Mixing binary interaction parameters

According to Flory-Huggins theory, the heat of mixing of solvent and polymer is proportional to the binary interaction parameter x in equation (3). The parameter x should be inversely proportional to absolute temperature and independent of solution composition. 

Thermodynamic models are widely used for the calculation of equilibrium and thermophysical properties of fluid mixtures. Two types of such models will be examined cubic equations of state and activity coefficient models. In this chapter cubic equations of state models are used. Volumetric equations of state (EoS) are employed for the calculation of fluid phase equilibrium and thermophysical properties required in the design of processes involving non-ideal fluid mixtures in the oil and gas and chemical industries. It is well known that the introduction of empirical parameters in equation of state mixing rules enhances the ability of a given EoS as a tool for process design although the number of interaction parameters should be as small as possible. In general, the phase equilibrium calculations with an EoS are very sensitive to the values of the binary interaction parameters. 

If we consider the seven components in tables 5.12 and 5.13 as representative of the chemistry of natural olivines, it is clear that 21 regular binary interaction parameters (disregarding ternary and higher-order terms) are necessary to describe their mixing properties, through a combinatory approach of the Wohl or Kohler type (cf section 3.10). In reality, the binary joins for which interactions have been sufficiently well characterized are much fewer. They are briefly described below. 

Table 5.40 Binary interaction parameters for pyroxenes. Parameters refer to an ionic mixing model in which n is the number of sites over which permutability is calculated—i.e., Gmixing = tiRT (Xi In Xj + X2 In X2). Data in J/mole (H), J/(mole X K) (5), and J/(bar X mole) (V), respectively.

Table 5.40 lists some of the binary interaction parameters that may be used to describe the mixing properties of monoclinic and orthorhombic pyroxenes. Readers are referred to sections 3.8 and 3.9 for the meanings of these parameters. Some of the interaction parameters in table 5.40 are deduced from experimental... 

A more recent model (Ghiorso, 1984) is based on the binary interaction parameters of Thompson and Hovis (1979) for the NaAlSi30g-KAlSi30g join and on the experimental results of Newton et al. (1980), coupled with the A1 avoidance principle of Kerrick and Darken (1975) extended to the ternary field. Ghiorso (1984) expressed the excess Gibbs free energy of mixing in the form... 

Once the standard state potentials at the P and T of interest have been calculated (ix° = Gf for a pure single-component phase), the ideal and excess Gibbs free energy of mixing terms are easily obtained on the basis of the molar fractions of the various melt components and the binary interaction parameters listed in table 6.15 (cf eq. 6.78). 

The composition dependence of the parameter Z i3 was calculated for the mixture SC CO2 and SC ethane at T = 350 K and P = 10 MPa. For this purpose, precise PVT data [30] were treated using the Soave-Redlich-Kwong [20] EOS and the classical van der Waals mixing rules. The binary interaction parameter qi2 was calculated by minimizing the sum yi.caic 2 where... 

A family of mixing rules for the cubic EOS was suggested in which the empirical binary interaction parameter 12 in the van der Waals mixing rule was replaced by a physically more meaningful parameter. In the new mixing rules, some mole fractions in the expressions of parameters a and b in the van der Waals mixing rules were replaced with various expressions for... 

For the prediction of the mixed-gas solubilities from the solubilities of the pure individual gases, the pressure dependence of the binary parameters ku is needed. The Peng—Robinson EOS was used to determine the binary parameters ku. The binary interaction parameter qi2 in the van der Waals mixing rule was taken from ref 28, where it was evaluated for the water-rich phases of water—hydrocarbon and water—carbon dioxide binary mixtures. The calculated binary parameters ku are listed in Table 1. One should note that, as expected for a liquid phase, the above parameters are almost independent of pressure, in contrast to their dependence on pressure in the gaseous phase near the critical point,... 

Wilson s equation of state is found from Equations (14) and (15). It can be seen that for obtaining the activity coefficient of a component 1 in a pure solvent 2, we need four interaction parameters (A12, A21, An a A22, which are temperature dependent. It is evident that for calculating the value of the binary interaction parameters, additional experimental data, such as molar volume is needed. Other models which belong to the first category have the same limitations as Wilson s method. The Wilson model was used in the prediction of various hydrocarbons in water in pure form and mixed with other solvents by Matsuda et al. [11], In order to estimate the pure properties of the species, the Tassios method [12] with DECHEMA VLE handbook [13] were used. Matsuda et al. also took some assumptions in the estimation of binary interactions (because of the lack of data) that resulted in some deviations from the experimental data. 

Conventional van der Waais Mixing Rules with a Single Binary Interaction Parameter (IPVDW Model)... 

In Figure 3.4,1 the results for the methane and n-pentane (Knapp et al. 1982) binary system are presented. This is a typical mixture for which the van der Waals one-fluid mixing rules with a single constant binary interaction parameter performs very well... 

Figure 3.4.1. VLE correlation of the methane and n-pentane binary system at 310, 377, and 444 K with the IPVDW mixing rule and the PRSV equation of state. The lines represent VLE results calculated with the binary interaction parameter ki2 = 0.0215. (Data are from the DECHEMA Chemistry Series, Gmehling, and Onken 1977, Vol. 6, p. 445 data files for this system on the accompanying disk are C1C5310.DAT, C1C5377.DAT, and C1C5444.DAT.)...

Figure 3.4.6. VLE correlation of the 2-propanot and water binary system at 523 K with the IPVDW mixing rule and the PRS V equation of state and v are the experimental data. A binary interaction parameter fei2 = —0.1120 was used. (Points are the data of Barr-David and Dodge 1959 the data file for this system on the accompanying disk is 2PW250.DAT.)...

This equation introduces the binary interaction parameter in a manner similar to that of eqn. (3.3.6) of the van der Waais one-lluid mixing rule. Next, the following modified form of the NRTL equation was used for the excess free-energy term ... 

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