A SIMPLE CALCULATION OF THE PRESSURE AND LIQUID MOLE FRACTION AT THE VLE OF ETHANE/LIGHT HYDROCARBON BINARY MIXTURES

An analytical expression for the calculation of the pressure and liquid mole fraction at the VLE of ethane/light hydrocarbon binary mixtures is proposed. The model is based on a simple analytical expression for the vapor pressure of pure non-polar fluids, which, for a given temperature, only requires as input the values of the Lennard-Jones molecular parameters and the acentric factor. A properly modified Lorentz-Berthelot mixing rule is used, the interaction parameters being given as simple functions of the temperature and composition with eight constants for each binary mixture. The model is shown to reproduce accurately and simply the pressure (for a given liquid mole fraction) or the liquid composition (for a given pressure) of six ethane + hydrocarbon systems at different temperatures.     

A new correlation for VLE data: Application to binary mixtures containing nitrogen

Recently we proposed simple analytical expressions for the calculation of the equilibrium pressure, as well as the mole fractions of both liquid and vapor phases at the vapor-liquid equilibrium of binary mixtures. They are based on a recently proposed molecular model for the vapor pressure of pure non-polar fluids, which, for a given temperature, only requires as input the values of the two Lennard-Jones molecular parameters and the acentric factor, which are parameters related to the molecular shape of each substance, and whose values are readily available. The mixing rules contain adjustable parameters that must be obtained for each mixture. In this work, we test the applicability of the models for some mixtures containing nitrogen. In particular, we find that the calculation of mole fractions must be performed with particular care in some cases. We show that the model for the pressure clearly improves the results obtained with classical equations of state for most of the mixtures studied.     

丙烷-乙醇-水体系相平衡研究

提出了改进的DDLC-MH(81)状态方程,用于丙烷-乙醇-水体系二元汽液平衡数据的关联计算,其模型参数与温度有良好的线性关系.并用汽相循环法测定了该体系在不同温度下的二元及三元VLE数据,结果与模型的推算值取得良好的一致.并用模型预测了超临界丙烷条件下的三元相平衡数据.结果表明,在液相乙醇浓度高于0.2的情况下,超临界丙烷比超临界二氧化碳有更高的乙醇溶解度和选择性.     

Adiabatic Adsorption Column: Pressure Reduction to Subatmospheric Levels

Abstract

An adiabatic equilibrium model to simulate the pressure reduction of an adsorption column from ambient pressure to subatmospheric pressure is presented. The column is initially saturated with a binary mixture of gases. The partial differential equations (PDEs) describing the mass and heat balances for the pressure reduction of the bulk binary gas mixture are reduced to simple ordinary differential equations (ODEs) by assuming no axial variation of gas-phase mole fraction, temperature, pressure, and solid-phase capacity. These ODEs describe the unique relationships between gas-phase mole fraction and column pressure, and column temperature and column pressure, as functions of equilibrium isotherm parameters and other constants. The ODEs are solved by first principles to generate gas-phase mole fraction, column temperature, solid-phase loading, and desorbed gas quantity as a function of column pressure. The simplified ODEs can be solved in approximately two seconds CPU time of an IBM 370/165, which is only a fraction of that required to solve the corresponding PDEs on a computer. Pressure reduction of a column initially saturated with a mixture of CO₂/N₂ on BPL carbon is used to illustrate the mathematical model. The simulation results for the subatmospheric pressure reduction step are compared against the results from the superatmospheric pressure reduction step where the pressure is reduced to ambient level.     

Calculation of ternary equilibrium vapor compositions from total vapor pressure-liquid composition data

A simple and direct method for evaluating ternary vapor-liquid equilibrium compositions from measurements of the total vapor pressure exerted by the liquid phase along lines of constant liquid mole fraction ratio is presented. Application has been successfully made to the ternary system nitrogen-argon-oxygen at 180°r. The proposed method modifies that for binary systems and can be conveniently applied to ternary systems at low to medium pressures.     

Modeling high pressure vapor–liquid equilibrium of ternary systems containing supercritical CO2 and mixed organic solvents using Peng–Robinson equation of state

High pressure vapor–liquid equilibrium (VLE) of CO₂-expanded organic solvents was investigated using Peng–Robinson-LCVM-UNIFAC equation of state. Bubble pressure of several ternary mixtures was predicted using this model and correlations were developed based only on binary experimental data. A sensitivity study of the LCVM parameter numerical value was done by considering the coherence between the mathematical features of the mixing rule and the quality of the simulation. The results provided by PR-LCVM-UNIFAC were compared with those ones given by Peng–Robinson equation of state using the classical quadratic mixing rules (PR-CMR). Despite the use of two adjustable parameters for each binary system, PR-CMR is not able to provide good results when applied to ternary systems. The capability of PR-LCVM-UNIFAC model to predict liquid mixture density for ternary systems using parameters regressed only from bubble pressure experimental data was also investigated. Due to the lack of liquid density experimental data, it was possible to perform only a qualitative assessment of the density curves calculated by this equation of state.     

