Multicomponent mixtures phase equilibria

Mixture phase equilibrium calculations, types of, 24 680-681 Mixture-process design type, 8 399 commercial experimental design software compared, 8 398t Mixtures. See also Multicomponent mixtures Nonideal liquid mixtures acetylene containing, 2 186 adsorption, 2 593-594 adsorption isotherm models,... 

Multicomponent diffusion, 1 43—46 Multicomponent mixtures, phase and chemical equilibrium criteria in, 24 675-678... 

There are two types of multicomponent mixtures which occur In polymer phase equilibrium calculations solutions with multiple solvents or pol ers and solutions containing poly-disperse polymers. We will address these situations In turn. 

The criterion for thermodynamic equilibrium between two phases of a multicomponent mixture is that for every component, i ... 

The area bounded by the bubble point and dew point curves on the phase diagram of a multicomponent mixture defines the conditions for gas and liquid to exist in equilibrium. This was discussed in Chapter 2. The quantities and compositions of the two phases vary at different points within the limits of this phase envelope. 

When a liquid hydrocarbon mixture is present, the Lw-V-Lhc line in Figure 4.2b broadens to become an area, such as that labeled CFK in Figure 4.2c. This area is caused by the fact that a single hydrocarbon is no longer present, so a combination of hydrocarbon (and water) vapor pressures creates a broader phase equilibrium envelope. Consequently, the upper quadruple point (Q2) evolves into a line (KC) for the multicomponent hydrocarbon system. 

From the point of view of traditional thermodynamics, a microemulsion is a multicomponent mixture formed of oil, water, surfactant, cosurfactant, and electrolyte. There is, however, a major difference between a conventional mixture and a microemulsion. In the former case, the components are mixed on a molecular scale, while in the latter, oil or water is dispersed as globules on the order of 10-100 nm in diameter in water or oil. The surfactant and cosurfactant are mostly located at the interface between the two phases but are also distributed at equilibrium between the two media. In conventional mixtures, the sizes of the component species are fixed. In the case of microemulsions, the sizes of the globules are not given but are provided by the condition of thermodynamic equilibrium. 

On its way downwards, the liquid phase is of course depleted with respect to its more volatile component(s) and enriched in its heavier component(s). At the decisive locus, however, where both phases have their final contact (i.e., the top of the column), the composition of the liquid is obviously stationary. For a desired composition of the gas mixture, the appropriate values for the liquid phase composition and the saturator temperature must be found. This is best done in two successive steps, viz. by phase equilibrium calculations followed by experimental refinement of the calculated values. The multicomponent saturator showed an excellent performance, both in a unit for atmospheric pressure [18] and in a high-pressure apparatus [19, 20] So far, the discussion of methods for generating well defined feed mixtures in flow-type units has been restricted to gaseous streams. As a rule, liquid feed streams are much easier to prepare, simply by premixing the reactants in a reservoir and conveying this mixture to the reactor by means of a pump with a pulsation-free characteristic. 

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. 

For binary diffusion, there is only one independent flow, force or concentration gradient, and diffusion coefficient. On the other hand, multicomponent diffusion differs from binary diffusion because of the possibility of interactions among the species in mixtures of three or more species. Some of the possible interactions are (1) a flow may be zero although its zero driving force vanishes, which is known as the diffusion barrier (2) the flow of a species may be in a direction opposite to that indicated by its driving force, which is called reverse flow and (3) the flow of a species may occur in the absence of a driving force, which may be called osmotic flow. The theory of nonequilibrium thermodynamics indicates that the chemical potential arises as the proper driving force for diffusion. This is also consistent with the condition of fluid phase equilibrium, which is satisfied when the chemical potentials of a species are equal in each phase. 

The design engineer dealing with polymer solutions must determine if a multicomponent mixture will separate into two or more phases and what the equilibrium compositions of these phases will be. Prausnitz et al. (1986) provides an excellent introduction to the field of phase equilibrium thermodynamics. 

It is of course well known that in nature heterogeneous chemical equilibria are possible systems in which chemical reactions may take place, and which at equilibrium will exist in mote than one phase. The question that arises is the analysis of the conditions under which heterogeneous chemical equilibria are possible in multicomponent mixtures. In this section, we follow closely the analysis that was recently presented by Astarita and Ocone (1989) earlier work on the subject is due to Caram and Scriven (1976) and Astarita (1976). 

Cotterman, R. L., and Prausnitz, J. M., Continuous thermodynamics for phase-equilibrium calculations in chemical process design. In Kinetic and Thermodynamic Lumping of Multicomponent Mixtures (G. Astarita and R. I. Sandler, eds.). Elsevier, Amsterdam, 1991, p. 229. 

All cases of practical importance in liquid chromatography deal with the separation of multicomponent feed mixtures. As shown in Chapter 2, the combination of the mass balance equations for the components of the feed, their isotherm equations, and a chromatography model that accounts for the kinetics of mass transfer between the two phases of the system permits the calculation of the individual band profiles of these compounds. To address this problem, we need first to understand, measure, and model the equilibrium isotherms of multicomponent mixtures. These equilibria are more complex than single-component ones, due to the competition between the different components for interaction with the stationary phase, a phenomenon that is imderstood but not yet predictable. We observe that the adsorption isotherms of the different compounds that are simultaneously present in a solution are almost always neither linear nor independent. In a finite-concentration solution, the amount of a component adsorbed at equilib-... 

In this section, we derive the equation that governs the shape of the freezing curve. Let s consider the freezing of a species in a general multicomponent mixture. We make the assumption that the solid phase consists of pure component a. At equilibrium, the chemical potential of the solid phase is the... 

The activity coefficient of a component in a mixture is a function of the temperature and the concentration of that component in the mixture. When the concentration of the component proaches zero, its activity coefficient approaches the limiting activity coefficient of th component in the mixture, or the activity coefficient at infinite dilution, y . The limiting activity coefficient is useful for several reasons. It is a strictly dilute solution property and can be used dir tly in nation 1 to determine the equilibrium compositions of dilute mixtures. Thus, there is no reason to extrapolate uilibrium data at mid-range concentrations to infinite dilution, a process which may introduce enormous errors. Limiting activity coefficients can also be used to obtain parameters for excess Gibbs energy expressions and thus be used to predict phase behavior over the entire composition range. This technique has been shown to be quite accurate in prediction of vapor-liquid equilibrium of both binary and multicomponent mixtures (5). 

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. 

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. 

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