Solid-liquid-vapor binary system

Figu re I. I. The pressure-temperature projection of a typical binary solvent-solute system. See text for discussion. SLV, solid/liquid/vapor LCEP, lower critical end point UCEP, upper critical end point. 

In recent years, studies of the phase behavior of salt-water systems have primarily been carried out by Russian investigators (headed by Prof. Vladimir Valyashko) at the Kurnakov Institute in Moscow, particularly for fundamental understanding of the phase behavior of such systems. Valyashko [37,39,42,43], Ravich [38], Urosova and Valyashko [40], and Ravich et al. [41] have given a classification of the existence of two types of salts, depending on whether the critical behavior is observed in saturated solutions. Type 1 does not exhibit critical behavior in saturated solutions. The classic example of Type 1 is the NaCl-water system and has been studied by many authors [36,37,44-47]. The Type 2 systems exhibit critical behaviors in saturated solutions, and therefore have discontinuous solid-liquid-vapor equilibria. Table 1 shows the classification of binary mixtures of salt-water systems. 

For ascertaining the process conditions of RESS and PGSS, it is essential to have knowledge of the equilibrium solubility of the solute in dense gas (SCF phase) and vice versa, and also the P-T trace for the solid-liquid-vapor (S-L-V) phase transition of the drug substance. If all three phases coexist, there is only a single degree of freedom for a binary system, and a P-T trace of the S-L-V equilibrium is sufficient to determine the phase equilibrium compositions. 

Mukhopadhyay M, Dalvi SV. A new thermodynamic method for solid-liquid-vapor equilibrium in Ternary systems from binary data for antisolvent crystallization. Proceedings of the 6th International Symposium, France, April 2003. 

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 binary and multicomponent systems. Predictive methods are based mostly on ideal phase behavior and have limited accuracy near eutectics. A predictive technique based on extracting liquid-phase activity coefficients from vapor-liquid equilibria that is useful for estimating nonideal binary or multicomponent solid-liquid phase behavior has been reported by Muir (Pap. 71f, 73d ann. meet., AIChE, Chicago, 1980). 

The Class I binary diagram is the simplest case (see Fig. 6a). The P—T diagram consists of a vapor—pressure curve (solid line) for each pure component, ending at the pure component critical point. The loci of critical points for the binary mixtures (shown by the dashed curve) are continuous from the critical point of component one, Ca , to the critical point of component two,Cp . Additional binary mixtures that exhibit Class I behavior are C02 -hexane and C02 benzene. More complicated behavior exists for other classes, including the appearance of upper critical solution temperature (UCST) lines, two-phase (liquid—liquid) immiscibility lines, and even three-phase (liquid—liquid—gas) immiscibility lines. More complete discussions are available (1,4,22). Additional simple binary system examples for Class III include C02—hexadecane and C02 H20 Class IV, C02 nitrobenzene Class V, ethane— -propanol and Class VI, H20— -butanol. 

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. 

The hydrate and phenol clathrate equilibrium data of the water-carbon dioxide, phenol-carbon dioxide, and water-phenol-carbon dioxide systems are presented in Table 1 and depicted in Figure 2. In order to establish the validity of the experimental apparatus and procedure the hydrate dissociation pressures of carbon dioxide measured in this work were compared with the data available in the literature (Deaton and Frost [7], Adisasmito et al. [8]) and found that both were in good agreement. For the phenol-carbon dioxide clathrate equilibrium results, as seen in Figure 2, the dramatic increase of the dissociation pressures in the vicinity of 319.0 K was observed. It was also found in the previous study (Kang et al. [9]) that the experimental phenol-rich liquid-phenol clathrate-vapor (Lp-C-V) equilibrium line of the binary phenol-carbon dioxide system could be well extended to the phenol clathrate-solid phenol-vapor (C-Sp-V) equilibrium line (Nikitin and Kovalskaya [10]). It is thus interesting to note that a quadruple point at which four individual phases of phenol-rich liquid, phenol clathrate, solid... 

Two early studies of the phase equilibrium in the system hydrogen sulfide + carbon dioxide were Bierlein and Kay (1953) and Sobocinski and Kurata (1959). Bierlein and Kay (1953) measured vapor-liquid equilibrium (VLE) in the range of temperature from 0° to 100°C and pressures to 9 MPa, and they established the critical locus for the binary mixture. For this binary system, the critical locus is continuous between the two pure component critical points. Sobocinski and Kurata (1959) confirmed much of the work of Bierlein and Kay (1953) and extended it to temperatures as low as -95°C, the temperature at which solids are formed. Furthermore, liquid phase immiscibility was not observed in this system. Liquid H2S and C02 are completely miscible. 

