EOS.