Fluids mixtures, equilibrium properties

Hiza, M. J., A. J. Kidnay, and R. C. Miller "Equilibrium Properties of Fluid Mixtures—A Bibliography of Data on Fluids of Cryogenic Interest," NSRDS Bibliographic Series. Plenum, New York, 1975. 

Two generally accepted models for the vapor phase were discussed in Chapter 3 and one particular model for the liquid phase (UNIQUAC) was discussed in Chapter 4. Unfortunately, these, and all other presently available models, are only approximate when used to calculate equilibrium properties of dense fluid mixtures. Therefore, any such model must contain a number of adjustable parameters, which can only be obtained from experimental measurements. The predictions of the model may be sensitive to the values selected for model parameters, and the data available may contain significant measurement errors. Thus, it is of major importance that serious consideration be given to the proper treatment of experimental measurements for mixtures to obtain the most appropriate values for parameters in models such as UNIQUAC. 

Volumetric equations of state (EoS) are employed for the calculation offluid phase equilibrium and thermo-physical properties required in the design of processes involving non-ideal fluid mixtures in the oil, gas and chemical industries. Mathematically, a volumetric EoS expresses the relationship among pressure, volume, temperature, and composition for a fluid mixture. The next equation gives the Peng-Robinson equation of state, which is perhaps the most widely used EoS in industrial practice (Peng and Robinson, 1976). 

It should be kept in mind that an objective function which does not require any phase equilibrium calculations during each minimization step is the basis for a robust and efficient estimation method. The development of implicit objective functions is based on the phase equilibrium criteria (Englezos et al. 1990a). Finally, it should be noted that one important underlying assumption in applying ML estimation is that the model is capable of representing the data without any systematic deviation. Cubic equations of state compute equilibrium properties of fluid mixtures with a variable degree of success and hence the ML method should be used with caution. 

All of the experiments in pure and mixed SSME systems, as well as in the Af-stearoyltyrosine systems, have one common feature, which seems characteristic of chiral molecular recognition in enantiomeric systems and their mixtures enantiomeric discrimination as reflected by monolayer dynamic and equilibrium properties has only been detected when either the racemic or enantiomeric systems have reverted to a tightly packed, presumably quasi-crystalline surface state. Thus far it has not been possible to detect clear enantiomeric discrimination in any fluid or gaseous monolayer state. 

Optimizing solvents and solvent mixtures can be done empirically or through modeling. An example of the latter involves a single Sanchez-Lacombe lattice fluid equation of state, used to model both phases for a polymer-supercritical fluid-cosolvent system. This method works well over a wide pressure range both volumetric and phase equilibrium properties for a cross-linked poly(dimethyl siloxane) phase in contact with CO2 modified by a number of cosolvents (West et al., 1998). 

Chapters 17 and 18 use thermodynamics to describe solutions, with nonelectrolyte solutions described in Chapter 17 and electrolyte solutions described in Chapter 18. Chapter 17 focuses on the excess thermodynamic properties, with the properties of the ideal and regular solution compared with the real solution. Deviations from ideal solution behavior are correlated with the type of interactions in the liquid mixture, and extensions are made to systems with (liquid + liquid) phase equilibrium, and (fluid -I- fluid) phase equilibrium when the mixture involves supercritical fluids. 

The grand canonical ensemble is appropriate for adsorption systems, in which the adsorbed phase is in equilibrium with the gas at some specified temperature. The use of a computer simulation allows us to calculate average macroscopic properties directly without having to explicitly calculate the partition function. The grand canonical Monte Carlo (GCMC) method as applied in this work has been described in detail earlier (55). The aspects involving binary fluid mixtures have been described previously in our Xe-Ar work (30). 

The properties of mixtures of ideal gases and of ideal solutions depend solely on the properties of the pure constituent species, and are calculated from them by simple equations, as illustrated in Chap. 10. Although these models approximate the behavior of certain fluid mixtures, they do not adequately represent the -behavior of most solutions of interest to chemical engineers, and Raoult s law is not in general a realistic relation for vapor/liquid equilibrium. However, these models of ideal behavior—the ideal gas, the ideal solution, and Raoult s law— provide convenient references to which the behavior of nonideal solutions may be compared. 

