On the representation of pure-compound saturated (ZV − ZL) values

An equation for determining the difference between the compressibility factors of saturated vapor and liquid (Z_V - Z_L) through cubic equations of state has been developed as a function of reduced vapor pressure P_r, reduced temperature T_r and the critical cohesion parameter Ω_ac of the chosen equation. The regressed equation has been presented in a polynomial expression of (P_r/T_r) and Ω_ac for simple non-iterative calculations.     

On the representation of liquid properties of pure polar compounds by means of a modified redlich-kwong equation of state

The temperature-dependent parameters ω_a and ω_b of the Redlich-Kwong equation of state were evaluated from saturated liquid volumes and vapor pressures for three polar compounds, water, ammonia and sulfur dioxide, and then correlated in terms of T_r. To demonstrate the applicability of the resulting correlation, the values of ω_a and ω_b computed from these equations were used to evaluate the liquid properties of these compounds, such as vapor pressures and liquid volumes at saturation, and the heat of vaporization at the normal boiling point. In addition, the enthalpy departures of liquid water as well as the liquid volumes of compressed water were calculated. The results obtained from the proposed correlations are generally superior than those obtained from the equations of state recently proposed by Fuller, and Peng and Robinson.     

Extension of EOS non-iterative methods to density calculations: Correlation of saturated molar volumes and heats of vaporization

Soave's direct calculation procedures for the vapor pressure of pure compounds with cubic equations of state (EOSs), have been extended to the calculation of phase densities at saturation for Peng-Robinson (PR) type EOSs. These universal relations have been used to propose EOS-based correlation methods for the pure compound saturated liquid and vapor molar volumes, at temperatures higher than the normal boiling point. The methods yield satisfactory results independently of the molecular nature of the chemical under consideration. The results for phase densities are used to correct the heats of vaporization predicted by the ZVPR-EOS. Complete relative error information is provided for calculated heats of vaporization and correlated vapor and liquid phase molar volumes for more than one hundred compounds of industrial interest.     

Une éequation d'éetat de clausius modifiée repréeasentant l'éeatat liquide

The three parameters of a modified Clausius state equation have been generalized with a view to calculating thermodynamic properties of saturated pure substances, from the normal boiling temperature to the critical one. The method described in the paper, which only requires the knowledge of the characteristic properties of the pure substances (T_c, P_c, Z_c, ω) has been tested on 28 different compounds (saturated and unsaturated hydrocarbons, simple and polar molecules). The results obtained show that the state equation proposed correctly describes the liquid-vapour equilibrium (saturation vapour pressure and vaporization enthalpy) and moreover provides a satisfactory representation of the saturated liquid condition.     

Investigation of the saturated vapor pressure of the Cu2Se and CuInSe2 compounds

The saturated vapor pressure of the Cu₂Se and CuInSe₂ compounds is investigated using the gravimetric method in the temperature ranges 1282–1450 and 1173–1423 K, respectively. It is demonstrated that, in the case of congruent vaporization, the temperature dependences of the saturated vapor pressure of the Cu₂Se and CuInSe₂ compounds in the temperature ranges under investigation are adequately described by the equation logP = ?A/T + B. The enthalpy and entropy of vaporization are estimated for both compounds.     

改进SRK方程提高正构烷烃饱和蒸气压和液体体积预测精度

<正>引言 在化学工程和油藏工程的相平衡和其他热力学性质计算中,两参数立方型SRK方程应用最为广泛。然而,在某些情况下由SRK方程预测的饱和蒸气压出预测的液体体积偏差较大,无法满足工程计算的需要,必须改进方程,提高其预测精度。1 饱和蒸气压的改进 SRK方程可以写为 p=RT/（V-b）-(a(T)）/V(V+b) （1）     

A FOUR-PARAMETER EXTENSION OF MODIFIED LEE-KESLER EQUATION OF STATE

A modified Lee-Kesler equation of state has been proposed to improve the accuracy for the subcooled and saturated liquid regions of normal fluids. It is further extended to polar fluids by the addition of a fourth parameter X. The extended equation has been found to be reliable over a wide vapor and liquid regions for polar fluids and it is easy for computer use. Fourteen kinds of normal fluids and twelve kinds of polar fluids have been tested. The total average absolute deviations for the normal fluids and polar fluids are 0.79% and 1.68% over the range of T_r = 0.3 to 4 and P_r - 0.01 to 10.     

Improving the simplified‐perturbed‐hard‐chain theory equation of state using a new non‐attracting hard‐sphere equation

In this research a new simple non‐attracting hard‐sphere equation is introduced. The equation meets the ideal gas and close‐packed limits and is in accordance with computer simulation data with reasonable accuracy. When this equation is used with the simpli‐fied‐perturbed‐hard‐chain theory equation of state, improvements on the calculation of vapour pressure and saturated liquid density of pure compounds are observed. For 35 pure compounds of different classes, the averages of absolute error are 3.31% and 4.20% for the calculation of vapour pressure and saturated liquid density, respectively. The respected errors for the original equation of state are 3.53% and 4.96%, respectively. Moreover, the use of the new hard‐sphere equation in place of the Carnahan‐Starling equation in the simplified‐perturbed‐hard‐chain theory equation of state, does not have any appreciable effect on the prediction of K factors in VLE calculations.     

