Critical loci

Step 4. Trace the critical locus of the binary consisting of the light component and psuedo heavy component. When the averaged pseudo heavy component is between two real hydrocarbons, an interpolation of the two critical loci must be made. 

At each point on the critical locus Equations 40a and b are satisfied when the true values of the binary interaction parameters and the state variables, Tc, Pc and xc are used. As a result, following an implicit formulation, one may attempt to minimize the following residuals. 

At pressures above the vapor pressure of propane and less than the critical locus of mixtures of methane and n-pentane, for instance 500 psia, dot 4, the methane-propane and methane-n-pentane binaries exhibit two-phase behavior, and propane-n-pentane mixtures are all liquid. Thus the saturation envelope appears as in Figure 2-28 (4). 

Convergence pressures of binary hydrocarbon mixtures may be estimated from the critical locus curves given in Figure 2-16. A similar curve which includes multicomponent mixtures is presented in Figure... 

Finally, we recall that in high-temperature aqueous solutions of NaCl near the L-G critical line, crossover has also been observed. Again, it has been concluded [152] that the critical locus may be affected by a virtual tricritical point. 

The critical locus shown in Figure 14.9 is only one (probably the simplest) of the types of critical loci that have been observed. Scott and van Konynen-burg10 have used the van der Waals equation to predict the types of critical loci that may occur in hydrocarbon mixtures. As a result of these predictions they developed a scheme that classifies the critical locus into one of five different types known as types I to type V.1 A schematic representation of these five types of (fluid-I-fluid) phase equilibria is shown in Figure 14.10. In the figure, the solid lines represent the vapor pressure lines for the... 

From Figure 14.10, we see that the system represented by Figure 14.9 is of type I. Shown for this type of system are several possible projections of the critical locus that can occur. Mixtures represented by (1), in which the critical locus is convex upwards, are the most common, and occur when there are not large polarity differences between the molecules of the components, but moderately large differences between the critical temperatures. 

Mixtures approximating curve (2), in which the critical locus is almost linear, usually are formed when the components have similar critical properties and form very nearly ideal mixtures. A minimum in the critical locus, as in curve (3), occurs when positive deviations from Raoult s law occur that are fairly large, but do not result in a (liquid + liquid) phase separation. Some (polar + nonpolar) mixtures and (aromatic + aliphatic) mixtures show this type, of behavior. 

Mixtures whose critical locus is represented by (4) are extremely rare. For these mixtures the critical locus extends to temperatures above the critical temperatures of both components. The phase separation that occurs along this critical locus is sometimes referred to as (gas + gas) immiscibility, since two phases are present at a temperature above the critical temperatures of both components. 

Retrograde Condensation For near-ideal mixtures, the intersection of the (p, X2 or y ) isotherm with the critical locus occurs at the maximum in the (p, y2) equilibrium line. For example, an enlargement of the two-phase (p, xi or yi) section for (xi oryi)Ar + (x2 or j2)Kr at T— 177.38 K is shown in Figure 14.12. The point of intersection with the critical locus at point (c) gives rise to an... 

Figure 14.11 The critical locus for (xiQHp + x2C6F6), a system with a maximum boiling azeotrope. In (A), the circles represent the critical points (a and b) of pure components (1) and (2) the solid lines represent (vapor + liquid) equilibrium for the pure substances the dashed line is the critical locus, and the short-dashed line represents the azeotrope composition, which intersects the critical locus at point c. (B) shows the intersection of the (vapor + liquid) equilibrium lines with the critical locus.

Figure 14.12 The top of the (vapor + liquid) isotherm for ( iAr + Kr) at T = 177.38 K. Point (c) is the intersection with the critical locus. The curve marked g gives the composition of the vapor phase in equilibrium with the liquid curve marked 1. The tubes shown schematically to the right demonstrate the changes in phase when the fluid is compressed at a mole fraction given by (a), or at a mole fraction corresponding to (b) where retrograde condensation occurs. Reprinted with permission from M. L. McGlashan, Chemical Thermodynamics, Academic Press, London, 1979, p. 276.

Figure 14.14 shows the critical locus, along with some isothermal and isobaric (vapor + liquid) sections, for a type III system. Lines ab and cd are the vapor... 

There is no evidence that this critical locus ever turns around again, although it is usually terminated at some high pressure by the formation of a solid phase. 

Referring again to Figure 14.14, the isotherms at temperatures T3 and T4 are of the typical (gas + liquid) type, but at T2, a temperature below u, two critical points occur, one at f and the other at h. The one at f is a typical (liquid + liquid) critical point while the one at h is better characterized as a (gas + liquid) critical point. In most systems with type III behavior, the critical locus bh occurs over a narrow temperature range, and the double critical points occur only over this small range of temperature. 

The critical locus has two parts, with the portion that begins at point b (the critical point of the more volatile component) ending at the UCST (point u), and the portion that starts at point d (the critical point of the less volatile component) ending at the LCST (point 1). Although not shown in Figure 14.15, an isotherm at a temperature between T2 and T3 would show two critical points (similar to the one at T2 in Figure 14.14). One critical point would be on the critical locus line bu while the other would be on the critical locus line dl. 

We now extend the discussion of excess properties to examples that help us to better understand the nature of interactions in a variety of nonelectrolyte mixtures. We will give examples showing temperature and pressure effects, including an example of solutions near the critical locus of the mixture and into the supercritical fluid region. 

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. 

For mixtures of carbon dioxide and hydrogen sulfide, a binary critical locus extends from the critical point of COz and terminates at the critical point of H2S. This is the case for H2S and COz, but not for all binary mixtures. 

For binary mixtures of hydrogen sulfide and carbon dioxide, the critical locus extends uninterrupted from the critical point of C02 to that of H2S. The critical point of a binary mixture can be estimated from the next two figures. Figure 3.4 shows the critical temperature as a function of the composition, and figure 3.5 gives the critical pressure. 

Huron, M.-J., G.-N. Dufour, and J. Vidal. 1978. "Vapor-Liquid Equilibrium and Critical Locus Curve Calculations with the Soave Equation for Hydrocarbon Systems with Carbon Dioxide and Hydrogen Sulphide" Fluid Phase Equil., 1 247-265. 

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