Viscosity and Thermal Conductivity Equations for Nitrogen, Oxygen, Argon, and Air

New formulations for the viscosity and thermal conductivity for nitrogen, oxygen, argon, and air are given. Air is treated as a pseudo-pure fluid using an approach adopted from previous research on the equation of state for air. The equations are valid over all liquid and vapor states, and a simplified cross-over equation was used to model the behavior of the critical enhancement for thermal conductivity. The extrapolation behavior of the equations for nitrogen and argon well below their triple points was monitored so that both could be used as reference equations for extended corresponding states applications. The uncertainties of calculated values from the equations are generally within 2% for nitrogen and argon and within 5% for oxygen and air, except in the critical region where the uncertainties are higher. Comparisons with the available experimental data are given.     

Prediction of the viscosity and thermal conductivity coefficients of mixtures

A corresponding states procedure to predict the viscosity and thermal conductivity coefficients of a pure fluid or mixture is discussed. We show the transport properties of a fluid or mixture can be calculated to within experimental error given only corresponding values for a reference fluid and equation of state data. With methane, as the reference fluid, we consider nitrogen, ethane, propane, butane, carbon dioxide, and mixtures of these fluids. LNG is also included. It is shown that the conventional corresponding states approach is not sufficient to predict correctly the transport properties. The effect of internal degrees of freedom on the thermal conductivity coefficient and the enhancement in the critical region for this coefficient is discussed briefly.     

Viscosity of Alternative Refrigerants R407C and R407E in the Vapor Phase from 298.15 to 423.15 K

This paper presents new measurements of the viscosity of gaseous R407C (23 mass% HFC-32, 25 mass% HFC-125, 52 mass% HFC-143a) and R407E (25 mass% HFC-32, 15 mass% HFC-125, 60 mass% HFC-143a). The measurements were carried out with an oscillating-disk viscometer of the Maxwell type at temperatures from 298.15 to 423.15 K. The densities of these two fluid mixtures were calculated with the equation-of-state model in REFPROP. The viscosity at normal pressures was analyzed with the extended law of corresponding states developed by Kestin et al., and the scaling parameters needed in the analysis were obtained from our previous studies for the viscosity of the binary mixtures consisting of HFC-32, HFC-125, and HFC-134a. The modified Enskog theory developed by Vesovic and Wakeham (V-W method) was applied to predict the viscosity for the ternary gaseous HFC mixtures under pressure. As for the calculation of pseudo-radial distribution functions in mixtures, a method based on the equation of state for hard-sphere fluid mixtures proposed by Carnahan-Starling was applied. It was found that the V-W method can predict the viscosity of R407C and R407E without any additional parameters for the ternary mixture.     

Monte Carlo Simulations of Binary Lennard–Jones Mixtures: A Test of the van der Waals One-Fluid Model

Monte Carlo simulations in the canonical ensemble have been performed in the liquid and supercritical regions of a binary Lennard–Jones mixture with differences in size parameters of 6.4% and energy parameters of 37%. The results are compared with a recent fundamental equation of state employing the van der Waals one-fluid model and new simulation data at the corresponding state conditions of the pure Lennard–Jones fluid. The van der Waals one-fluid model describes the mixture properties well at high densities, while at low densities the predicted internal energies and isochoric heat capacities are too low.     

Temperature Dependence of Densities and Excess Molar Volumes of the Ternary Mixture (1-Butanol + Chloroform + Benzene) and its Binary Constituents (1-Butanol + Chloroform and 1-Butanol + Benzene)

Densities ρ of the 1-butanol + chloroform + benzene ternary mixture and the 1-butanol + chloroform and 1-butanol + benzene binaries have been measured at six temperatures (288.15, 293.15, 298.15, 303.15, 308.15, and 313.15) K and atmospheric pressure, using an oscillating U-tube densimeter. From these densities, excess molar volumes (V ^E) were calculated and fitted to the Redlich–Kister equation for all binary mixtures and to the Nagata and Tamura equation for the ternary system. The Radojković et al. equation has been used to predict excess molar volumes of the ternary mixtures. Also, V ^E data of the binary systems were correlated by the van der Waals (vdW1) and Twu–Coon–Bluck–Tilton (TCBT) mixing rules coupled with the Peng–Robinson–Stryjek–Vera (PRSV) equation of state. The prediction and correlation of V ^E data for the ternary system were performed by the same models.     

