Ternary mixing rule

Schwartzentruber J., F. Galivel-Solastiuk and H. Renon, "Representation of the Vapor-Liquid Equilibrium of the Ternary System Carbon Dioxide-Propane-Methanol and its Binaries with a Cubic Equation of State. A new Mixing Rule", Fluid Phase Equilibria, 38,217-226 (1987). 

Experimental results are presented for high pressure phase equilibria in the binary systems carbon dioxide - acetone and carbon dioxide - ethanol and the ternary system carbon dioxide - acetone - water at 313 and 333 K and pressures between 20 and 150 bar. A high pressure optical cell with external recirculation and sampling of all phases was used for the experimental measurements. The ternary system exhibits an extensive three-phase equilibrium region with an upper and lower critical solution pressure at both temperatures. A modified cubic equation of a state with a non-quadratic mixing rule was successfully used to model the experimental data. The phase equilibrium behavior of the system is favorable for extraction of acetone from dilute aqueous solutions using supercritical carbon dioxide. 

We have applied some of these principles to the extraction of 1-butene from a binary mixture of 1,3-butadiene/1-butene. Various mixtures of sc solvents (e.g., ethane, carbon dioxide, ethylene) are used in combination with a strongly polar solvent gas like ammonia. The physical properties of these components are shown in Table I. The experimental results were then compared with VLE predictions using a newly developed equation of state (18). The key feature of this equation is a new set of mixing rules based on statistical mechanical arguments. We have been able to demonstrate its agreement with a number of binary and ternary systems described in the literature, containing various hydrocarbon compounds, a number of selected polar compounds and a supercritical component. 

A new mixing rule has been proposed and tested coupled with SRK EOS and UNIFAC in this work. The new mixing rule, which is obtained by introducing a correction parameter to the Ge from the original UNIFAC in MHV1, is accurate for both binary and ternary gas/large n-alkane systems. The correction parameters have been correlated as a simple function of carbon number for a certain kind of gas/n-alkane system, which is convenient for engineering purposes. 

Figure 4. Three-phase equilibrium LtL2V in the system carbon dioxide-water-1-propanol at 333 K and 13.1 MPa exp., this work — Calculated with Peng-Robinson EOS using Panagiotopoulos and Reid mixing rule, left side prediction from pure component and binary data alone, right side interaction parameters fitted to ternary three-phase equilibria at temperatures between 303 and 333 K...

Figure 6.2 Illustration of mixing rule in ternary system.

The solubilities of carbon dioxide in aqueous solutions of seven binary and three ternary mixed salts chosen from eight kinds of electrolytes were measured at 25°C and 1 atm partial pressure of carbon dioxide by the saturation method. The experimental results were not correlated easily by the modified Setschenow equation, but they were correlated very well by the empirical two-parameter equation. The parameters in the equation for the binary and ternary solutions could be estimated by assuming an additive rule for the parameters of the component salt systems. This method, therefore, is useful for predicting the solubility of carbon dioxide in aqueous mixed-salt solutions. 

Ohta, T., 1989. Prediction of ternary phase equilibria by the PRSV2 equation of state with the NRTL mixing rule. Fluid Phase Eq., 47 1-15. 

VDW one-fluid rules. Comparisons of predicted and experimental vapor-liquid equilibrium for ternary and multicomponent systems are given in Tables V, VI, and VII, for both the semiempirical and VDW one-fluid mixing rules. In these calculations, the unlike interaction parameters for interactions of ethane and heavier components with each other were taken to be unity. This is a reasonable approximation for the unlike interaction parameters for the heavier components for the interaction of ethane and... 

The method can be extended to include nonpherical, nonpolar species (such as the lower molecular weight alkanes) by introduction of a third parameter in the equation of state, namely the Prigogine factor for chain-type molecules (9). This modified hard-sphere equation of state accurately describes VE(T, x) for liquefied natural gas mixtures at low pressures. Ternary and higher mixture VE values are accurately predicted using only binary mixing rule deviation parameters. 