COMPARISON OF A PAIR OF THREE PARAMETER EQUATIONS OF STATE

The lattice fluid (LF) equation of state derived by Sanchez and Lacombe from a lattice model is compared to the empirical Peng-Robinson (PR) equation for normal alkane fluids ranging from methane to heptadecane in molecular weight. With respect to vapor pressure predictions, the equations are both good. The LF equation is superior, especially for higher molecular weight fluids, to the Peng-Robinson equation in predicting saturated liquid densities. For carbon numbers less than 6, the PR equation predicts heats of vaporization more accurately, whereas for carbon numbers greater than 9 the LF equation is more accurate than the PR one for temperatures lower than about 95% of critical.     

Densities of hydrocarbons in their saturated vapor and liquid states

The Sum and differences of the saturated vapor and liquid densities of 23 hydrocarbons were used to develop the following reduced density relationships for these saturated states The hydrocarbons considered included n-parafins, olefins, diolefins, naphthenes, and aromatics. Constants β, γ, and δ, and exponent n were found to be dependent on,. Equation (a) can reproduce liquid densities with an overall average deviation of 1.1 % over the entire temperature range, while Equation (b) was found to apply only in the interval 0.900 ≤ T_R ≤ 1.00 with an average deviation of 2.2%. For temperatures of T_k < 0.90, the saturated vapor density was found to depend on temperature as follows where k and m were also found to be Z_c dependent. Values calculated using Equation (c), when compared with 81 available experimental densities for 12 hydrocarbons, produced an average deviation of 3.0%.     

AN IMPROVED PENG-ROBINSON EQUATION OF STATE WITH A NEW TEMPERATURE DEPENDENT ATTRACTIVE TERM

An improved form of the Peng-Robinson cubic equation of state has been proposed. The temperature dependence of the attractive term has been modified so as to accurately represent vapor pressures of several fluids with large acentric factors from triple point to close to the critical point. The prediction of saturated liquid volume is also improved by introducing volume translation term in the equation of state. Comparisons of theoretical results with experimental data are made for the vapor/liquid phase equilibria of 44 pure fluids including nonpolar, polar and associating fluids. Our results show that the modified Peng-Robinson equation of state can represent accurately saturated vapor pressures of the fluids investigated in this paper, and it is more accurate than the Peng-Robinson equation of state and its earlier modifications due to Stryjek and Vera (1986) and Twu et al. (1995rpar;. Incorporation of the volume translation term in the equation of state has been found to improve the accuracy of saturated liquid volume significantly.     

立方型状态方程用于蒸发热的计算

推导出立方型状态方程计算纯流体蒸发热的新公式,该计算式的特点是式中含有能量参数对温度的导数 da/dT,而与 a(T)无关。根据这一公式对立方型状态方程推算蒸发热进行了比较分析,提出a(T)与 da/dT 相互独立的计算方法,并用 Peng-Robinson 方程对70多种物质(包括烃、醇、卤代烃、酮、无机气体等)进行了关联计算,蒸汽压和蒸发热的平均相对误差分别为0.70%和1.33%。     

A correlation for heat of vaporization of pure compounds

Twenty-seven selected equations were tested on 162 compounds with 1958 calorimetric data for their abilities to reflect the temperature influence on the heat of vaporization of pure compounds. A new equation is recommended (overall percent deviation 0.27% and percent deviation 0.59% above 0.9T _r ).     

Taking advantage of available cubic equations of state

All available simple cubic equations of state (EOS) are developed for specific representations. An effort has been made to take advantage of these existing equations for binary vapor-liquid equilibrium (VLE) as well as density calculations by assigning different EOS to different components of the mixture under consideration. A four-parameter cubic equation was used for combining the equations in the calculation. The effect of substance-dependent Ω_ac on vapor-liquid equilibrium calculations was further investigated, using two sets of mixing rules. A criterion for selection of equations for VLE calculation by means of the proposed approach was suggested. The improvement in the prediction of liquid volumes for binary mixtures based on the fitting of pure component liquid volumes was very satisfactory.     

PRSV — An improved peng-Robinson equation of state with new mixing rules for strongly nonideal mixtures

Two new composition dependent mixing rules for cubic equations of state are proposed. Both mixing rules contain two adjustable binary parameters and reduce to the conventional one parameter mixing rule when the parameters are equal. Vapor-liquid equilibrium data for mixtures of polar (associated or not) compounds with saturated hydrocarbons and for systems water/alcohol have been used to test the new mixing rules applied to the PRSV cubic equation of state. For these highly nonideal systems, correlation of the data with a new mixing rule of the Van Laar type for the PRSV equation gives better results than those obtained using excess Gibbs energy functions like the Wilson equation, NRTL and UNIQUAC.     

