Phase mixture critical line

Figure 9. Critical lines for a binary mixture of components with several critical points. Solid lines (A, B, C) indicate binary mixture critical lines dashed lines are phase existence curve of pure components Cn rn are the m critical point ( w > i) for the pure component (n = 1,2% m = 1 identifies the vapor-liquid critical point m > 1 corresponds to the fluid-fluid critical points.

The simplest class of binary phase diagram is class I as shown in Figure 1.2-3. The component with the lower critical temperature is designated as component 1. The solid lines in Figure 1.2-3(b) represent the pure component liquid-vapor coexistence curves which terminate at the pure component critical points (Cj and C2). The feature of importance in this phase diagram is that the mixture critical line (dashed line in Figure 1.2-3(b)) is continuous between the two critical points. The mixture critical line represents the locus of critical points for all mixtures of the two components. The area bounded by the solid and dashed lines represents the two-phase, liquid-vapor (LV) region. The mixture-critical... 

The presence of the LLV line in Figure 1.2-4 causes the upper mixture critical line to pass continuously from L = V to L = L in the vicinity of the UCEP. At a temperature T, between Ci and the UCEP, the p-x diagram has the characteristics shown in Figure 1.2-5. As pressure is increased frompi to p2, a single vapor phase splits into a two-phase LV region and eventually a three-phase LLV point is reached. The horizontal line at p2 is a tie line which connects the three coexisting phases at a fixed temperature and pressure. It is the p-T projection of the... 

At pressures higher than p2 there are two distinct two-phase regions in the form of closed domes. The stationary point on each closed dome represents the critical point of the two-phase mixture. The critical point of the LL envelope at the right (M2) represents a point on the mixture critical line which originates from C2. The other critical point (Mi) appears on the mixture critical line from Ci. 

Binary mixtures can exhibit so many different kinds of fiuid-phase behavior [23, 24] that we need a way to organize and classify them. The classification presented here is based on a scheme first suggested by Scott and van Kon)menbm g [25, 26]. In their original work Scott and van Konynenbmg used the van der Waals equation to identify different forms for mixture critical lines. Since that work, more complicated PvT equations of state have been used to identify additional shapes for critical lines however, many of those have not been observed experimentally. 

Class A. These binaries never exhibit LLE and therefore have no critical end points, although many form azeotropes. However, most mixtures in class A would exhibit LLE with UCEPs, except that solidification occurs at temperatures above that at which a liquid-liquid split would occur. Although the mixture critical line is continuous, the mixture critical T and P may not be bounded by the pure-component critical points. In a few class A mixtures phase splits occur at temperatures above the critical points of both pures. This could hardly be called liquid-liquid equilibrium instead, such an immisdbility is called gas-gas equilibrium (GGE). Three kinds of gas-gas equilibria have been identified that in class A is called GGE of the third kind. 

When the mixture critical line is discontinuous, it is divided into two branches by a three-phase VLLE line, as shown in Figure 9.22. The high temperature end of the VLLE line is a UCEP that connects one branch of the critical line to the critical point of the more volatile component. This branch of the critical line is usually short. Based on the behavior of the critical branch emanating from the critical point of the less volatile component, we divide these mixtures into two classes. 

Figure A2.5.11. Typical pressure-temperature phase diagrams for a two-component fluid system. The fiill curves are vapour pressure lines for the pure fluids, ending at critical points. The dotted curves are critical lines, while the dashed curves are tliree-phase lines. The dashed horizontal lines are not part of the phase diagram, but indicate constant-pressure paths for the T, x) diagrams in figure A2.5.12. All but the type VI diagrams are predicted by the van der Waals equation for binary mixtures. Adapted from figures in [3].

Glassification of Phase Boundaries for Binary Systems. Six classes of binary diagrams have been identified. These are shown schematically in Figure 6. Classifications are typically based on pressure—temperature (P T) projections of mixture critical curves and three-phase equiHbria lines (1,5,22,23). Experimental data are usually obtained by a simple synthetic method in which the pressure and temperature of a homogeneous solution of known concentration are manipulated to precipitate a visually observed phase. 

As mentioned earlier, the physical properties of a liquid mixture near a UCST have many similarities to those of a (liquid + gas) mixture at the critical point. For example, the coefficient of expansion and the compressibility of the mixture become infinite at the UCST. If one has a solution with a composition near that of the UCEP, at a temperature above the UCST, and cools it, critical opalescence occurs. This is followed, upon further cooling, by a cloudy mixture that does not settle into two phases because the densities of the two liquids are the same at the UCEP. Further cooling results in a density difference and separation into two phases occurs. Examples are known of systems in which the densities of the two phases change in such a way that at a temperature well below the UCST. the solutions connected by the tie-line again have the same density.bb When this occurs, one of the phases separates into a shapeless mass or blob that remains suspended in the second phase. The tie-lines connecting these phases have been called isopycnics (constant density). Isopycnics usually occur only at a specific temperature. Either heating or cooling the mixture results in density differences between the two equilibrium phases, and separation into layers occurs. 

Consider the enlarged nose section of a single PT loop shown in Fig. 12.5. The critical point is at C. The points of maximum pressure and maximum temperature are identified as MP and MT. The dashed curves of Fig. 12.5 indicate the fraction of the overall system that is liquid in a two-phase mixture of liquid and vapor. To the left of the critical point C a reduction in pressure along a line such as BD is accompanied by vaporization from the bubble point to the dew Point, as would be expected. However, if the original condition corresponds to Point F, a state of saturated vapor, liquefaction occurs upon reduction of the pressure and reaches a maximum at G, after which vaporization takes place until the dew point is reached at H. This phenomenon is called retrograde condensation. It is of considerable importance in the operation of certain deep natural-gas wells where the pressure and temperature in the underground forma-... 

Z. Vaporization of a mixture of two liquids critical line dew surface, ebullition surface.—It is the same when the two phases into which the liquid mixture is divided are a liquid phase (lower... 

The phase behavior that is exhibited by a critical or supercritical mixture of several components is usually not simple Street (jO reports six classes of phase behavior diagrams In the simplest classes of systems (classes 1 and 2), the critical lines are continuous between the critical points of pure components Study of reaction equilibrium at SCF conditions requires knowledge of critical properties of the reacting mixture at various levels of conversion Three different approaches to evaluate critical properties are available, viz, empirical correlations, rigorous thermodynamics criteria and the theory of conformal solutions (10) The thermodynamic method is more general and reliable because it is consistent with the calculation of other thermodynamic properties of the reacting mixture (11) ... 

P. Van Konynenburg and R. L. Scott (1980) Critical lines and phase-equilibria in binary vanderwaals mixtures. Philos. Trans. Soc. London Series A 298, pp. 495-540... 

Van Konynenburg, P.H. Scott, R.L. Critical lines and phase behavior in binary van der Waals mixtures. Phil. Trans. Roy. Soc. London Ser. 1980, A298 (1442), 495-540. 

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