A Generalized Model for the Thermodynamic Properties of Mixtures

A mixture model explicit in Helmholtz energy has been developed which is capable of predicting thermodynamic properties of mixtures containing nitrogen, argon, oxygen, carbon dioxide, methane, ethane, propane, n-butane, i-butane, R-32, R-125, R-134a, and R-152a within the estimated accuracy of available experimental data. The Helmholtz energy of the mixture is the sum of the ideal gas contribution, the compressibility (or real gas) contribution, and the contribution from mixing. The contribution from mixing is given by a single generalized equation which is applied to all mixtures studied in this work. The independent variables are the density, temperature, and composition. The model may be used to calculate the thermodynamic properties of mixtures at various compositions including dew and bubble point properties and critical points. It incorporates accurate published equations of state for each pure fluid. The estimated accuracy of calculated properties is ±0.2% in density, ±0.1 % in the speed of sound at pressures below 10 MPa, ±0.5% in the speed of sound for pressures above 10 MPa, and ±1% in heat capacities. In the region from 250 to 350 K at pressures up to 30 MPa, calculated densities are within ±0.1 % for most gaseous phase mixtures. For binary mixtures where the critical point temperatures of the pure fluid constituents are within 100 K of each other, calculated bubble point pressures are generally accurate to within ±1 to 2%. For mixtures with critical points further apart, calculated bubble point pressures are generally accurate to within ±5 to 10%.     

Statistical thermodynamic approach to the prediction of vapor-liquid equilibria of multi-component mixtures

A Hard Sphere Expansion (HSE) conformal solution theory, which is a result of the application of statistical mechanics, is developed in order to predict the vapor-liquid equilibria properties of multicomponent mixtures. The HSE mixing rules are derived with consideration of the Kihara spherical-core function as the pair potential together with the 3-body potential function. Based on this HSE conformal solution theory, an equation of state for multi-component fluid is developed. In this conformal solution theory perturbation equation of state of pure fluids is used as the reference equation of state. The vapor-liquid equilibria properties of several properly chosen binary and ternary non-polar mixtures are predicted. These mixtures include: argon-krypton, argon-methane, methane-krypton, nitrogen-methane, nitrogen-argon, argon-neopentane, methane-neopentane, methane-perfluoromethane, carbon dioxideethylene, carbon dioxide-ethane, nitrogen-argon-oxygen, and nitrogen-argon-methane. The predicted results obtained in the present investigation compare quite favorably with the experimental vapor-liquid equilibria values. Furthermore, the present approach, being a purely molecular theory of fluid mixtures, provides detailed insight into the peculiar behavior of the azeotropic fluid mixture. It is shown that the vapor-liquid equilibria properties of multicomponent fluid systems may be predicted correctly through the present statistical mechanic approach provided that like- and unlike-interaction parameters of the species of the mixtures are known a priori. Generally, the present investigation shows that the use of the molecular theory of fluid mixtures in predicting the mixture properties is very promising.     

Excess Molar Isentropic Compressibilities,Excess Molar Volumes,and Excess Sound Speeds of the 1-Propanol + Diethyl Ether + 1-Octanol Ternary Mixture and Constituent Binary Mixtures at 298.15 K

The sound speeds and densities of the 1-propanol + diethyl ether + 1-octanol ternary mixture and constituent binary mixtures, 1-propanol + diethyl ether, 1-propanol + 1-octanol, and diethyl ether + 1-octanol, have been measured at 298.15 K as a function of composition. Isentropic compressibilities, molar isentropic compressibilities, excess molar isentropic compressibilities, excess molar volumes, and excess sound speeds have been calculated from the experimental density and sound speed data. Excess molar volumes, excess molar isentropic compressibilities, and excess sound speeds of the binary mixtures were fitted to the Redlich–Kister equation. By using the free length theory (FLT), Schaaff’s collision factor theory (CFT), Nomoto’s relation (NR), Van Deal’s ideal mixing relation (IMR), and Junjie’s relation (JR), sound-speed values of the investigated mixtures were calculated. These values were compared with the experimental sound-speed results.     

Pseudo-Pure Fluid Equations of State for the Refrigerant Blends R-410A, R-404A, R-507A, and R-407C

Pseudo-pure fluid equations of state explicit in Helmholtz energy have been developed to permit rapid calculation of the thermodynamic properties of the refrigerant blends R-410A, R-404A, R-507A, and R-407C. The equations were fitted to values calculated from a mixture model developed in previous work for mixtures of R-32, R-125, R-134a, and R-143a. The equations may be used to calculate the single-phase thermodynamic properties of the blends; dew and bubble point properties are calculated with the aid of additional ancillary equations for the saturation pressures. Differences between calculations from the pseudo-pure fluid equations and the full mixture model are on average 0.01%, with all calculations less than 0.1% in density except in the critical region. For the heat capacity and speed of sound, differences are on average 0.1% with maximum differences of 0.5%. Generally, these differences are consistent with the accuracy of available experimental data for the mixtures, and comparisons are given to selected experimental values to verify accuracy estimates. The equations are valid from 200 to 450 K and can be extrapolated to higher temperatures. Computations from the new equations are up to 100 times faster for phase equilibria at a given temperature and 5 times faster for single-phase state points given input conditions of temperature and pressure.     

