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.     

Modification of the Peng–Robinson equation of state for helium in low temperature regions

Helium shows the nearest behaviour to ideal gas in the room conditions. In contrast, thermodynamic behaviour of helium in the critical region, in which its liquefaction is possible, is extremely complicated. The equation of state (EOS), which is in common use for helium, is the modified Benedict–Webb–Rubin (MBWR) EOS developed by McCarty and Arp which is a 13th-order equation with 32 substance-dependent parameters. MBWR is a complicated EOS and its use is time consuming. In this work, the modified Peng–Robinson EOS introduced by Feyzi et al. is customised with 10 adjustable parameters for helium in the temperature range of 2.20–15.20 K and pressures up to 16 bar. The proposed EOS is able to predict the properties of helium in the vapour–liquid equilibrium (VLE) conditions and in the single gas-phase region. In addition, a temperature-dependent correlation for constant pressure heat capacity of helium from very low up to normal temperatures is proposed. The liquefaction process of helium, which is being done by cooling it to very low temperatures by passing through a Joule–Thomson valve, is predicted by the proposed EOS. Very accurate results are observed.     

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.     

Data driven temperature dependence of EOS parameters

Using three kinds of experimental data (p_c, V_c and T_c at the critical state or P_s, V_s^v and V^sL at different temperatures for saturation data) three parameters of the EOS may be directly determined and the temperature dependence of the parameters may be established from thermodynamic conditions of vapour-liquid critical point or vapour-liquid phase equilibria respectively. The principle was demonstrated on the BACK EOS. Examples of argon and n-alkanes were used to demonstrate the idea. It was found, that there are two parameter sets of the BACK equation that satisfy the critical or saturation conditions for certain pure compounds. The BACK equation is able to reproduce experimental Z_c values for compounds above Z_c = 0.2764 (that is, for argon, methane, ethane), but it is improper for higher alkanes. In case of n-alkanes we found that there is no simple function for T dependence of BACK parameters. Parameter values obtained in the way demonstrated may be useful to give initial values for parameter estimation from experimental (e.g., VLE) data.     

Equation of state for the NH3−H2O system

An equation of state (EOS) for the NH₃–H₂O system has been developed. This EOS incorporates a highly accurate end-member EOS and on an empirical mixing rule. The mixing rule is based on an analogy with high order contributions to the virial expansion for mixtures. Comparison with experimental data indicates that the mixed system EOS can predict both phase equilibria and volumetric properties for this binary system with accuracy close to that of the experimental data from 50°C and 1 bar to critical temperatures and pressures.     

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.     

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.     

Density-and-temperature-dependent volume translation for the SRK EOS: 1. Pure fluids

A mathematical framework for applying a density-and-temperature-dependent volume translation in a thermodynamically consistent manner was developed. Volumetric equations of state (EOS)s that incorporate this translation procedure can be used to generate derived properties, such as fugacity and enthalpy departure, that are based on isothermal departure or residuals from ideal gas state conditions. This kind of translation serves to improve the original EOS and not simply act as a correlation for molar volumes. A density-and-temperature-modified translation of this type was applied to the Soave–Redlich–Kwong EOS and was shown to possess accuracy for saturation pressure predictions equivalent to the untranslated EOS, as well as greatly improved density predictions compared to what is available when using only constant valued translation. The EOS translated in this manner retains many of the important features of the untranslated EOS, such as explicit calculation of volume roots, while having the representation capabilities of substantially more complicated models, such as the extended virial equation of Benedict, Webb, Rubin, and Starling.     

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.     

盐酸酸洗终点电化学判断方法的研究

酸洗是去除钢铁材料表面氧化皮的有效方法,在酸洗工艺研究中酸洗终点的判断尤为重要.本文依据热轧带钢表面氧化皮在盐酸溶液中的反应历程,提出一种酸洗终点判断方法.以该法用于带钢酸洗的试验获得很好的精度.     

Towards understanding the effect of electrostatic interactions on the density of ionic liquids

In order to have a better understanding on the electrostatic contribution to the thermodynamic property of ionic liquids (ILs), a two-parameter equation of state (EOS) is developed on the basis of hard sphere perturbation theory by accounting for the dispersion interaction with Cotterman et al.’s EOS for L-J fluid and electrostatic interaction with mean spherical approximation (MSA) approach. The EOS is applicable for the density correlation of molecular liquids, and the resulting parameters, viz. Lennard–Jones dispersive parameter ?/k and soft-core diameter σ, can be used to predict the density of molecular mixtures and the corresponding ILs. The results indicate that the density of IL is always about 10% higher than the corresponding stoichiometric molecular mixture with which the IL is produced as an ionic adduct, for example, IL 1-methyl-3-methylimidazolium dimethylphosphate ([MMIM][DMP]) versus equimolar mixture of 1-methylimidazole (MIM) and trimethylphosphate (TMP). Furthermore, the density enhancement of ILs with respect to their corresponding stoichiometric molecular mixtures can be well represented by the electrostatic contribution among ionic species involved.     

