Phase behavior multicomponent mixtures

This paper reviews the experiences of the oil industry in regard to asphaltene flocculation and presents justifications and a descriptive account for the development of two different models for this phenomenon. In one of the models we consider the asphaltenes to be dissolved in the oil in a true liquid state and dwell upon statistical thermodynamic techniques of multicomponent mixtures to predict their phase behavior. In the other model we consider asphaltenes to exist in oil in a colloidal state, as minute suspended particles, and utilize colloidal science techniques to predict their phase behavior. Experimental work over the last 40 years suggests that asphaltenes possess a wide molecular weight distribution and they may exist in both colloidal and dissolved states in the crude oil. 

Next we will consider the phase behavior of mixtures of two components. The petroleum engineer does not normally work with two-component systems usually mixtures consisting of many components are encountered. However, it is instructive to observe the differences in phase behavior between two-component mixtures and pure substances. These differences are amplified in multicomponent mixtures. 

Figure 2-37 shows phase diagrams for several mixtures of ethane and n-heptane. These are two-component mixtures however, the shapes of the phase diagrams can. be used in understanding the behavior of multicomponent mixtures. 

For industrial applications, determining the stable hydrate structure at a given temperature, pressure, and composition is not a simple task, even for such a simple systems as the ones discussed here. The fact that such basic mixtures of methane, ethane, propane, and water exhibit such complex phase behavior leads us to believe that industrial mixtures of ternary and multicomponent gases with water will exhibit even more complex behavior. Spectroscopic methods are candidates to observe such complex systems because, as discussed earlier, pressure and temperature measurements of the incipient hydrate structure are not enough. 

The differential heat of adsorption for each component in the mixture is estimated using the Clapeyron equation, extended to multicomponent mixtures and assuming ideal behavior of the gas phase (fugacity of i-th components Pi.)> that is,... 

For a pure supercritical fluid, the relationships between pressure, temperature and density are easily estimated (except very near the critical point) with reasonable precision from equations of state and conform quite closely to that given in Figure 1. The phase behavior of binary fluid systems is highly varied and much more complex than in single-component systems and has been well-described for selected binary systems (see, for example, reference 13 and references therein). A detailed discussion of the different types of binary fluid mixtures and the phase behavior of these systems can be found elsewhere (X2). Cubic ecjuations of state have been used successfully to describe the properties and phase behavior of multicomponent systems, particularly fot hydrocarbon mixtures (14.) The use of conventional ecjuations of state to describe properties of surfactant-supercritical fluid mixtures is not appropriate since they do not account for the formation of aggregates (the micellar pseudophase) or their solubilization in a supercritical fluid phase. A complete thermodynamic description of micelle and microemulsion formation in liquids remains a challenging problem, and no attempts have been made to extend these models to supercritical fluid phases. 

In principle, mixtures containing a very large number of components behave in a way described by the same general laws that regulate the behavior of mixtures containing only a comparatively small number of components. In practice, however, the procedures for the description of the thermodynamic and kinetic behavior of mixtures that are usually adopted for mixtures of a few components rapidly become cumbersome in the extreme as the number of components grows. As a result, alternate procedures have been developed for multicomponent mixtures. Particularly in the field of kinetics, and to a lesser extent in the field of phase equilibria thermodynamics, there has been a flurry of activity in the last several years, which has resulted in a variety of new results. This article attempts to give a reasoned review of the whole area, with particular emphasis on recent developments. 

Reaction mixtures are complex multicomponent systems, and their phase behavior is dictated by the composition of the mixture and operating conditions. Organic solvents present in the reaction medium as reagents may act as cosolvents and result in solute solubility enhancement (as discussed in Section 4.2). For example, the decrease in reaction rate observed at high ethanol concentrations for the lipase-catalyzed esterification of myristic acid + ethanol in SCCO2 has been, in part, attributed to the solubility enhancement of water, resulting in drying of the enzyme... 

Phase diagrams for multicomponent mixtures possess additional degrees of freedom and are inherently multidimensional. In practice, construction and interpretation of phase diagrams of multicomponent mixtures are similar to, and based on, those of binary mixtures. " " The phase behavior of multicomponent mixtures can also be depicted as sections in PTxiX2-space, keeping one or more of the variables constant. A widely used section for ternary mixtures is an equilateral triangle composition diagram at fixed pressure and temperature (Fig. 7). 

In tills section, we examine the thermodynamics of systems which contain a mixture of species. First, we generalize the thermodynamic analysis of the previous section to multicomponent systems, deriving the Gibbs phase rule. Then we describe the general phase behavior of binary and ternary mixtures. 

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. 

In this work, we have analyzed the phase behavior of various freeze-dried mixtures of DPPE, DPPC, and cholesterol and have examined the effects of trehalose addition to these liposomes. Generally, dehydration leads to increase in transition temperature of the phospholipids and also to phase separation. Addition of trehalose, however, can prevent the increase in transition temperature and phase separation freeze-dried DPPC-cholesterol liposomes exhibit only one transition and their retention capability increases by more than 40%. Further studies on the phase separation and stability of multicomponent model membranes will be required to understand better its relation to the survival of cells to freeze-drying procedures. 

The principle of distillation is the use of differences in volatiHties of the components to be separated. Distillation processes are usually carried out in countercurrent mode in multistage units. The differences that can be obtained in concentrations of the components in the vapor and liquid phases are determined by the vapor-liquid equihbrium (VLE). Until the 1970s reliable data for vapor-liquid equilibria could only be obtained by measurement, which, for a mixture containing more than two components, required a large number of time-consuming measurements. Advances in chemical thermodynamics have resulted in methods activity coefficient models (g models or equations of state) for the calculation of the phase-equihbrium behavior of multicomponent mixtures on the basis of binary subsystems. In the case that no information about the binary subsystems is available, predictive methods (group contribution methods) are available to allow estimation of the required phase equilibria. 

---