Let us consider vapor-liquid (or vapor-solid) equilibria for binary mixtures. For the sake of simplicity it will be assumed that all gases are ideal. In addition to the vapors of each component of the condensed phase, the gas will be assumed to contain a completely insoluble constituent, the partial pressure p of which may be adjusted so that the total pressure of the system, p, assumes a prescribed value. Therefore, C = 3, P = 2, and, according to equation (51), F = 3. Let us study the dependence of the equilibrium vapor pressures of the two soluble species p and P2 on their respective mass fractions in the condensed phase X and X2 at constant temperature and at constant total pressure. Since it is thus agreed that T and p are fixed, only one remaining variable [say X ( = l — "2)] is at our disposal p, P2 and the total vapor pressure p = p + p2 will depend only on X. ... 

Solid lines represent the liquid-vapor phase equilibria of the two pure components that end in critical points marked by arrows. When a small amount of solvent is added to the pure pol3uner, the liquid-vapor coexistence shifts and so does the critical point. The loci of critical points for the binary system form a critical line that is shown by the dashed line with squares for = 1 and triangles for = 0.886. In the former case - phase behavior of t3q>e I -the critical line connects the critical points of the two pure components and the two coexisting phases gradually change from vapor and solvent-rich liquid... 

It is important to note that while SCWO is formally defined in terms of the critical point of pure water, addition of any other constituents to the water will alter the critical point, and the system may or may not be supercritical with respect to this mixture critical point. Rather than a single critical point, for a binary system a critical curve exists that in the simplest cases joins the critical point of pure water to the critical point of the second substance across the composition space. For ternary mixtures the critical curve becomes a critical surface, and so on. In general, mixtures of water with higher volatility substances such as noncondensable gases or liquid organics will remain supercritical, while mixtures of water with lower-volatility substances such as salts will become subcritical and liquid or solid phases will precipitate from the vapor/ gas phase. 

As described in Figure 4b the phase behavior of a type II binary system is depicted by the vapor pressure (L-V boundary) curves for the pure components, sublimation (S-V boundary) and melting (S-L boundary) curves for the solid component, and especially the S-L-V line on the P-T space. For an organic solid drug solute, the triple-point temperature is sufficiently higher than the critical temperature of the SCF solvent. The (L = V) critical locus has two branches and is intersected by two S-L-V lines at LfCEP and LCEP, respectively, in the presence of the solid phase. The S-L-V line indicates that the melting of the solid is lowered in the presence of the SCF solvent component as it is dissolved in the molten (liquid) phase. The S-L-V line... 

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. 

The essential features of vapor-liquid equilibrium (VLE) behavior are demonstrated by the simplest case isothermal VLE of a binary system at a temperature below the critical temperatures ofboth pure components. Forthis case ( subcritkaT VLE), each pure component has a well-defined vapor-liquid saturation pressure ff, and VLE Is possible for the foil range of liquid and vapor compositions xt and y,. Figure 1.5-1 ffiustrates several types of behavior shown by such systems. In each case, (he upper solid curve ( bubble curve ) represents states of saturated liquid (he lower solid curve ( dew curve ) represents states of saturated vtqtor. 

Temperature is thus the main variable parameter for the investigation of properties of interfaces in binary systems consisting of condensed phases. This makes such interfaces similar to those in liquid-vapor (or solid-vapor)... 

Binary systems are known that form solid solutions over the entire range of composition and which exhibit either a maximum or a minimum in the melting point. The Uquidus-solidus curves have an appearance similar to that of the liquid-vapor curves in systems which f orm azeotropes. The mixture having the composition at the maximum or minimum of the curve melts sharply and simulates a pure substance in this respect just as an azeotrope boils at a definite temperature and distills unchanged. Mixtures having a maximum in the melting-point curve are comparatively rare. 

Apart from these exceptions, the activity coefficient generally is a function of concentration, temperature, and pressrtre. Before discussing these correlations it is advisable to discuss the heat effects of solutions or binary systems, which corrsist of a vaporous and a condensed phase (liquid or solid). 

A few binary systems when cooled do not deposit one of the components in a totally pure slate. Instead, behavior resembles that of many vapor-liquid systems and the solid is a true solution. Figure 11.2-3 de ricis... 

Depending on the state of the phases a and p vapor-liquid equilibria (VLE), liquid-liquid equilibria (LLE), solid-liquid equilibria (SLE), and so on, can be distinguished. In the case of VLE the phase equilibrium behavior is shown in Figure 5.4 as a Pxy-diagram for the binary system ethanol-water at 70 C. For a given composition in the liquid phase the system pressure and the composition in... 

The two most important cases are shown in Fig. 14 [4-6,12]. In Fig. 14a, the three-phase line S2gl, where pure solid component 2 is in equilibrium with a saturated liquid and a coexisting vapor phase, is situated at pressures below the critical curve Ig of the binary system. A characteristic isothermal p x) diagram for 7tt2 > Ta > Tci is shown in Fig. 14c. For the system in Fig. 14b, however, the three-phase line is shifted to higher pressures and intersects the critical curve Ig twice at the critical endpoints CEa and CEb. Typical isothermal p x) sections for Ta = const. (Fig. 14c) and Tb = const. (Fig. 14d) are presented. The curve in Fig. 14d corresponds to the solubility of pure solid 2 in the supercritical solvent 1 (e.g., CO2) for Tcea < < Tceb-... 

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