Modeling high-pressure densities at wide temperature range with volume scaling: Cyclohexane + n-hexadecane mixtures

High-pressure density data for cyclohexane + n-hexadecane mixtures at a wide temperature range was modeled with several classical equations of state (EOS) and correlative models. A modification for softening the co-volume and another for a volume scaling of the Peng–Robinson EOS (VS-PR) were proposed. The VS-PR model is able to correlate the pure component experimental data employing only five adjustable parameters, with root-mean-square deviation (RMSD) between calculated and experimental densities essentially within the experimental error. This result is superior to widely used approaches, i.e., a six parameter Tait model and six parameter volume translations (temperature and pressure dependent) for Peng–Robinson and Patel–Teja EOS. The VS-PR model also represents well the isobaric thermal expansion and the isothermal compressibility coefficients of the pure cyclohexane, a small naphthenic substance as well as a long chain n-alkane hydrocarbon, n-hexadecane. When modeling the mixture data, the use of VS-PR model of pure components along with the Redlich–Kister expansion, truncated at the first term, the density was correlated within a RMSD only 60% greater than the experimental error. The proposed model is able to accurately represent all the tested mixture data with a relatively small number of parameters.     

PVT properties of imidazolium-, phosphonium-, pyridinium- and pyrrolidinium-based ionic liquids using critical point constants

Song and Mason equation of state (EOS) with a simple modification has been extended to modelling PVT properties of ionic liquids (ILs). The considered ILs are [C₁mim][MeSO4], [C₁mim][CH₃OC₂H₅SO₄], [C₁mim][(CH₃)₂PO₄], [C₂mim][MeSO4], [C₂mim][BF₄], [C₂mim][SCN], [C₂eim][NTf₂], [C₄mim][C(CN)₃], [C₄mim][CF₃SO₃], [C₄mim][SCN], [C₅mim][NTf₂], [C₈mim][NTf₂], [(C₆H₁₃)₃P(C₁₄H₂₉)][Cl], [(C₆H₁₃)₃P(C₁₄H₂₉)][NTf₂], [(C₆H₁₃)₃P(C₁₄H₂₉)][Ac], [C₃mpyr][NTf₂], [C₄mpyr][NTf₂] and [Py][C₂H₅OC₂H₄SO₄]. Three temperature-dependent parameters in the proposed EOS have been scaled as functions of reduced temperature with the use of the law of corresponding states. It is shown that the knowledge of just critical temperature and critical density is sufficient to predict the PVT properties of these ILs. The overall average absolute deviation of calculated densities from literature values for 1347 data points of 18 ILs was found to be 0.58%. The predicted density of ILs from proposed EOS has been compared with those obtained by other literature work. Moreover, we indicate that the Zeno line regularity can well be predicted by proposed model for ILs.     

Boyle temperatures for pure substances

We report Boyle temperatures of 83 pure substances calculated using the Zeno (unit compressibility) line from standard or reference equations of state (EOS). We compare the results using different EOS and from correlations already published in the literature. The maximum absolute difference in the calculation of the Boyle temperature from different EOS is 15, 3, 24 and 63 K for hydrocarbons, gases, freons, and other substances, respectively. For alcohols, the difference in calculated Boyle temperatures is 300 K for methanol and 5 K for ethanol.     

Quintic equation of state for pure substances in sub- and supercritical range

A new quintic equation of state (EOS) for pure substances and mixtures is proposed. The equation is based on critical parameters and one saturation point. The proposed Q5EOS is a generalisation of many cubic equations of state. Equation Q5 has five parameters, four of which are temperature-independent. The temperature-dependent parameter a is expressed by a relation based on a simple power function. Parameters defining this function can be calculated from saturation data, Boyle temperature and supercritical data.     

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.     

A new equation of state for studying the thermodynamic properties of real gases

In this study, based on the compressibility effect of gas molecules, a new three-parameter cubic equation of state (EOS) is derived. To validate this EOS, density predictions of methane, ethane, carbon dioxide and oxygen have been studied using the new EOS at the temperature of 373 K and at the pressures up to 100 MPa. The results show a good agreement with reference data and this suggests that the proposed EOS would help to improve the study of thermodynamic properties for real gases.     

缔合马丁-侯状态方程I 方程的建立

An associating MH equation of state (AMH EOS) is developed on the basis of the MH equation of state by incorporating the chemical association into it, a constant evaluation method is proposed for the AMH EOS. The AMH EOS is used to calculate thermodynamic properties of water, some alcohols and carboxylic acids, good results are obtained. It shows that the constant evaluation method is feasible.     

Modelling the volumetric properties of ionic liquids using a modified perturbed hard-sphere-chain equation of state

In this paper, a modified perturbed hard-sphere-chain equation of state (EOS) by Eslami [H. Eslami, Fluid Phase Equilib. 216 (2004) 21–26], is applied for modelling the thermodynamic properties of some ionic liquids (ILs). Two reliable scaling constants are used to determine two temperature-dependent parameters in the proposed EOS. The unique adjustable parameter that is reflecting the number of segments per molecule, r, compensates the uncertainties in the calculated temperature-dependent parameters. The reliability of the proposed EOS has been checked by comparing the results with 1561 experimental data points for 18 ILs over a broad range of pressures and temperatures. The overall average absolute deviation is 0.35%. A comparison of the predicted results, using the present EOS with the results of some previous models, indicates that the determined results of this EOS are in more accordance with experimental data than those.     

A comparison of mixing rules for the combination of COSMO-RS and the Peng–Robinson equation of state

In this work, the COSMO-RS model is combined with a volume-translated Peng–Robinson equation of state (EOS) via a G^E$G^{\text{E}}$-based mixing rule. The performance of several mixing rules previously published for this purpose is compared and semi-empirical modifications to one of them are introduced to improve its performance in our application. The new mixing rule contains three internal parameters that are adjusted to achieve consistency between the mixing rule and COSMO-RS. No experimental binary data is needed for our EOS. The new COSMO-RS-based, predictive EOS introduces a density dependence into COSMO-RS and extends its applicability to higher pressures and to mixtures containing supercritical components.