Solid-liquid-vapor multicomponent system

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. 

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-... 

In developing the thermodynamic framework for ECES, we attempted to synthesize computer software that would correctly predict the vapor-liquid-solid equilibria over a wide range of conditions for multicomponent systems. To do this we needed a good basis which would make evident to the user the chemical and ionic equilibria present in aqueous systems. We chose as our cornerstone the law of mass action which simply stated says "The product of the activities of the reaction products, each raised to the power indicated by its numerical coefficient, divided by the product of the activities of the reactants, each raised to a corresponding power, is a constant at a given temperature. ... 

Despite these apparent weaknesses, within the context of a general purpose system for predicting the vapor-liquid-solid equilibria of multicomponent aqueous solutions, GCES as a tool succeeds remarkably well as will be seen in a few illustrations after the following description of the software structure and use. 

Unfortunately, the study of phase equilibria in solution, e.g., liquid-solid adsorption, is not a highly popular area of research. Gas-solid adsorption and vapor-solution equilibria have been studied in far more detail, although most of the information available concerns the fate of single components in a diphasic system. Liquid-solid adsorption has benefited mainly from the extension of the concepts developed for gas phase properties to the case of dilute solutions. Multicomponent systems and the competition for interaction with the stationary phase are research areas that have barely been scratched. The problems are difficult. The development of preparative chromatography and its applications are changing this situation. 

These three approaches have found widespread application to a large variety of systems and equilibria types ranging from vapor-liquid equilibria for binary and multicomponent polymer solutions, blends, and copolymers, liquid-liquid equilibria for polymer solutions and blends, solid-liquid-liquid equilibria, and solubility of gases in polymers, to mention only a few. In some cases, the results are purely predictive in others interaction parameters are required and the models are capable of correlating (describing) the experimental information. In Section 16.7, we attempt to summarize and comparatively discuss the performance of these three approaches. We attempt there, for reasons of completion, to discuss the performance of a few other (mostly) predictive models such as the group-contribution lattice fluid and the group-contribution Flory equations of state, which are not extensively discussed separately. 

It is more complicated to calculate LLE in multicomponent systems accurately than to describe vapor-liquid or solid-hquid equilibria. The reason is that in the case of LLE the activity coefficients have to describe not only the concentration dependence but also the temperature dependence correctly, whereas in the case of the other phase equilibria (VLE, SLE) the activity coefficients primarily have to describe the deviation from ideal behavior (Raoult s law resp. ideal solid solubility), and the temperature dependence is mainly described by the standard fugacities (vapor pressure resp. melting temperature and heat of fusion). 

Starting from either side of the phase diagram, the situation is very much like a liquid-vapor phase change One component will preferentially change phase, and the other component will become more and more concentrated within the remaining liquid. Until, that is, a certain composition labeled is reached Then the two components will freeze simultaneously, and the solid that forms will have the same composition as the liquid. This composition is called the eutectic composition. At this composition, this liquid acts as if it were a pure component, so the solid and liquid phases have the same composition when in equilibrium at the eutectic temperature Tg. This pure component is called the eutectic. The eutectic is similar to the azeotrope in liquid-vapor phase diagrams. Not all systems will have eutectics some systems may have more than one, and the composition of the eutectic(s) of a multicomponent system is characteristic of the components. That is, you cannot predict a eutectic for any given system. 

We take up the topic of multicomponent equilibria by drawing a distinction between systems in which several or all components are present in the two equilibrated phases, and those in which only one component plays a key role by distributing itself in significant amounts between the phases in question. Vapor-liquid equilibria of mixtures and other similar multicomponent systems involving the appearance of several solutes in each phase are the prime example of the former, while distributions of a single component occur in a number of different contexts, which we take up in turn below. They include the equilibrium of a single gas with a liquid solvent, or a solid (gas... 

For a multicomponent system Eqs. (1.2) and (1.3) can be primary extended by a term describing the composition influence of the participated components xa,b,c,...-The thermodynamic activity of any component (e. g. A) is expressed by the chemical potential gA = ftA + T-T In Xa i corresponds to solid or liquid or vapor. The chemical potential can be understood in terms of the Gibbs free energy per mole of substance, and it demonstrates the decreasing influence of a pure element or a compound in a diluted system. If any pure component is diluted then the term R- T In Xa will always take values lower than zero (note, that only an ideal solution behavior is considered by the mole fraction Xa- Eor real cases the so-called activity... 

Very few generalized computer-based techniques for calculating chemical equilibria in electrolyte systems have been reported. Crerar (47) describes a method for calculating multicomponent equilibria based on equilibrium constants and activity coefficients estimated from the Debye Huckel equation. It is not clear, however, if this technique has beep applied in general to the solubility of minerals and solids. A second generalized approach has been developed by OIL Systems, Inc. (48). It also operates on specified equilibrium constants and incorporates activity coefficient corrections for ions, non-electrolytes and water. This technique has been applied to a variety of electrolyte equilibrium problems including vapor-liquid equilibria and solubility of solids. 

The processes discussed in this chapter demonstrate the great variety of phase equilibrium that can arise beyond the basic vapor-liquid problems discussed in most of the previous chapters. Many other systems could be included The adsorption of gases onto solids (used in the removal of pollutants from air), the distribution of detergents in water/oil systems, the wetting of solid surface by a liquid, the formation of an electrochemical cell when two metals make contact are all examples of multiphase/multicomponent equilibrium. They all share one important common element their equilibrium state is determined by the requirement that the chemical potential of any species must be the same in any phase where the species can be found. These problems are beyond the scope of this book. The important point is this The mathematical development of equilibrium (Chapter 10) is extremely powerful and encompasses any system whose behavior is dominated by equilibrium. 

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