Solid-fluid system, phase behavior

This chapter provides an introduction to supercritical fluid behavior. As a tutorial, qualitative fluid behavior is stressed rather than quantitative description. Solubilities in solid-fluid systems are interpreted with a simple fluid model. Enhancement factors are introduced to demonstrate the importance of repulsive forces. Intermolecular interactions in cosolvent systems are discussed. Liquid-fluid phase behavior and phase transitions in liquid-fluid and solid-fluid systems are briefly presented. Transport properties are briefly presented to stress their density dependence. 

Although modeling of supercritical phase behavior can sometimes be done using relatively simple thermodynamics, this is not the norm. Especially in the region of the critical point, extreme nonidealities occur and high compressibilities must be addressed. Several review papers and books discuss modeling of systems comprised of supercritical fluids and solid or liquid solutes (rl,r4—r7,r9,r49,r50). 

Chapter 14 describes the phase behavior of binary mixtures. It begins with a discussion of (vapor -l- liquid) phase equilibria, followed by a description of (liquid + liquid) phase equilibria. (Fluid + fluid) phase equilibria extends this description into the supercritical region, where the five fundamental types of (fluid + fluid) phase diagrams are described. Examples of (solid + liquid) phase diagrams are presented that demonstrate the wide variety of systems that are observed. Of interest is the combination of (liquid + liquid) and (solid 4- liquid) equilibria into a single phase diagram, where a quadruple point is described. 

As indicated in Figures 5 and 6, there is a nearly linear relationship between the log[AOT] solubility and the fluid density over several order of magnitude of AOT concentration. This type of behavior would be expected for the solubility of a non-aggregate forming, solid substance in a supercritical fluid (XL). The solubility and phase behavior of solid-supercritical fluid systems has been described by Schneider (2H) and others, and such behavior can be predicted from a simple Van der Waal s equation of state. Clearly, this approach is not appropriate for predicting surfactant solubilities in fluids, because it does not account for the formation of aggregates or their solubilization in a supercritical fluid phase. 

To begin this simulation, we first need to set up an EQBATCH model. The difference between a phase behavior model and a flow model of an alkaline-surfactant system is that the matrix does not exist in the phase behavior test tube thus, there is no ion exchange on the matrix in the phase behavior model. Therefore, in the phase behavior model, we define 6 elemenfs and 14 fluid species based on Example 10.4 and remove Ihe calion exchanges only on fhe malrix. In particular, we keep fhe solid species Ca(OH)2(s) and CaC03(s). Af leasl one advantage is that we can ensure that there should not be any solid precipitation in the model, or any precipitation should be consistent with the observation in the test tube. The rest of the procedures to set up the EQBATCH model are similar to those in Example 10.4. 

Figure 4 Binary solid-fluid phase behavior of (a) type I and (b) type II systems (13).

Besides the theoretical interest in the unusual phase behavior encountered in these systems, the principles involved can be applied in operations wherein the nonideality is intentionally created. The magnitude of solubility of a compound of low volatility in a gas above its critical temperature. .. is sufficient to consider the gas as an extracting medium, that is fluid-liquid or fluid-solid extraction analogous to liquid-liquid extraction and leaching. In this case the solute is removed and the solvent recovered by partial decompression. Thus compression of a gas over a mixture of compounds could selectively dissolve one compound, permitting it to be removed from the mixture. Partial decompression of the fluid elsewhere would drop out the dissolved compound, and the gas could be reused for further extraction. 

Although these simplified models of hydrogen-bonded systems give a far from complete picture of the solid-fluid phase behavior of water, this kind of approach to identifying the key features required in the molecular model is an instructive one. Indeed, the inability of the PMW to generate reentrant melting of the low-density solid at thermodynamically stable states is an important result. It shows us that more than just short-range directional forces are required for this to occur. 

Although most of the studies of this model have focused on the fluid phase in connection with the theory of electrolyte solutions, its solid-fluid phase behavior has been the subject of two recent computer simulation studies in addition to theoretical studies. Smit et al. [272] and Vega et al. [142] have made MC simulation studies to determine the solid-fluid and solid-solid equilibria in this model. Two solid phases are encountered. At low temperature the substitutionally ordered CsCl structure is stable due to the influence of the coulombic interactions under these conditions. At high temperatures where packing of equal-sized hard spheres determines the stability a substitutionally disordered fee structure is stable. There is a triple point where the fluid and two solid phases coexist in addition to a vapor-liquid-solid triple point. This behavior can be qualitatively described by using the cell theory for the solid phase and perturbation theory for the fluid phase [142]. Predictions from density functional theory [273] are less accurate for this system. 

While the melting point depressions for binary systems may not seem to be of great concern because most studies are performed near the solvent critical point, in ternary systems with two solids and one supercritical fluid the melting points may be lowered significantly. For example, the phase behavior of two solids in contact with a supercritical fluid is shown in Figure 9. The dotted lines represent the phase behavior in the pure systems and the binary systems discussed above. New phase boundaries in the ternary system are indicated by the solid lines. Note that the... 

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