Mixing rules Huron-Vidal

In addition, an alternative mixing rule (referred as the second order modified Huron-Vidal mixing rule, MHV2) was also derived [43] ... 

In order to correlate the results obtained, a modified SRK equation of state with Huron-Vidal mixing rules was used. Details about the model are reported in the paper by Soave et al. [16]. This approach is particularly adequated when experimental values of the critical temperature and pressure are not available as it was the case for limonene and linalool. Note that the flexibility of the thermodynamic model to reproduce high-pressure vapor-liquid equilibrium data is ensured by the use of the Huron-Vidal mixing rules and a NRTL activity coefficient model at infinite pressures. Calculation results are reported as continuous curves in figure 2 for the C02-linalool system and in figure 3 for C02-limonene. Note that the same parameters values were used to correlated the data of C02-limonene at 45, 50 e 60 °C. 

Huron, M.J. Vidal, J. New mixing rules in simple equations of state for representing vapour-liquid equilibria of strongly non-ideal mixtures. Fluid Phase Equilib. 1979, 3, 255. 

Huron and Vidal showed that equating the infinite pressure Gibbs energy of mixing to that of an activity model like the NRTL or UNIQUAC models provided a mixing rule that was sufficiently flexible to describe very complex phase behavior. With this modification, simple cubic equations like Soave s could be applied to nearly any kind of mixture at any conditions, including supercritical conditions. The Huron-Vidal mixing rule combined with NRTL activity model is illustrated below. 

The results for the carbon dioxide and propane binary system, shown as dashed lines in Figure 4.2.2, on the other hand are not as good. When compared with the performance of the IPVDW model (solid lines in Figure 4.2.2), the use of the same parameters for all isotherms leads to inferior results at higher temperatures despite the use of an extra parameter in the Huron-Vidal model. This indicates that, for the mixtures containing supercritical components, the HVO mixing rule, when combined... 

Figure 4.2.1. VLE correlation of the methane and pentane binary system at 310, 377, and 444 K with the Huron-Vidal original (HVO) mixing rule with the van Laar excess fiee-energy model and the PRS V equation of state. The van Laar model parameters used are = A12/A21 = 0.1201/0.1430. Points are experimental data from the DECHEMA Chemistry Data Series, Gmehiing and Onken 1977, Vol. 6, p. 445 data tiles for this system on the accompanying disk are C1C5310.DAT, C1C5377.DAT andClC5444.DAT.

Figure 4.2.5. VLE correlation of the 2-propanol and water binary system at 353 K with the Huron-Vidal original (HVO) mixing rule combined with the NRTL excess free-energy model and the PRSV equation of state. The dashed lines represent results calculated with a = 0.2893 and ri2/r2i =0.7882/3.9479 obtained from fitting the experimental data, and the solid lines denote results calculated with a —...

The modified Huron-Vidal (MHV) mixing rule of Michelsen (1990b) is one of the most used of this class. The idea behind this mixing rule is to use eqn. (4.1.4) at E = 0 to obtain... 

In the Huron-Vidal mixing rule the mixture EOS parameters are given as... 

Modified Huron-Vidal First-Order Mixing Rule (MHVI)... 

Modified Huron-Vidal Second-Order Mixing Rule (MHV2)... 

H. Orbey-Sandler Modification of the Huron-Vidal Mixing Rule (HVOS) Again h = used, and the a parameter relation is... 

D.4. Program HV Binary VLE with the Huron-Vidal Mixing Rule (HVO) and Its Modifications (MHVI, MHV2, LCVM, and HVOS)... 

This results in the selection of the original Huron-Vidal model, HVO, for the mixing rule model.)... 

Example D.7.A Use of the Huron-Vidal Class of Mixing Rule,... 

SELECT A MIXING RULE MODEL HV 0=HURON-VinAL ORIGINAL MKVl=HODIFIED HURON-VIDAL 1ST ORDER MHV2=HODIFIED HURON-VIIUUJ 2ND ORDER... 

HVIIUT BINARY VLiE CALCULATIONS WITH HURON-VIDAL TYPE MIXING RULES AND THE UNIFAC MODEL... 

E.3. Program HVMMAIN Multicomponent VLE Calculations with Modified Huron-Vidal (HVOS) Mixing Rule... 

Boukouvalas, C., Spiliotis, N., Coutsikos, P., and Tzouvaras, N., 1994. Prediction of vapor-liquid equilibrium with the LCVM model. A linear combination of the Huron-Vidal and Michelsen mixing rules coupled with the original UNIFAC and the t-mPR equation of state. Fluid Phase Eq., 92 75-106. 

Michelsen, M. L., 1990b. A modified Huron—Vidal mixing rule for cubic equations of state. Fluid Phase Eq., 60 213-219. 

Tochigi, K., Kolar, R, Izumi, T., and Kojima, K., 1994. A note on a modified Huron-Vidal mixing rule consistent with the second virial coefficient condition. Fluid Phase Eq., 96 215-221. 

Predict (using the modified Huron-Vidal second order (MHV2) mixing rule) the sorption of CO2 in polyethylene glycol over extended pressure ranges Predict (using EoS/G mixing rules) Henry s law constants for different polymer solutions... 

Keshtkar, a., Jalali, F. Moshfeghian, M. 1997. Evaluation of vapor-liquid equilibrium of CO2 binary systems using UNIQUAC-based Huron-Vidal mixing rules. Fluid Phase Equilibria, 140(1/2), 107-128. 

It is important to note that in the equation (6.19) G is excess Gibbs free energy. This function can be calculated accurately by means of liquid activity models. C is a constant depending on the particular type of EOS. Note also that in the mixing rules of Huron Vidal the parameters in the liquid activity model are not equal with those found at other pressures, and must be regressed again from experimental data. 

The required parameters k j are fitted to experimental binary VLE data. However, problems with this empirical mixing rules arise for highly polar or associating mixtures. g mixing rules as introduced by Huron and Vidal (1979) lead to an improved description of these systems. These types of mixing rules include g , which can be calculated from a g model like UNIQUAC. 

One of the first implementations of the above procedure was that by Huron and Vidal [8]. They retained the simple mixing rule for the Redlich-Kwong parameter b,... 

M. J. Huron and J. Vidal, "New Mixing Rules in Simple Equations of State for Representing Vapour-Liquid Equilibria of Strongly Non-Ideal Mixtures," Fluid... 

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