Thermodynamic Properties for R-404A

An 18-coefficient modified Benedict–Webb–Rubin equation of state has been developed for R-404A, a ternary mixture of 44% by mass of pentafluoroethane (R-125), 52% by mass of 1,1,1-trifluoroethane (R-143a), and 4% by mass of 1,1,1,2-tetrafluoroethane (R-134a). Correlations of bubble point pressures, dew point pressures, saturated liquid densities, and saturated vapor densities are also presented. This equation of state has been developed based on the reported experimental data of PVT properties, saturation properties, and isochoric heat capacities by using least-squares fitting. These correlations are valid in the temperature range from 250 K to the critical temperature. This equation of state is valid at pressures up to 19 MPa, densities to 1300 kg·m^–3, and temperatures from 250 to 400 K. The thermodynamic properties except for the saturation pressures are calculated from this equation of state.     

Visualization for heat and mass transport phenomena in supercritical artificial air

A laser holography interferometer is applied to investigate heat and mass transport phenomena around the pseudo-critical line of supercritical artificial air with a composition of 79% nitrogen and 21% oxygen. In a previous study, we successfully observed the heat transport phenomenon, the piston effect, around the pseudo-critical line of nitrogen. The same experimental set-up is applied to the supercritical artificial air, which is a compressible binary mixture fluid. We attempt to suppress the generation of natural convection, and successfully observe the heat and mass transport phenomena, which are the soret effect and the piston effect, respectively. Here, we discuss these effects observed in the supercritical artificial air.     

Thermodynamic properties of lubricant/refrigerant mixtures using statistical mechanics and artificial intelligence

In this research, the volumetric properties of sixteen lubricant/refrigerant mixtures are predicted using the developed statistical mechanical equation of state at a broad range of temperatures, pressures and mole fractions. The equation of state have been examined using corresponding states correlation based on just one input parameter (density at room temperature) as scaling constants. Besides, the artificial neural network (ANN) based on back propagation training with 19 neurons in hidden layer was tested to predict the behavior of binary mixtures of lubricant/refrigerant. The AADs% of a collection of 3961 data points for all binary mixtures using the EOS and the ANN at various temperatures and mole fractions are 0.92% and 0.34%, respectively. Furthermore, the excess molar volume of all binary mixtures calculated from obtained densities of ANN, and the results shown these properties have good harmony with literature.     

R1234yf/R290/R134a系气液相平衡的模拟

本文从理论方面研究了混合制冷剂的相平衡特性,基于Peng-Robinson(PR)状态方程与Wong-Sandler(WS)混合法则,结合Predictive Soave Redlich Kwong(PSRK)方程中使用的UNIFAC基团贡献法,构建了混合物气液相平衡预测模型(PRWS-UNIFAC-PSRK)。结果表明:二元混合物R32/R1234yf的压力及气相质量分数的模拟结果与实验值偏差分别在±2.5%和±0.02内;三元混合物R134a/R1234yf/R600a的压力及气相组分质量分数计算值与实验数据的偏差基本在±3%和±0.04内;建立了R1234yf/R290/R134a系的三元相平衡图,当质量分数在0.25/0.70/0.05左右时存在共沸点。通过采用多参数状态方程,改进活度系数模型,获取更为准确的二元相互作用系数,可进一步提高模型的预测精度。     

An Extended Equation of State Modeling Method II. Mixtures

This work is the extension of previous work dedicated to pure fluids. The same method is extended to the representation of thermodynamic properties of a mixture through a fundamental equation of state in terms of the Helmholtz energy. The proposed technique exploits the extended corresponding-states concept of distorting the independent variables of a dedicated equation of state for a reference fluid using suitable scale factor functions to adapt the equation to experimental data of a target system. An existing equation of state for the target mixture is used instead of an equation for the reference fluid, completely avoiding the need for a reference fluid. In particular, a Soave–Redlich–Kwong cubic equation with van der Waals mixing rules is chosen. The scale factors, which are functions of temperature, density, and mole fraction of the target mixture, are expressed in the form of a multilayer feedforward neural network, whose coefficients are regressed by minimizing a suitable objective function involving different kinds of mixture thermodynamic data. As a preliminary test, the model is applied to five binary and two ternary haloalkane mixtures, using data generated from existing dedicated equations of state for the selected mixtures. The results show that the method is robust and straightforward for the effective development of a mixture- specific equation of state directly from experimental data.     