R32+R1234yf+R1234ze（E）混合制冷剂气液相平衡实验研究

基于液相循环法搭建的气液相平衡实验装置,在263.15~323.15 K温度范围内,实验测量了R32+R1234yf和R1234yf+R1234ze（E）二元混合物以及R32+R1234yf+R1234ze（E）三元混合物的气液相平衡数据,利用PRSV状态方程结合WS混合法则和NRTL活度系数模型进行关联拟合,获得二元混合工质的交互参数,并在其基础上预测了三元混合工质气液相平衡性质。计算结果与实验数据对比表明,二元体系R32+R1234yf和R1234yf+R1234ze（E）的压力平均绝对偏差分别为0.71%和0.20%,气相摩尔分数平均绝对偏差均约为0.0016,三元体系R32+R1234yf+R1234ze（E）的压力平均绝对偏差为0.82%,系统组分R32和R1234yf的气相摩尔分数平均绝对偏差均约为0.007。     

Calculation of Vapor‐Liquid Equilibrium Data of Binary Mixtures Using Vapor Pressure Data

The design of plants or unit operations requires the knowledge of data for multicomponent systems. An approach is presented for the regression of binary interaction parameters required for the calculation of activity coefficients. Binary vapor pressure data are used to correlate these parameters for calculation of vapour/liquid equilibrium data. The advantage of the approach is the fact that only easily measured vapor pressure data are required. The procedure is demonstrated by means of two binary mixtures. Parameter regression, prediction of vapour/liquid equilibrium data as well as their experimental verification are demonstrated.     

二元体系汽液相平衡数据的测定与关联

在101.325 kPa下,测定了碳酸二甲酯-碳酸二乙酯二元体系在不同平衡温度时的汽相和液相的折光率,并用事先测定的工作曲线拟合得到汽、液相的摩尔分率,用积分检验法检验其热力学一致性;用最小二乘法分别求出了碳酸二甲酯-碳酸二乙酯二元体系的液相活度系数Wilson,NRTL和UNIQUAC模型参数,由这些模型参数推算的结果与实验数据吻合很好。     

Liquid–Vapor Equilibrium in Multicomponent Mixtures of Higher Aliphatic Acids

A procedure is suggested for calculating the liquid–vapor equilibrium compositions for multicomponent mixtures of higher aliphatic acids with 12 to 18 carbon atoms at given liquid composition, total saturation vapor pressure, and boiling points of the pure components. It is based on equations for the saturation vapor pressures of the components at the boiling point of the mixture (which is determined by iterations) and uses the component activity coefficient estimated by the method of analytical solutions of groups.     

A four parameter cubic equation of state with temperature dependent covolume parameter

A four-parameter, Ghoderao–Dalvi–Narayan 2 cubic equation of state(GDN2 CEOS), is presented which incorporates the following: 1. The experimental value of the critical compressibility factor has been used as a fixed input parameter for calculations; 2. All the parameters(a, b, c, d) of CEOS are temperature dependent functions in the subcritical region and are temperature independent functions in the supercritical region and; 3. A new α function is introduced with two compound specific parameters which are estimated by matching saturated vapor pressure at two fixed temperature points T_r= 0.5, 0.7. Our formalism enables us to cast three of the four parameters of the CEOS as a function of the remaining parameter. The proposed CEOS is used to predict properties of 334 pure compounds, including saturated vapor pressure and liquid density, compressed liquid density, heat capacities at the constant pressure and volume, enthalpy of vaporization, sound velocity. To calculate thermodynamic properties of a pure compound, the present CEOS require the critical temperature, the critical pressure, the Pitzer's acentric factor, the critical compressibility factor, and two parameters of the alpha function. The saturated liquid density predictions for pure fluids are very accurate when compared with GDN1(Ghoderao–Dalvi–Narayan 1),MPR(Modified Peng–Robinson), and PT(Patel–Teja) equations of state. Unlike MPR EOS, the proposed temperature dependent covolume parameter b in the present work satisfies all the constraints mentioned in the literature to avoid thermodynamic inconsistencies at the extreme temperature and pressure. Using van der Waals one-fluid mixing rule, the present CEOS is further used to predict bubble pressure and the vapor mole fraction of binary mixtures.     