In addition to the experimental data, the partitioning behavior of MMA between water and CO2 has been modeled. The Peng-Robinson equation of state combined with various mixing rules as described in Section 14.4.1 has been assessed on the ability to correlate phase equilibrium data from literature of the binary subsystems CO2-H2O, MMA-CO2 and MMA-H2O. Subsequently, the model has been used to predict the phase equilibrium behavior of the ternary system CO2-H2O-MMA. Partition coefficients were calculated at four different temperatures at pressures ranging from 5 to 10 MPa. In order to provide a means for comparison, the experimentally determined partition coefficients obtained in the high-pressure extraction unit were used to evaluate the results of the predictive model for phase equilibrium behavior. 

Based on the interaction parameters for the mixing rules obtained from the binary subsystems, the ternary phase behavior has been modeled by inter- and extrapolation of the interaction parameters. Because of lack of suflicient experimental data, extrapolation is considered to be the only option in some cases, although it obviously wiU introduce errors. Table 14.7 shows the interaction parameters of the various mixing rules used for the prediction of the ternary phase behavior, whereas the resulting partition coefficients per isothermal series... 

In summary, from an extensive comparison of the calculations with the experimentally obtained results [40], it can be concluded that the phase behavior of the ternary system MMA-H2O-CO2 can be quahtatively predicted by the Peng-Robinson equation of state in combination with the Panagiotopoulos-Reid mixing rule. In general, more experimental data are required concerning the binary systems for a better optimization of the interaction parameters. To obtain a more quantitative description of the phase behavior, especially close to the critical point, a more rigorous approach such as the SAFT-VRX model [46, 47] can be used. 

While Figs. 1.7-1 and 1.7-2 are for binaiy mixtures, the equation-of-state method for calculating vapor-liquid equilibria can be applied to mixtures with any number of components. When the quadratic mixing rules [Eqs. (1.3-32) and (1.3-33)] are used, only pure-component and binary constants are required these mixing rules therefore provide a powerful tool for scale-up" in the sense that only binary mixture data are needed to calculate equilibria for a mixture containing more than two components. For example, in the ternary mixture containing components 1, 2 and 3. only binary constants k,j, k2i (and perhaps c,. 

It was shown in Section 4.9.2 that in the quadratic mixing rules a binary parameter is required to describe the behavior of the binary system. For fitting the binary parameter usually VLE data are used. With the help of all the required binary parameters ky (in the case of a ternary system fen, fe2s) the ternary or... 

With the help of the binary parameters kn or g -model parameters now the phase equilibrium behavior, densities, enthalpies, Joule-Thomson coefficients, and so on, for binary, ternary and multicomponent systems can be calculated. For the calculation of the VLE behavior the procedure is demonstrated in the following example for the binary system nitrogen-methane using classical mixing rules. The same procedure can be applied to calculate the VLE behavior of multicomponent systems and with g -mixing rules as well. 

Fortunately, there is an appreciable body of good density data available on a broad spectrum of H20-salt binary systems. Furthermore, the availability of high quality density measurements in a number of ternary and quarternary systems means that the mixing rules can be adequately tested. The references given at the end of this chapter include a number of important sources for these data. 

The first systematic approach to a derivation the global phase diagram of ternary fluid mixture using an analytical investigation of the Van der Waals equation of state with standard one-fluid mixing rules was developed by Bluma and Deiters (1999). Eight major classes of ternary fluid phase diagrams were outlined and their relationship to the main types of binary subsystems were established. 

The normal mixing rule for b (equation 7.15) was retained. Used in conjunction with the Peng-Robinson equation of state (see below), these mixing rules have proved successful in collating data for the water/carbon dioxide, etha-nol/carbon dioxide and ethanol/water systems and the carbon dioxide/etha-nol/water and carbon dioxide/acetone/water ternary systems [14, 56]. 

In the first following section some of the principles of the glass transition will be outlined, free volumes will be related to T in accordance with established viewpoints, and mixing rules for binary and ternary mixtures will be reformulated and discussed... 

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