Critical pressure, mixture

Basic pure component constants required to characterize components or mixtures for calculation of other properties include the melting point, normal boiling point, critical temperature, critical pressure, critical volume, critical compressibihty factor, acentric factor, and several other characterization properties. This section details for each propeidy the method of calculation for an accurate technique of prediction for each category of compound, and it references other accurate techniques for which space is not available for inclusion. 

Liquid-Fluid Equilibria Nearly all binary liquid-fluid phase diagrams can be conveniently placed in one of six classes (Prausnitz, Licntenthaler, and de Azevedo, Molecular Thermodynamics of Fluid Phase Blquilibria, 3d ed., Prentice-Hall, Upper Saddle River, N.J., 1998). Two-phase regions are represented by an area and three-phase regions by a line. In class I, the two components are completely miscible, and a single critical mixture curve connects their criticsu points. Other classes may include intersections between three phase lines and critical curves. For a ternary wstem, the slopes of the tie lines (distribution coefficients) and the size of the two-phase region can vary significantly with pressure as well as temperature due to the compressibility of the solvent. 

Figure 3.65 Sound velocity in hydrogen mixture against wRd2, at atmospheric pressure. Critical quality Xc = 0.375. (From Clinch and Karplus, 1964. Reprinted with permission of NASA Science and Technical Information, Linthicum Heights, MD.)... 

Belles prediction of the limits of detonability takes the following course. He deals with the hydrogen-oxygen case. Initially, the chemical kinetic conditions for branched-chain explosion in this system are defined in terms of the temperature, pressure, and mixture composition. The standard shock wave equations are used to express, for a given mixture, the temperature and pressure of the shocked gas before reaction is established (condition 1 ). The shock Mach number (M) is determined from the detonation velocity. These results are then combined with the explosion condition in terms of M and the mixture composition in order to specify the critical shock strengths for explosion. The mixtures are then examined to determine whether they can support the shock strength necessary for explosion. Some cannot, and these define the limit. 

The critical loci of binary systems composed of normal paraffin hydrocarbons are shown in Figure 2-16.2 Obviously, the critical pressures of mixtures are considerably higher than the critical pressures of the components of the mixtures. In fact, a larger difference in molecular size of the components causes the mixtures to have very large critical pressures. 

When the temperature exceeds the critical temperature of one component, the saturation envelope does not go all the way across the diagram rather, the dew-point and bubble-point lines join at a critical point. For instance, when the critical temperature of a mixture of methane and ethane is minus 100°F, the critical pressure is 750 psia, and the composition of the critical mixture is 95 mole percent methane and 5 mole percent ethane. 

At atmospheric pressure, all mixtures of these components will be gas. See Figure 2-28(1). The temperature is well above the critical temperature of methane, and atmospheric pressure is well below the vapor pressures of propane and n-pentane at 160°F. 

As pressure is increased, the size of the two-phase region decreases, Figure 2-28(7), until the critical pressure of a methane-n-pentane mixture is reached, 2350 psia at this temperature, dot 8. At this pressure and at all higher pressures, all mixtures of methane, propane, and n-pentane are single-phase. 

A mixture of acetone (1) + butanone (2) + ethylacetate (3) with the composition x1 = x2 = 0.3 and x3 = 0.4 is at 20 atm. Data for the system such as vapor pressures, critical properties, and Wilson coefficients are given with a computer program in Walas (1985, p. 325). The bubblepoint temperature was found to be 468.7 K. Here only the properties at this temperature will be quoted to show deviations from ideality of a common system. The ideal and real K, differ substantially. 

If the components exhibit strong physical or chemical interaction, the phase diagrams may be different from those shown in Figs, 1,1 and 1,5, and more like those shown in Fig, 1.8. In such systems there is a critical composition (the point of intersection of the equilibrium curve with the 45 diagonal) for which the vapor and liquid compositions are identical, Once this vapor and liquid composition is reached, the components cannot be separated at the given pressure, Such mixtures are called azeotropes. 

The SRK EOS parameters of the pure components can be calculated in terms of their critical pressure and temperature [29]. The binary interaction parameter q can be found from phase equilibria data for the binary mixture. Because, such data are not available, the critical loci data for the systems CO2 (1) + methanol (2) and CO2 (1) + acetone (2) [30] were used to calculate qn (Reference [30]), provided the binary critical data in the form X2 — Pa — Ta, where X2 is the molar fraction of component 2 in the critical mixture. Per the critical pressure and Per the critical temperature of the mixture. The mixture parameter a (a ) in the SRK EOS was calculated for every X2 — P — Per point using the expression [29]... 

In order to maximize the value of the applied thermodynamics system throughout the enterprise, it must be accessible to all process engineers and chemists who require accurate thermophysical property calculations in their daily work. Web applications, which do not require installation of the calculation engine on the user s computer, facilitate ea.sy access to the system. Web applications can be designed to provide pure component data such as normal boiling point and critical properties. They can also provide access to the most frequently carried out calculations, such as phase equilibrium calculations, tabulation, and plotting of pure component properties as a function of temperature and pressure, and mixture property calculations. 

At the point C the two liquid layers become identical, and this is called the critical solution point or con-solute point. If the total applied pressure is varied, both the critical temperature and composition of the critical mixture alter and we obtain a critical solution line. As an example of this we give in table 16. If the dependence of the critical solution temperature on pressure for the system cyclohexane -f aniline. An increase of pressure raises the critical solution temperature, and the mutual solubility of the two substances is decreased. We saw earlier that the applied pressure had only a small effect on the thermodynamic properties of condensed phases, and we notice in this case that an increase of pressure of 250 atm. alters the critical temperature by only 1.6 °C. 