PRSV: An improved peng—Robinson equation of state for pure compounds and mixtures

The temperature and acentric factor dependence of the attractive term of the Peng—Robinson equation of state have been modified. The introduction of a single pure compound parameter allows the accurate reproduction of the vapor pressure data for a wide variety of substances. Nonpolar, polar nonassociating and associating compounds are equally well represented by the cubic PRSV equation of state. The conventional one-binary-parameter mixing rule allows the correlation of the vapor—liquid equilibrium data for a wide variety of binary systems. Only for systems formed by a polar compound (associating or not) and a saturated hydrocarbon, are results poorer than those obtained with conventional excess Gibbs energy functions.     

AN IMPROVED GENERALIZED WATSON EQUATION FOR PREDICTION OF LATENT HEAT OF VAPORIZATION

In this paper, an improved generalized Watson equation for the prediction of latent heats of vaporization at any temperature in the two-phase region for any substance has been proposed. Generalized relations for exponents n ₁, and n _2, have also been established, respectively.

In the current work, the latent heats of vaporization calculated with the proposed equation are compared with corresponding experimental values presented in the literature for 108 substances involving a total of 3361 points. These comparisons are further examined using the results of the original Watson equation and three other well-known equations available in the literature. The results of these comparisons indicate that the proposed equation is more accurate than the other four equations.     

An improvement on Martin–Hou equation of state for more precise prediction in the liquid region

A modified Martin–Hou (M–H) equation of state (EOS) for the accurate representation of thermodynamic property data of some pure substances in liquid phase is presented in this work. The improvement is achieved by substituting a new parameter η into the original M–H EOS. Eighteen pure substances are chosen to construct the dependency relationship of η on reduced temperature T_r and acentric factor ω. Furthermore, to verify the effectiveness and improvement of the modified M–H EOS, the calculated values of the saturated vapor and liquid molar volumes are compared with the literature data in the reduced temperature ranging from approximately 0.6 to 1.0. The results show that the modified M–H EOS perform a good prediction in gaseous phase for pure substances with the average absolute deviation (AAD) generally less than 1%, and more precise liquid molar volume values can be obtained with the modified equation. In liquid phase, the AAD of the modified M–H EOS is 3.71%, which is much lower than 6.16% of the original M–H EOS.     

Application of cubic equation of state models in prediction of vapor–liquid equilibria for binary polyvinyl acetate/solvent solutions

The cubic equation of state (CEoS) is a powerful method for calculation of (vapor + liquid) equilibrium (VLE) in polymer solutions. Using CEoS for both the vapor and liquid phases allows one to calculate the non‐ideality of polymer solutions based on a single EoS approach. In this research, vapor–liquid equilibria calculations of polyvinyl acetate (PVAc)/solvent solutions were performed. In this approach, eight models containing PRSV and SRK CEoS separately combined with four mixing rules namely vdW1, vdW2, Wong–Sandler (WS), and Zhong–Masuoka (ZM) were applied to calculations of bubble point pressure. For the better prediction, the adjustable binary interaction parameters existing in any mixing rule were optimized. The results were very acceptable and satisfactory. Absolute average deviations (%AAD) between predicted results and experimental bubble point pressure data were calculated and presented. The capability of two cubic equations of state had a good agreement with experimental data and predict the correct type of phase behavior in all cases, but the performance of the PRSV + vdW2 was more reliable than the other models with 2.65% in AAD for total of solution systems. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 40651.     

Micronization of polyethylene terephthalate via freezing of highly sheared emulsions of polyethylene terephthalate in saturated liquid tetrahydrofuran

A novel technique for micronizing polyethylene terephthalate (PET) resin (∼ 3 mm) with saturated liquid tetrahydrofuran (THF) has been developed. PET pellets were introduced to a high-pressure vessel filled halfway with THF at loadings up to ∼ 7 wt % PET. When the vessel was closed and heated, the PET pellets exhibited significant melting point depression at 190°C in saturated liquid THF at 17.1 bar. Although other organic solvents were also able to depress the melting point of PET, only THF was able to facilitate the formation of an emulsion of PET-rich liquid droplets in the saturated liquid solvent when the mixture was agitated. In an attempt to generate the smallest possible PET droplets, a high-speed (5000 rpm), close-clearance, radial flow impeller was used to shear and disperse the droplets at ∼ 200°C and 20.1 bar. Emulsion was rapidly cooled while mixing. The PET droplets froze at ∼ 190°C, and the vessel was then cooled to ambient temperature. The excess liquid THF was decanted, and the PET particles were dried in a vacuum oven to remove residual THF. The PET particle sizes ranged between 2 and 70 μm, with number, area, and volume average diameters of 6, 20, and 30 μm, respectively. A comparison between the PET resin and PET powder properties indicated that the micronization reduced the M_w from 32,700 to 22,800. DSC results suggest that the rapid quench leads to a morphology different from equilibrium, with small somewhat imperfect crystallites, a lower overall degree of crystallinity, and a suppressed ΔC_p at the glass transition. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012