醋酸-水二元系25——75℃恒温汽液平衡的研究

建立了利用静态法测定溶液蒸气压的装置,它包括平衡器、零压计、水银压差计、脱气室以及高真空设备。在此装置中测定了醋酸-水二元系在25—75℃范围内的蒸气压。为了得到完整的恒温汽液数据,利用我们先前发展的一个直接热力学方法来计算平衡汽相组成,计算时考虑了汽相缔合。本文中用表格形式发表了所得的计算结果。 为了拟合实验数据,用了一个由热力学推导得到的关联活度系数与温度的多项式,多项式参数由最小二乘法求得。利用这些参数,并外推至常压,预测所得泡点和汽相组成与文献报导的恒压实验数据,具有良好地一致。这些参数,可在低压至常压的广阔范围内的实际汽液平衡计算中使用。     

New models for the binary interaction parameters of nitrogen–alkanes mixtures based on the cubic equations of state

In this study, the goal was to derive a new purely predictive model to obtain binary interaction parameters based on intermolecular theories. The Lorentz–Berthelot and Halgren HHG molecular combining rules were coupled with the vdw1 mixing rule to derive the new equations for binary interaction parameters. These equations were used with the PR and ER EoSs to calculate the vapor–liquid equilibria of 14 binary mixtures of nitrogen with either methane, ethane, propane, iso-butane, n-butane, iso-pentane, n-pentane, n-hexane, n-heptane, n-octane, n-nonae, n-decane, n-dodecane, or n-tetradecane over wide ranges of temperature and pressure. To increase the accuracy for all of the investigated systems, we have additionally suggested a new correlative mode for the proposed equations. For some of the systems, the proposed predictive equations enhance the accuracy of vapor–liquid equilibria predictions up to three times in comparison to the case where binary interaction parameters are set to zero.     

Calculation of solution-vapor thermodynamic equilibria by the method of minimizing the Gibbs energy

An algorithm of direct numerical minimization of the Gibbs energy for calculating the liquid-vapor thermodynamic equilibrium in multicomponent systems is proposed. The method makes it possible to simultaneously determine the distributions of concentrations in the vapor and solution and the vapor mole fractionwhen the temperature, pressure, and initial mixture composition are given. The developed algorithm is distinguished from the existing equilibrium calculation methods by a higher stability and the capability of obtaining solutions in the range of parameters in which the conventional algorithms are not able to produce a physically meaningful result. The Peng-Robinson equation of state is used to simulate the Gibbs energy. The accuracy of the proposed algorithm is illustrated by comparison with experimental data.     

甲烷二元体系的固液相平衡预测

超导能源管道是以液化天然气（LNG）冷却超导电缆,实现两种能源同时输送的前瞻性能源输送技术。超导能源管道的经济运行温度一般在77~100 K,而在此温区LNG有凝固风险,因此必须研究LNG主要成分的固液相平衡特性。为此,针对甲烷+乙烯、甲烷+乙烷、甲烷+丙烷、甲烷+正丁烷、甲烷+正戊烷5种二元混合物,借助以PR-vdW为代表的状态方程法,以NRTL、WILSON、UNIQUAC等模型为代表的活度系数法,基于所研究体系的二元汽液相平衡数据,回归二元相互作用参数,预测其二元固液相平衡,预测结果与文献数据进行了比较。结果表明,PR-vdW方程对5种甲烷二元体系的固液平衡预测结果最好。进而研究了PR-vdW方程中二元相互作用参数对甲烷二元体系汽液平衡及固液平衡计算结果的影响,分析了模型对温度的依赖关系。     

状态方程模拟醇胺系统的密度和汽液相平衡

通过考虑醇胺分子间的缔合作用,结合先前开发的非缔合变阱宽链流体状态方程(SWCF-VREOS)建立了一个缔合方阱链流体状态方程,并利用方程模拟了醇胺系统的密度和汽液相平衡。通过关联不同温度下醇胺的饱和蒸气压和液体体积得到了18种醇胺流体的分子参数,新方程计算的饱和蒸气压和液体密度总的平均误差分别为0.94%和0.88%。结合简单的混合规则,将此方程扩展到混合系统。研究发现,建立的方程可预测二元和三元醇胺混合物的密度。当引入一个与温度无关的可调参数时,方程能满意关联二元系统的汽液相平衡数据,并可进一步预测多元混合系统的汽液相平衡,预示着新方程可模拟醇胺系统的相行为。     