At the critical point the mole fraction of CO2 Xi is 0.888 (Figure 9). In Figure 9 the part of the curve with Xi < 0.888 is the bubble point curve, and a homogenous mixture above the bubble point can be regarded as a subcritical fluid. The part of the curve with X] > 0.888 is the dew point curve, and a homogeneous mixture above the dew point is a vapor or a supercritical mixture. The mixed solvent near critical region at fixed temperature is defined as the solvent of which the composition and pressure are close to the critical composition and critical pressure ofthe mixture. 

Type II (Solid-Fluid) System. In type II systems (when the solid and the SCF component are very dissimilar in molecular size, structure, and polarity), the S-L-V line is no longer continuous, and the critical (L = V) mixture curve also is not continuous. The branch of the three-phase S-L-V line starting with the triple point of the solid solute does not bend as much toward lower temperature with increasing pressure as it does in the case of type I system. This is because the SCF component is not very soluble in the heavy molten solute. The S-L-V line rises sharply with pressure and intersects the upper branch of the critical mixture (L = V) curve at the upper critical end point (LfCEP), and the lower temperature branch of the S-L-V line intersects the critical mixture curve at the lower critical end point (LCEP). Between the two branches of the S-L-V line there exists S-V equilibrium only (13). 

Equations (65) and (66) show that the process of creating supersaturation within the droplets is much slower than in homogeneous mixtures (i.e., at pressures above the critical mixture pressure). Increase of the solute concentration from Cco to 2cco is observed after 0.206tvap> which for t ap = 0.125 s... 

Figure 2 shows values of the critical temperature and critical concentration in nitrobenzene - -alkanes homologous series. Noteworthy is the power-type evolution of the critical concentration, described by the power exponent 1/2. The pressure dependence of the critical consolute temperature for these critical mixtures are shown in Fig. 3. Noteworthy is the change of the sign from dT(2 jdP < 0 to dT jdP > 0 when increasing the length of -alkane.

Constituents from a particular homologous series, such as the normal paraffins, usually deviate from type-I phase behavior only when the size difference between them exceeds a certain value. This is because the constituents are so close in molecular structure that they cannot distinguish whether they are surrounded by like or unlike species. It is important to remember that the critical curve depicted in figure 3.1a is only one possible representation of a continuous curve. It is also possible to have continuous critical mixture curves that exhibit pressure minimums rather than maximums with increasing temperature, that are essentially linear between the critical points of the components (Schneider, 1970), and that exhibit an azeotrope at some point along the curve. 

If an experiment is performed at an overall composition equal to x in figure 3.2d, the vapor-liquid envelope is first intersected along the dew point curve at low pressures. The vapor-liquid envelope is again intersected at its highest pressure, which corresponds to the mixture critical point at T2 and x. This mixture critical point is identified with the intersection of the dashed curve in figure 3.2b and the vertical isotherm at T2. At the critical mixture point, the dew point and bubble point curves coincide and all the properties of each of the phases become identical. Rowlinson and Swinton (1982) show that P-x loops must have rounded tops at the mixture critical point, i.e., (dPldx)T = 0. This means that if the dew point curve is being experimentally determined, a rapid increase in the solubility of the heavy component will be observed at pressures close to the mixture critical point. The maximum pressure of the P-x loop will depend on the difference in the molecular sizes and interaction energies of the two components. 

Figure 3.5d shows the construction of a P-x diagram at temperature Tj, an isotherm that intersects the vapor pressure curve of the less volatile component, the LLV line, and both branches of the critical mixture curve (see figure 3.5b). At low pressures, a single vapor phase exists until the dew point curve of the vapor-liquid envelope is intersected and a liquid phase is formed. Vapor-liquid equilibrium is observed as the pressure is increased further until the three-phase LLV line is intersected, indicated by the horizontal tie line shown in figure 3.5d. There now exists a single vapor phase and two liquid phases. 

At temperatures above T4 the isotherms only intersect the vapor pressure curve of the less volatile component and the critical mixture curve. The three-phase LLV line is no longer intersected, therefore the simple P-x loops described for type-I systems are now observed. One such simple P-x loop is shown in figure 3.5a at temperature T. ... 

Eventually the UCST curve will superpose onto the critical mixture curve to give rise to the critical mixture curve that is shown schematically in figure 3. Id. Once again there are two branches of the critical mixture curve. But the branch of the critical mixture curve that starts at the critical point of the less volatile component no longer intersects a region of LLV behavior, as it did for type-III phase behavior. The first P-x diagram is constructed at Tj, a temperature less than the critical temperature of the more volatile component. An isotherm at Tj intersects the vapor pressure curve of the less volatile component, the three-phase LLV line, and the vapor pressure curve of the more volatile component shown in figure 3.7b. 

If the temperature is raised to Tj, the phase behavior shown in figure 3.7e occurs. This temperature is greater than the UCEP temperature, therefore two phases exist as the pressure is increased as long as the critical mixture curve is not intersected. The two branches of the vapor-liquid phase envelope approach each other in composition at an intermediate pressure and it appears that a mixture critical point may occur. But as the pressure is further increased, a mixture critical point is not observed and the two curves begin to diverge. To avoid confusion, the phase behavior shown in figure 3.7e is not included in the P-T-x diagram. 

Figure 3.8 Critical mixture curves for water-normal hydrocarbon mixtures near the critical point of water (Yiling, Michelberger, and Franck, 1991). The solid line is the vapor pressure curve for pure water.

Figure 3.10 Examples of the various types of critical mixture curves that can occur for a type-IV system (Schneider, 1970). For clarity the vapor pressure curves for squalane, hexadecane, and the 2,5-hexanediol are not shown.

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