Activity coefficient models DECHEMA

Since the degree of coupling is directly proportional to the product Q (D/k)in, the error level of the predictions of q is mainly related to the reported error levels of Q values. The polynomial fits to the thermal conductivity, mass diifusivity, and heat of transport for the alkanes in chloroform and in carbon tetrachloride are given in Tables C1-C6 in Appendix C. The thermal conductivity for the hexane-carbon tetrachloride mixture has been predicted by the local composition model NRTL. The various activity coefficient models with the data given in DECHEMA series may be used to estimate the thermodynamic factors. However, it should be noted that the thermodynamic factors obtained from various molecular models as well as from two sets of parameters of the same model might be different. 

Equilibrium Data Collection in the Chemistry Data Series published by DECHEMA. VLE calculations are performed assuming an ideal vapor phase and a standard Wilson liquid activity coefficient model. This takes the form... 

The more difficult problem is deciding upon the appropriate choice of activity coefficient model and values of the model parameters. Numerous models are available, some of which are presented in Section 2.4. A valuable reference for choosing an appropriate model is Volume 1 - Vapor-Liquid Equilibrium Data Collection of the DECHEMA Chemistry Data Series (Gmehling and Onken 1977), This volume ... 

In each of these models two or more adj ustable parameters are obtained, either from data compilations such as the DECHEMA Chemistry Data Series mentioned earlier or by fitting experimental activity coefficient or phase equilibrium data, as di.scussed in standard thermodynamics textbooks. Typically binary phase behavior data are used for obtaining the model parameters, and these parameters can then be used with some caution for multicomponent mixtures such a procedure is more likely to be successful with the Wilson, NRTL, and UNIQUAC models than with the van Laar equation. However, the activity coefficient model parameters are dependent on temperamre, and thus extensive data may be needed to use these models for multicomponent mixtures over a range of temperatures. 

Comments The calculation is more involved than that of the Pxy graph because temperature affects the liquid-liquid boundary while pressure does not. To establish the liquid-liquid boundary, it is important to have an activity coefficient model with temperature dependent coefficients. The coefficients used in this example were taken from the DECHEMA series (Sorensen and Artl, Liquid-Liquid Equilibrium Data Collection, Chemistry Data Series, vol. V, Part 1). 

In eq 5.71, i) is a constant that depends on the particular equation of state used and Gm is an excess Gibbs function of mixing obtained from an activity coefficient model. Activity coefficients are usually obtained from measurements of (vapour-f liquid) equilibria at a pressure relatively low compared with the requirement of eq 5.67 for which p- ao the activity coefficients are tabulated, for example, those in the DECHEMA Chemistry Data Series. This distinction in pressure is particularly important because the excess molar Gibbs function of mixing, obtained from experiment and estimated from an equation of state, depends on pressure d(G /7 r)/d/)<0.002MPa for (methanol-f benzene) at a temperature of 373 K. Equation 5.71 does not satisfy the quadratic composition dependence required by the boundary condition of eq 5.3. However, equations 5.70 and 5.71 form the mixing rules that have been used to describe the (vapour + liquid) equilibria of non-ideal systems, such as (propanone + water), successfully in this particular case the three-parameter Non-Random Two Liquid (known by the acronym NRTL) activity-coefficient model was used for G and the value depends significantly on temperature to the extent that the model, while useful for correlation of data, cannot be used to extrapolate reliably to other temperatures. 

The Wong-Sandler mixing rules extend the use of cubic equations of state to mixtures that were previously only correlated with activity-coefficient models. For many mixtures, the Gibbs-function model parameters in the equation of state could be taken to be independent of temperature, thereby allowing extrapolation of phase behaviour over wide ranges of temperature and pressure. For example, for (ethanol-h water) the activity-coefficient model reported in DECHEMA is at a pressure of 0.4 MPa and this model provides reasonable predictions of the phase boundaries at pressures up to 20 MPa. This means the method can be used with UNIversal Functional Activity Coefficient (known by the acronym UNIFAQ and other group-contribution methods to predict properties at elevated pressure. 

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. 

Figure 3.5.7. VLE correlation of the methyl acetate and cyclohexane binary system at 313 K with the 2PVDW mixing rule and the PRSV equation of state. Solid lines are model predictions obtained by direct correlation of VLE data, and the dashed lines are predictions using infinite dilution activity coefficient data. See text for details. (Points are experimental data from the DECHEMA Chemistry Series, Gmehling and Onken 1977, Vol. 1, Pt. 5, p. 392 the data file for this system on the accompanying disk is MAC640.DAT.)...

Figure 6.2.2. Excess enthalpy for the benzene and cyclohexane system at 293 K (dots) and at 393 K (triangles), Tlie lines denote correlations at 293 K and predictions at 393 K using various models. The solid line reflects predictions using the 2PVDW model, the dotted line represents the predictions using the van Laar activity coefficient mode , the short dashed lines signify predictions using the HVOS model, and the long dashed line denotes predictions made with the WS model. Data are from the DECHEMA Chemistry Series (Gmehling and Onken 1977, Vol. 3, Pt. 2, p. 992).

DECHEMA m-model UNIFAC activity coefficients Equation of state —ideal gas law Vapor pressure—Antoine equation Excess enthalpy from UNIFAC model Specifications ... 

---