RG-CPA方程计算超临界CO2-醇体系汽液相平衡

综合考虑缔合作用和密度涨落的影响,将经重整化群修正的CPA方程（RG-CPA方程）扩展到二元体系汽液相平衡的计算。通过一个温度下的汽液相平衡数据回归得到二元交互作用参数,预测其他温度下的相平衡。采用这种方法计算了超临界CO₂与醇二元体系的汽液相平衡性质和临界曲线。结果表明,RG-CPA方程预测超临界CO₂与醇二元体系的气液相组成和密度具有较高的精度,液相组分平均绝对偏差为0.032,气相组分平均绝对偏差为0.019。与原始CPA方程相比,RG-CPA方程能更好地预测气液临界曲线。     

Modeling of vapor-liquid equilibrium of gasoline-ethanol blended fuels for flash boiling simulations

Flash boiling is a physical phenomenon which governs the non-equilibrium phase change of a high temperature fluid as it is depressurized below its vapor pressure. The modeling of this process is of importance to a number of industrial applications and requires the vapor-liquid equilibrium properties of the fluid under consideration. The highly non-ideal nature of gasoline-ethanol fuel blends makes vapor-liquid equilibrium calculations extremely difficult for such fluids. A simple model known as GEFlash (Gasoline-Ethanol Flash), based on existing literature and fundamental chemical engineering thermodynamics is proposed to calculate the properties of gasoline-ethanol fuel blends that are required to perform flash boiling simulations. In addition, a second model based on the chemical engineering software Aspen Plus is also proposed and the predictions of the two models are validated against experimental data available in open literature. The results indicate that both models reproduce the trend in experimental data for vapor pressures and saturated liquid density for blends with different ethanol contents. The GEFlash model does not match the vapor mole fraction predictions of the Aspen Plus model for fuels with low ethanol content (E20 and E40). However, the vapor mole fractions for high ethanol content fuels (greater than E60) are accurate over the majority of the temperature range tested.     

On the predictive capabilities of CPA for applications in the chemical industry: Multicomponent mixtures containing methyl-methacrylate,dimethyl-ether or acetic acid

The predictive performance of the CPA (Cubic-Plus-Association) equation of state for applications relevant to the chemical industry is illustrated in this work. Three such applications inspired by industrial requests/interest are illustrated here, all of which involve aqueous multicomponent mixtures exhibiting vapor–liquid (VLE) and/or liquid–liquid (LLE) equilibrium. The first two cases include mixtures of methyl-methacrylate with acetone or methanol and dimethyl-ether with ethanol, respectively. In these two cases, the classical form of CPA is used. The third case involves aqueous mixtures with acetic acid, esters, ethers and alcohols, and in this case for water–acetic acid the CPA-Huron Vidal (CPA-HV) version of the model is used. For the latter binary mixture, new CPA-HV binary parameter sets are estimated using, among others, data for activity coefficients at infinite dilutions. The modeling approach is similar in all three cases, i.e. the binary parameters are solely fitted to binary data and thus all multicomponent calculations are considered predictions.It is shown that CPA correlations for binary systems are excellent in all cases using temperature independent parameters except for the acetic acid–water system for which different parameter sets at different temperatures can be recommended. Even with the use of CPA-HV mixing rules, modeling of the acetic acid–water system with few interaction parameters remains a challenging task. Excellent simultaneous VLE and LLE correlation is obtained for complex systems such as aqueous mixtures with ethers and esters. The multicomponent results are, with a few exceptions, very satisfactory, especially for the vapor–liquid equilibrium cases. For the demanding aqueous acetic acid–water containing systems, one parameter set is recommended at the end for modeling ternary or multicomponent mixtures containing acetic acid and water.     

甲醇-乙酸-丙酸多元体系汽液平衡

用新型泵式沸点仪测定了在100kPa下甲醇-乙酸、甲醇-丙酸、乙酸-丙酸3个二元体系以及甲醇-乙酸-丙酸三元系在不同液相组成时的沸点,并用间接法T-p-x(温度、压力和液相摩尔分数)推算了3个二元体系的汽相平衡组成。3个二元体系活度系数分别用Wilson模型、NRTL模型、Margules模型和van Laar模型进行关联,用最小二乘法求出了它们的液相活度系数模型参数,同时,用这些模型参数来计算它们的汽相摩尔分数。所得的液相活度系数来计算3个二元体系的过量吉布斯自由能函数,且所研究的所有体系中各组分之间不存在共沸点。用3个二元体系Wilson模型参数对所测的三元体系数据进行关联,建立该系统汽液平衡的热力学模型并计算平衡时的汽相摩尔分数和泡点温度。由面积积分法检验这些模型参数计算的3个二元体系相平衡数据,得到很好的热力学一致性。