Isothermal vapor liquid equilibrium measurements for difluoromethane (R32) + fluoroethane (R161) + trans-1,3,3,3-tetrafluoropropene (R1234ze(E)) ternary mixtures

Difluoromethane (R32) + fluoroethane (R161) + trans-1,3,3,3-tetrafluoropropene (R1234ze(E)) ternary system could be a promising alternative refrigerant mixture. The vapor liquid equilibrium (VLE) data for this system are important for the evaluation of its performance. In this work, the VLE of R32 + R161 + R1234ze(E) were measured for the first time by a quasi-static analytical apparatus over the temperature range of 283.15 to 323.15 K. The ternary system of R32 + R161 + R1234ze(E) is a zeotropic system within the studied temperature range. The Peng–Robinson–Stryjek–Vera (PRSV) equation of state combined with the Wong–Sandler (WS) mixing rule and the non-random two-liquid (NRTL) activity coefficient model was used to predict the ternary VLE data by using the parameters of binary mixtures (R32 + R161, R32 + R1234ze(E) and R161 + R1234ze(E)). The calculated values show excellent agreement with the experimental results. The average absolute deviation (AAD) of pressure is 0.16%. The average absolute deviations of vapor phase mole fractions for R32 and R161 are 0.0021 and 0.0028, respectively.     

Predicting the virial coefficients and thermodynamic properties of a multicomponent mixture with application to the ternary mixture of CH2F2+CF3CHF2+CF3CH2F

A model for estimating second and third virial coefficients, which has been used successfully to represent the behavior of pure gases and binary mixtures, was applied to a ternary mixture. An estimate for the ternary third virial coefficient.C ₁₂₃, was added to the model. Three experimentally determined binary interaction parameters were also used. The model has been applied to the ternary mixture CH₂F₂+CF₃CHF₂+CF₃CH₂F (R32+R125+R134a). The results are useful for calculating gas-phase densities, thermodynamic properties, and fugacities for phase equilibrium calculations. The use of such models leads to a considerable economy of effort in the case of multicomponent mixtures. Examples of the thermodynamic properties are given for the equimolar ternary mixture in the range from the dew-point temperature to 400 K at pressures of 0.5, 1, and 2 MPa. Calculated densities and speeds of sound are compared with new experimental values for a near-equimolar composition.     

Co-treatment of single, binary and ternary mixture gas of ethanethiol, dimethyl disulfide and thioanisole in a biotrickling filter seeded with Lysinibacillus sphaericus RG-1

The work reports the aerobic co-treatment characteristics of single, binary and ternary mixture gas of ethanethiol, dimethyl disulfide (DMDS) and thioanisole in a biotrickling filter seeded with Lysinibacillus sphaericus RG-1. 100% removal efficiency (RE) was achieved for sole ethanethiol, DMDS and thioanisole at inlet concentration below 1.05, 0.81 and 0.33 mg/L, respectively, at empty bed resident time 110 s. In addition, 100% RE was also obtained with binary ethanethiol and DMDS (1:1) and ternary ethanethiol, DMDS and thioanisole (3:2:1). Michaelis-Menten equation was modified to incorporate the plug flow behavior of the bioreactor. The maximum removal rate (V(max)) was calculated as 56.18, 57.14 and 22.78 g/m(3)/h for sole ethanethiol, DMDS and thioanisole, respectively, while the V(max) was 41.84 and 14.56 g/m(3)/h for DMDS and thioanisole in binary and ternary systems, respectively. Overall, these suggest that not only sole but also binary and ternary mixture can be efficiently removed in this system.     

强非共沸工质R1234yf/R170/R14系气液相平衡的模拟

超额吉布斯自由能-状态方程法(G~E-EoS)是继传统的状态方程法和活度系数法之后预测气液相平衡的一个新思路。本文采用PRWS-UNIFAC-PSRK模型对R161/R1234yf、R32/R125/R134a及强非共沸工质R1234yf/R170/R14系的气液相平衡数据进行计算。结果表明:R161/R1234yf系压力和气相组分质量分数的计算值与实验值的偏差在±1.5%和±0.02以内,优于REFPROP9.0软件的计算结果,而R32/R125/R134a系的偏差分别在±4%和±0.02以内。根据计算结果及三维相平衡图发现,R1234yf/R170/R14在质量分数比为0.4/0.2/0.4附近时体系的温度滑移现象最为明显,最大的滑移温度达到72.5 K;且R1234yf组分的质量分数越大,泡点温度与露点温度越高。     

Excess Molar Volumes of the Ternary Mixture (Cyclohexane+Tetrahydrofuran+Chlorocyclohexane) and the Binary Mixtures (Cyclohexane + Tetrahydrofuran and Cyclohexane + Chlorocyclohexane) at 298.15 and 313.15 K

Densities of the ternary mixture (cyclohexane + tetrahydrofuran + chlorocyclohexane) and the binary mixtures (cyclohexane + tetrahydrofuran and cyclohexane + chlorocyclohexane) have been measured at 298.15 and 313.15 K. Excess molar volumes for the binary and ternary systems were fitted to the Redlich-Kister and Cibulka equations. Flory's theory has been used to predict excess molar volumes of binary and ternary mixtures at 298.15 K.