Temperature multicomponent phase equilibrium

Processes for supercritical extraction of oils have been described in numerous literature references, including Paulaitis et al. ( ), Ely and Baker (2), Gerard (3.), Stahl et al. (4K and Robey and Sunder (5). The literature lacks detailed phase equilibrium data on multicomponent essential oils with supercritical solvents in the proximity of the solvent critical temperature. 

There are several characteristics common to the describing equations of all types of multicomponent, vapor-liquid separation processes, both single- and multi-stage, that make it possible to exploit the inside-out concept in similar ways to solve them efficiently and reliably. The equations have as common members component and total mass balance, enthalpy balance, constitutive and phase equilibrium equations. In addition, all such processes require K-value or fugacity coefficient and vapor and liquid enthalpy models. In all cases the describing equations have similar forms, and depend on the primitive variables (temperature, pressure, phase rate and composition) in essentially the same ways. Before presenting the inside-out concept, it will be useful to identify two classes of conventional methods and discuss their main characteristics. 

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 Aspen Plus, solid components are identified as different types. Pure materials with measurable properties such as molecular weight, vapor pressure, and critical temperature and pressure are known as conventional solids and are present in the MIXED substream with other pure components. They can participate in any of the phase or reaction equilibria specified in any unit operation. If the solid phase participates only in reaction equilibrium but not in phase equilibrium (for example, when the solubility in the fluid phase is known to be very low), then it is called a conventional inert solid and is listed in a substream CISOLID. If a solid is not involved in either phase or reaction equilibrium, then it is a nonconventional solid and is assigned to substream NC. Nonconventional solids are defined by attributes rather than molecular properties and can be used for coal, cells, catalysts, bacteria, wood pulp, and other multicomponent solid materials. 

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. 

Thus, for phase equilibrium to exist in a closed, nonreacting multicomponent system at constant energy and volume, the pressure must be the same in both phases (so that mechanical equilibrium exists), the temperature must be the same in both phases (so that thermal equilibrium exists), and the partial molar Gibbs energy of each species must be the same in each phase fso that equilibrium with respect to species diffusion exists). ... 

A phase diagram is a map that indicates the areas of stability of the various phases as a function of external conditions (temperature and pressure). Pure materials, such as mercury, helium, water, and methyl alcohol are considered one-component systems and they have unary phase diagrams. The equilibrium phases in two-component systems are presented in binary phase diagrams. Because many important materials consist of three, four, and more components, many attempts have been made to deduce their multicomponent phase diagrams. However, the vast majority of systems with three or more components are very complex, and no overall maps of the phase relationships have been worked out. 

For multicomponent mixtures, graphical representations of properties, as presented in Chapter 3, cannot be used to determine equilibrium-stage requirements. Analytical computational procedures must be applied with thermodynamic properties represented preferably by algebraic equations. Because mixture properties depend on temperature, pressure, and phase composition(s), these equations tend to be complex. Nevertheless the equations presented in this chapter are widely used for computing phase equilibrium ratios (K-values and distribution coefficients), enthalpies, and densities of mixtures over wide ranges of conditions. These equations require various pure species constants. These are tabulated for 176 compounds in Appendix I. By necessity, the thermodynamic treatment presented here is condensed. The reader can refer to Perry and Chilton as well as to other indicated sources for fundamental classical thermodynamic background not included here. 

A first estimate of whether a multicomponent feed gives a two-phase equilibrium mixture when flashed at a given temperature and pressure can be made by inspecting the K-values. If all X-values are greater than one, the exit phase is superheated vapor above the dew point (the temperature and pressure at which the first drop of condensate forms). If all X-values are less than one, the single exit phase is a subcooled liquid below the bubble point (at which the first bubble of vapor forms). 

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. 

Before energy balances can be used in the analysis or design of multicomponent flow processes, we must have data or correlations for mixture enthalpies as functions of composition. Such correlations can be developed from models for volumetric equations of state or from models for g in the latter case, we would need a form for the temperature-dependence of the parameters in the g model. In this section we discuss how an equation of state can be used to compute an enthalpy-concentration diagram for a two-phase equilibrium situation such diagrams contribute to the analysis or design of distillation columns. 

In synthetic methods, a mixture of known composition is prepared and the phase equilibrium is observed subsequently in an equilibrium cell (the problem of analyzing fluid mixtures is replaced by the problem of synthesizing them). After known amounts of the components have been placed into an equilibrium cell, pressme and temperature are adjusted so that the mixture is homogeneous. Then temperature or pressure is varied until formation of a new phase is observed. This is the common way to observe cloud points in demixing polymer systems. No sampling is necessary. Therefore, the experimental equipment is often relatively simple and inexpensive. For multicomponent systems, experiments with synthetic methods yield less information than with analytical methods, because the tie lines carmot be determined without additional experiments. This is specially trae for polymer solutions where fractionation accompanies demixing. 

Phase equilibrium of a multicomponent mixture under the given pressure p and temperature T. The mixture is separated into a = 1,2,..., n phases. 

There are two major approaches for the synthesis of crystallization-based separation. In one approach, the phase equilibrium diagram is used for the identification of separation schemes (For example Cisternas and Rudd, 1993 Berry et al., 1997). While these procedures are easy to understand, they are relatively simple to implement only for simple cases. For more complex systems, such as multicomponent systems and multiple temperatures of operation, the procedure is difficult to implement because the graphical representation is complex and because there are many alternatives to study. The second strategy is based on simultaneous optimization using mathematical programming based on a network flow model between feasible thermodynamic states (Cisternas and Swaney, 1998 Cisternas, 1999 Cisternas et al. 2001 Cisternas et al. 2003). 

A study involving a multicomponent fibrous system can now be examined in terms of the above analysis. The tension required to maintain equilibrium between the crystalline and amorphous phases of cross-linked collagen has been deter-mined.(44) In these experiments the fiber is immersed either in a large excess of pure water or in an aqueous KCNS solution. The experiments were conducted over a wide temperature range. The equilibrium force at a given temperature was approximately independent of the total sample length and consequently the extent of the transformation. When the supernatant phase consists solely of pure water, the system is univariant and the aforementioned result is to be expected. However, the results obtained when the supernatant phase contains two components indicates that the single-liquid approximation is also valid in this particular case. 

A unique solution for the equilibrium concentrations of each ion is obtained by fixing the temperature and chloride concentration. The resulting atmospheric level of CO2 can also be calculated. An example of the numerical solution to this multicomponent equilibrium concentration calculation is shown in Table 21.10. The predicted major ion concentrations are close to the observed values. Nevertheless, this model is not widely accepted as realistic because little evidence has been found for the establishment of equilibria between seawater and the solid phases. In feet, concentration gradients in the bottom and pore waters suggest that equilibrium is not being attained (Figure 21.2). This model is also not able to predict chloride concentrations because the major sedimentary component (halite) is nowhere near saturation with respect to average seawater. 

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