Equilibria in Nonideal Systems

Castier M., P. Rasmussen, and A. Fredenslund, Calculation of simultaneous chemical and phase equilibria in nonideal systems, Chem. Eng. Sci. 44, 237-248 (1989). 

As discussed in Chapter 3, at moderate pressures, vapor-phase nonideality is usually small in comparison to liquid-phase nonideality. However, when associating carboxylic acids are present, vapor-phase nonideality may dominate. These acids dimerize appreciably in the vapor phase even at low pressures fugacity coefficients are well removed from unity. To illustrate. Figures 8 and 9 show observed and calculated vapor-liquid equilibria for two systems containing an associating component. 

Gas Separation by Adsorption Processes Ralph T. Yang Heterogeneous Reactor Design Hong H. Lee Molecular Thermodynamics of Nonideal Fluids Lloyd L. Lee Phase Equilibria in Chemical Engineering Stanley M. Walas Transport Processes in Chemically Reacting Flow Systems Darnel E. Rosner... 

Like azeotropic distillation, extractive distillation involves highly nonideal phase equilibria as well as the addition of an agent, often called a solvent, that modifies and improves the phase equilibria among the system components. However, extractive distillation is different in that no azeotropes are involved, and the agent added is essentially nonvolatile and introduces no new azeotropes. 

It has been shown that models for DCFIs can lead to successful descriptions of solution properties and phase equilibria, especially for strongly nonideal systems such as dilute solutions of gases and solids. Because FST formulations are for composition derivatives of pressure and chemical potential or fugacity, the evaluation can appear complex and requires property values at certain reference states. This may be the reason such models have not been implemented into process simulators. However, the reliability and accuracy of models based on perturbations from hard spheres, such as Equation 9.4, is quite good for very many systems, and the results can at least be used to generate local parameterizations and to validate EOS models. Ultimately, results from molecular simulations, as described in Chapter 6, may lead to new relations for the thermodynamic models for use in process simulators. 

Two factors play important roles in the study of adsorption equilibria of mixtures on heterogeneous adsorbents like activated carbon and hence have received attention in the development of various models. They are (1) the size difference between the adsorbate molecules and (2) the adsorption energetic heterogeneity, or the structural heterogeneity of the adsorbent if the adsorbate is nonpolar. For many conditions, these two factors are adequate to account for the nonideal behavior of the adsorbed phase, and they are readily accounted for by the MPSD model. This model needs to be further applied and tested in many systems to verify its capability, and it needs to be modified (fine-tuned) to account for many factors such as the irregular structure of the micropore as well as the inclusion of functional groups to deal with polar adsorbates. 

Chimowitz, E.H., S. Macchietto, T.F. Anderson, L.F. Stutzman (1993) Local models for representing phase equilibria in multicomponent, nonideal vapor-liquid and liquid-liquid systems. 1. Thermodynamic approximation functions. Ind. Eng. Chem. Process Des. Dev. 22, 217 - 225... 

Such a process depends upon the difference in departure from ideally between the solvent and the components of the binary mixture to be separated. In the example given, both toluene and isooctane separately form nonideal liquid solutions with phenol, but the extent of the nonideality with isooctane is greater than that with toluene. When all three substances are present, therefore, the toluene and isooctane themselves behave as a nonideal mixture and then-relative volatility becomes high. Considerations of this sort form the basis for the choice of an extractive-distillation solvent. If, for example, a mixture of acetone (bp = 56.4 C) and methanol (bp = 64.7°Q, which form a binary azeotrope, were to be separated by extractive distillation, a suitable solvent could probably be chosen from the group of aliphatic alcohols. Butanol (bp = 117.8 Q, since it is a member of the same homologous series but not far removed, forms substantially ideal solutions with methanol, which are themselves readily separated. It will form solutions of positive deviation from ideality with acetone, however, and the acetone-methanol vapor-liquid equilibria will therefore be substantially altered in ternary mixtures. If butanol forms no azeotrope with acetone, and if it alters the vapor-liquid equilibrium of acetone-methanol sufficiently to destroy the azeotrope in this system, it will serve as an extractive-distillation solvent. When both substances of the binary mixture to be separated are themselves chemically very similar, a solvent of an entirely different chemical nature will be necessary. Acetone and furfural, for example, are useful as extractive-distillation solvents for separating the hydrocarbons butene-2 and a-butane. 

At pressures to a few bars, the vapor phase is at a relatively low density, i.e., on the average, the molecules interact with one another less strongly than do the molecules in the much denser liquid phase. It is therefore a common simplification to assume that all the nonideality in vapor-liquid systems exist in the liquid phase and that the vapor phase can be treated as an ideal gas. This leads to the simple result that the fugacity of component i is given by its partial pressure, i.e. the product of y, the mole fraction of i in the vapor, and P, the total pressure. A somewhat less restrictive simplification is the Lewis fugacity rule which sets the fugacity of i in the vapor mixture proportional to its mole fraction in the vapor phase the constant of proportionality is the fugacity of pure i vapor at the temperature and pressure of the mixture. These simplifications are attractive because they make the calculation of vapor-liquid equilibria much easier the K factors = i i ... 

Physical Equilibria and Solvent Selection. In order for two separate Hquid phases to exist in equiHbrium, there must be a considerable degree of thermodynamically nonideal behavior. If the Gibbs free energy, G, of a mixture of two solutions exceeds the energies of the initial solutions, mixing does not occur and the system remains in two phases. Eor the binary system containing only components A and B, the condition (22) for the formation of two phases is... 

There are many types of phase diagrams in addition to the two cases presented here these are summarized in detail by Zief and Wilcox (op. cit., p. 21). Solid-liquid phase equilibria must be determined experimentally for most binary and multicomponent systems. Predictive methods are based mostly on ideal phase behavior and have limited accuracy near eutectics. A predictive technique based on extracting liquid-phase activity coefficients from vapor-liquid equilibria that is useful for estimating nonideal binary or multicomponent solid-liquid phase behavior has been reported by Muir (Pap. 71f, 73d ann. meet., AIChE, Chicago, 1980). 

In all the above discussions regarding liquid-vapor equilibria we have assumed that our representative systems were ideal, that is, there are no differences in attractions between molecules of different types. Few systems are ideal and most show some deviation from ideality and do not follow Raoult s law. Deviations from Raoult s law may be positive or negative. Positive deviations (for binary mixtures) occur when the attraction of like molecules, A-A or B-B, are stronger than unlike molecules, A-B (total pressure greater than that computed for ideality). Negative deviations result from the opposite effects (total pressure lower than that computed for ideality). A mixture of two liquids can exhibit nonideal behavior by forming an azeotropic mixture (a constant boiling mixture). 

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