Multicomponent Phase Behavior

Multiphase phenomenon is more frequently encountered in multicomponent mixtures, such as reaction mixtures. From a thermodynamic perspective, multiphase phenomena exist because multiple phases reduce the Gibbs free energy of the system. More components mean more ways and phases in which to partition this energy. Due to the Gibbs phase rule, a third component extends multiphase equilibrium as seen in binary mixtures, such as LLV and SLV equihbrium, from a lirte to a region of pressure and concentration at a given temperature. 

As a general observation, a solid solute increases the likelihood of forming an additional liquid phase for two reasons. Assuming the fluid phase is composed of the supercritical solvent and an ambient liquid, the solid solute acts as an impurity inducing a form of boiling point elevation higher pressures are needed in order to maintain a single fluid phase. Secondly, in this mixed fluid, the solid solute can melt more easily due to both the interaction with the pressurized gas and the liquid component present 

Examples of Combined Reaction/Phase Behavior Studies 

Stradi et al. [30] have performed a detailed phase equilibrium study of the binary and multicomponent mixtures of the reactants, products, and catalysts involved in the allylic epoxidation of trans-hexen-l-ol in SCCO2. Their studies indicate that, depending on the reaction conditions and conversion, vapor-hquid, vapor-liquid-hquid, and regions of multicomponent critical endpoints can exist. They were able to model the phase equilibrium with a reliable equation-of state approach and were able to simulate different reaction conditions. 

Baiker and co-workers [31, 32] investigated the role of phase behavior in the interpretation of the chemoselective oxidation of octyl alcohols in CO2 and the enantioselective hydrogenation of ethyl pyruvate in supercritical ethane. They found that the effects of temperature and pressure and the concentration of the reaction gases (H2 or O2) had a large impact upon the selectivities. Only through careful consideration of the number of phases and their behavior through different conversion levels cotxld the results be properly interpreted. 

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The dilated van Laar model is readily generalized to the multicomponent case, as discussed in detail elsewhere (C3, C4). The important technical advantage of the generalization is that it permits good estimates to be made of multicomponent phase behavior using only experimental data obtained for binary systems. For example, Fig. 14 presents a comparison of calculated and observed -factors for the methane-propane-n-pentane system at conditions close to the critical.7... 

The development of SCF processes involves a consideration of the phase behavior of the system under supercritical conditions. The influence of pressure and temperature on phase behavior in such systems is complex. For example, it is possible to have multiple phases, such as liquid-liquid-vapor or solid-liquid-vapor equilibria, present in the system. In many cases, the operation of an SCF process under multiphase conditions may be undesirable and so phase behavior should first be investigated. The limiting case of equilibrium between two components (binary systems) provides a convenient starting point in the understanding of multicomponent phase behavior. 

In this chapter, the possibihty of using late transition metal catalysts to synthesize polyolefins in supercritical carbon dioxide was demonstrated [43]. The multicomponent phase behavior of polyolefin systems at supercritical conditions was studied experimentally by measuring cloud-point curves as well as by modeling polymer systems at supercritical conditions. The cloud-point measurements show that CO2 acts as a strong antisolvent for the ethylene-PEP system, which implies that the polymerization concerned will involve a precipitation reaction. The model calculations prove that SAFT is able to describe the ethylene-PEP-CO2 system accurately. Solubility measurements of the Brookhart catalyst reveal that the maximum catalyst solubility is rather low (in the order of 1x10 mol L ). However, a number of strategies are given to enhance this value. 

We have sectioned this chapter into four main parts synthesis, biodegradation, toxicology, and single- and multicomponent phase behavior and dilute solution properties. The synthesis is discussed because it is an area of... 

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 binaiy and multicomponent systems. Predictive methods are based mostly on ideal phase behavior and have limited accuracy near eutectics. A predic tive technique based on extracting liquid-phase activity coefficients from vapor-liquid equilib-... 

Antia, F. D. and Horvath, Cs., Dependence of retention of the organic modifier concentration and multicomponent adsorptive behavior in reversed-phase chromatography, /. Chromatogr., 550, 411, 1991. 

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. 

Understanding of phase behavior in concentrated salts systems requires liquid-phase activity coefficients for the electrolytes and for water in the multicomponent system. 

While classical phase diagrams provide a powerful methodology for grasping the thermodynamic behavior of few-component systems, it is evident that the restricted 2D or 3D realm of human graphical intuition cannot adequately cope with the complexities of many-component systems. Hence, it is important to find generalized analytical techniques that can accurately represent many-component phase behavior for arbitrary values of c. Such techniques will be considered in the metric geometric representation of multicomponent phenomena (Chapter 12). 

After a careful examination of the phase behavior of a pure substance, we will discuss the behavior of systems which contain two or more components and point out the differences between multicomponent behavior and pure substance behavior. 

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. 

Phase behavior of multicomponent reservoir fluids is similar. Reservoir gases, which are predominately methane, have relatively small phase diagrams with critical temperatures not much higher than the orSiranempnatiire of nietfiahe. The critical point is"fairdown the left slope of the envelope. 

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. 

Civilian applications are numerous, but most funding of SCWO technology has stemmed from the military s need to find a safe and effective alternative to incineration of their wastes, as well as the need to clean up mixed wastes (radioactive and hazardous organic materials) at DOE weapons facilities. For better utilization of SCWO for its application to a wide range of waste types, a better fundamental understanding of reaction media, including reaction rates, reaction mechanisms, and phase behavior of multicomponent systems is required. Such an understanding would help optimize the process conditions to minimize reactor corrosion and salt... 

A novel approach to reduce the experimental effort associated with constructing pseudoternary phase diagrams is by using expert systems to predict the phase behavior of multicomponent ME-forming systems. Artificial neural networks have been investigated and were shown to be promising in phase behavior studies [17,35,36] as well as in the process of ingredient selection [37]. 

Another AFM-based technique is chemical force microscopy (CFM) (Friedsam et al. 2004 Noy et al. 2003 Ortiz and Hadziioaimou 1999), where the AFM tip is functionalized with specific chemicals of interest, such as proteins or other food biopolymers, and can be used to probe the intermolecular interactions between food components. CFM combines chemical discrimination with the high spatial resolution of AFM by exploiting the forces between chemically derivatized AFM tips and the surface. The key interactions involved in food components include fundamental interactions such as van der Waals force, hydrogen bonding, electrostatic force, and elastic force arising from conformation entropy, and so on. (Dther interactions such as chemical bonding, depletion potential, capillary force, hydration force, hydrophobic/ hydrophobic force and osmotic pressure will also participate to affect the physical properties and phase behaviors of multicomponent food systems. Direct measurements of these inter- and intramolecular forces are of great interest because such forces dominate the behavior of different food systems. 

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. 

It will he shown that the behavior of heterogeneous systems is influenced by the number of components it contains. A system which consists of a single, pure substance will behave differently from one which is made up of two or more components when the pressure and temperature are such that both a liquid phase and a gas phase are present. Consequently, the discussion of phase behavior will begin with a description of single-component systems. This will be followed by a description of two-component systems. Finally, multicomponent... 

The phase behavior of multicomponent hydrocarbon systems in the liquid-vapor region is very similar to that of binary systems. However, it is obvious that two-dimensional pressure-composition and temperature-composition diagrams no longer suffice to describe the behavior of multicomponent systems. For a multicomponent system with a given overall composition, the characteristics of the P-T and P-V diagrams are very similar to those of a two-component system. For systems involving crude oils which usually contain appreciable amounts of relatively r on-volatile constituents, the dew points may occur at such low pressures that they are practically unattainable. This fact will modify the behavior of these systems to some extent. 

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