Huron-Vidal model

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... 

HV BINARY VLE CALCULATIONS WITH THE HURON-VIDAL MODEL AND ITS VARIATIONS... 

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

Example D.4.C Binary VLE Predictions Using the Huron-Vidal Model... 

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 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. 

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 —...

Figure 4.3.9. Comparison of VLB predictions of the 2-propanoi and water binary system at 353 K from the Wong-Sandler (solid lines) and Huron-Vidal original (dashed lines) models with both model parameters obtained by fitting the experimental data at 303 K. Points are the experimental data of Barr David and Dodge 1959.

In this model, eqns. (4.4.12 and 3.3.8) are used to obtain the EOS parameters a and b. This model is referred to as Huron-Vidal as modified by Orbey-Sandler (HVOS) model in this monograph and is also included in the programs supplied on the accompanying disk. It is an approximate model but is in agreement with the spirit of the van der Waals hard core concept, and it is algebraically very similar to several of the commonly used zero-pressure models mentioned in this section. Yet it does not... 

II.G. Linear Combination of Huron-Vidal and Michelsen Models (LCVM)... 

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... 

KVUSfP VLE CALCULATIONS WITH HURON-VIDAL TYPE MODELS AND UHIFAC ab2 5 dat... 

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. 

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 direct adjustment of the interaction parameters of the g model (usually Wilson, NRTL or UNIQUAC) to experimental data usually yields an accurate correlation of VLE data. Problems can arise if published interaction parameters are used (e.g., from the DECHEMA data series [12]). In most cases, these have been fitted to data at moderate pressures, whereas the Huron-Vidal g mixing rule has been derived for infinite pressure (see above), which can cause poor results. 

In an attempt to improve the behaviour of the cubic equation of state, the more elaborate Huron-Vidal mixing rules were used with the Peng-Robinson equation of state.As shown in Figure 4.5 for the (vapour + liquid + liquid) (VLLE) equilibrium of (water + hex-1-ene) the Huron-Vidal mixing rules improved significantly the predicted solubility of hex-1-ene over the standard van der Waals mixing rules however, there was also a significant decrease in the ability of the model to correlate of solubility of water. 

Boukouvalas et al proposed a mixing rule by forming the following linear combination of the Huron-Vidal and Michelsen models known by the acronym... 

The cubic Soave-Redlich-Kwong equation of state with the modified Huron-Vidal mixing rules developed by Michelsen (herein after assigned the acronym MHV2) is a model that fulfils these requirements and it is very attractive due to its mathematical simplicity details of Huron-Vidal mixing... 

The first systematic successful effort in developing an EoS/ g model is that of (Huron Vidal, 1979). Starting from Eq. (47), they obtained ... 

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