In Chap. 6 we treated the thermodynamic properties of constant-composition fluids. However, many applications of chemical-engineering thermodynamics are to systems wherein multicomponent mixtures of gases or liquids undergo composition changes as the result of mixing or separation processes, the transfer of species from one phase to another, or chemical reaction. The properties of such systems depend on composition as well as on temperature and pressure. Our first task in this chapter is therefore to develop a fundamental property relation for homogeneous fluid mixtures of variable composition. We then derive equations applicable to mixtures of ideal gases and ideal solutions. Finally, we treat in detail a particularly simple description of multicomponent vapor/liquid equilibrium known as Raoult s law. 

Weiss, V.C., and Schroer, W. Macroscopic theory for equilibrium properties of ionic-dipolar mixtures and application to an ionic model fluid. J. Chem. Phys., 1998, 108, p. 7747-57. 

Economou, I.G., Statistical Associating Fluid Theory a successful model for the calculation of thermodynamic and phase equilibrium properties of complex fluid mixtures, Ind. Eng. Ghent. Res., 41(5), 953-962, 2002. 

Most of the common separation methods used in the chemical industry rely on a well-known observation when a multicomponent two-phase system is given sufficient ttmu to attain a statioenry state called equilibrium, the composition of one phase is different from thet of the other. It is this property of nature which eenbles separation of fluid mixtures by distillation, extraction, and other diffusions operations. For rational design of such operations it is necessary to heve a quantitative description of how a component distributes itself between two contacting phases. Phase-equilibrium thermodynamics, summarized here, provides a framework for establishing that description. 

For the calculations, different EoS have been used the lattice fluid (LF) model developed by Sanchez and Lacombet , as well as two recently developed equations of state - the statistical-associating-fluid theory (SAFT)f l and the perturbed-hard-spheres-chain (PHSC) theoryt ° . Such models have been considered due to their solid physical background and to their ability to represent the equilibrium properties of pure substances and fluid mixfures. As will be shown, fhey are also able to describe, if not to predict completely, the solubility isotherms of gases and vapors in polymeric phases, by using their original equilibrium version for rubbery mixtures, and their respective extensions to non-equilibrium phases (NELF, NE-SAFT, NE-PHSC) for glassy polymers. 

These and all previous results of thermodynamic mixture which also fulfil Gibbs-Duhem equations (4.263) show the complete agreement with the classical thermodynamic of mixtures but moreover all these relations are valid much more generally. Namely, they are valid in this material model—linear fluid mixture—in all processes whether equilibrium or not. Linear irreversible thermodynamics [1-4], which studies the same model, postulates this agreement as the principle of local equilibrium. Here in rational thermodynamics, this property is proved in this special model and it cannot be expected to be valid in a more general model. We stress the difference in the cases when (4.184) is not valid—e.g. in a chemically reacting mixture out of equilibrium—the thermodynamic pressures P, Pa need not be the same as the measured pressure (as e.g. X =i Pa) therefore applications of these thermodynamic... 

In Sections 2 to 4 critical phenomena will be of primary importance since they make possible a systematic discussion of all types of phase behaviour in fluid mixtures and of the relationships between them. The definition of a critical point for a mixture is essentially the same as that for a pure component at a critical point all intensive properties of two phases in equilibrium become identical. Whereas pure substances are characterized by a critical point for the equilibrium gas-liquid, binary systems exhibit a critical line in the three-dimensional p-T-x space (where x denotes mole fraction), and systems with n components an ( — l)-dimensional critical surface in the ( i + l)-dimensional p-T-Xi-X2. .. Xn-i space for all kinds of fluid-fluid equilibria. 

Once potential parameters have been determined, we can start calculation downward following arrow in the figure. The first key quantity is radial distribution function g(r) which can be calculated by the use of theoretical relation such as Percus-Yevick (PY) or Hypemetted chain (HNC) integral equation. However, these equations are an approximations. Exact values can be obtained by molecular simulation. Ifg(r) is obtained accurately as functions of temperature and pressure, then all the equilibrium properties of fluids and fluid mixtures can be calculated. Moreover, information on fluid structure is contained in g(r) itself. 

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