Critical temperature, vapor-liquid equilibrium

The (vapor + liquid) equilibrium line for a substance ends abruptly at a point called the critical point. The critical point is a unique feature of (vapor + liquid) equilibrium where a number of interesting phenomena occur, and it deserves a detailed description. The temperature, pressure, and volume at this point are referred to as the critical temperature, Tc. critical pressure, pc, and critical volume, Vc, respectively. For COi, the critical point is point a in Figure 8.1. As we will see shortly, properties of the critical state make it difficult to study experimentally. 

The critical point is unique for (vapor + liquid) equilibrium. That is, no equivalent point has been found for (vapor + solid) or (liquid + solid) equilibria. There is no reason to suspect that any amount of pressure would eventually cause a solid and liquid (or a solid and gas) to have the same //m, Sm, and t/m. with an infinite o and at that point. mC02 was chosen for Figure 8.1 because of the very high vapor pressure at the (vapor + liquid + solid) triple point. In fact, it probably has the highest triple point pressure of any known substance. As a result, one can show on an undistorted graph both the triple point and the critical point. For most substances, the triple point is at so low a pressure that it becomes buried in the temperature axis on a graph with a pressure axis scaled to include the critical point. 

The phase equilibrium for pure components is illustrated in Figure 4.1. At low temperatures, the component forms a solid phase. At high temperatures and low pressures, the component forms a vapor phase. At high pressures and high temperatures, the component forms a liquid phase. The phase equilibrium boundaries between each of the phases are illustrated in Figure 4.1. The point where the three phase equilibrium boundaries meet is the triple point, where solid, liquid and vapor coexist. The phase equilibrium boundary between liquid and vapor terminates at the critical point. Above the critical temperature, no liquid forms, no matter how high the pressure. The phase equilibrium boundary between liquid and vapor connects the triple point and the... 

Finally, note that the LE/G equilibrium region disappears above a certain temperature that is the two-dimensional equivalent of the critical temperature for liquid-vapor equilibrium (see Fig. 7.8). 

Figure 14.9 is a three-dimensional graph that shows the extension of (vapor + liquid) equilibrium isotherms or isobars to the critical region. Line ab at X2 = 0 is the vapor pressure line for pure component 1, with point b as the critical point. In a like manner, line cd at x2 = 1 is the vapor pressure line for pure component 2, with point d as the critical point. Note that at temperatures and pressures below points b and d, the isotherms and isobars (shown as the shaded areas) intersect the vapor pressure curves.k However,... 

Figure 14.10 The five types of (fluid + fluid) phase diagrams according to the Scott and van Konynenburg classification. The circles represent the critical points of pure components, while the triangles represent an upper critical solution temperature (u) or a lower critical solution temperature (1). The solid lines represent the (vapor + liquid) equilibrium lines for the pure substances. The dashed lines represent different types of critical loci. (l) [Ar + CH4], (2) [C02 + N20], (3) [C3H8 + H2S],...

Heterogeneous catalysis is preferred over homogeneous catalysis. A critical issue is the catalyst design, which should ensure compatibility between the reaction and the separation. The temperature profile dominated by the vapor-liquid equilibrium, as well as the residence-time distribution controlled by the hydrodynamics of internals must comply with the achievable reaction rate and with the desired selectivity pattern. 

In order to correlate the results obtained, a modified SRK equation of state with Huron-Vidal mixing rules was used. Details about the model are reported in the paper by Soave et al. [16]. This approach is particularly adequated when experimental values of the critical temperature and pressure are not available as it was the case for limonene and linalool. Note that the flexibility of the thermodynamic model to reproduce high-pressure vapor-liquid equilibrium data is ensured by the use of the Huron-Vidal mixing rules and a NRTL activity coefficient model at infinite pressures. Calculation results are reported as continuous curves in figure 2 for the C02-linalool system and in figure 3 for C02-limonene. Note that the same parameters values were used to correlated the data of C02-limonene at 45, 50 e 60 °C. 

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. 

Bian, B., Y. Wang, J. Shi, E. Zhao, and B.C.-Y. Lu. 1993. "Simultaneous Determination of Vapor-Liquid Equilibrium and Molar Volumes for Coexisting Phases up to the Critical Temperature with a Static Method", Fluid Phase Equil., 90 177-187. 

The vapor-liquid equilibrium curve terminates at the critical temperature and critical pressure (7c nnd Pc). Above and to the right of the critical point, two separate phases never coexist. 

The vapor pressure curve forms the basis for the description of vapor-liquid equilibrium for a pure fluid. As the temperature increases, the vapor pressure curve for the vapor-liquid situation ends at the critical pressure. In the case of a binary or multicomponent solution, the critical point is not necessarily a maximum with respect to either temperature or pressure. It is then possible for a vapor or liquid to exist at temperature or pressures higher than the critical pressure of the mixture. At constant temperature, it is then possible for condensation to take place as the pressure is decreased. At constant pressure, condensation may take place as the temperature is increased. Vaporization can take place at constant temperature as the pressure is increased and decreased. This unusual behavior can be useful in some process situations, for example, in the recovery of natural gas from deep wells. If the conditions are right, liquefaction of the product stream is possible. At the same time, the heavier components of the mixture may be separated from the lighter components. 

This presents difficulties when we want to examine the solubility of gases, such as oxygen which has a critical temperature of Tc = 154.59 K and nitrogen which has a critical temperature of Tc = 126.21 K, in liquids. The critical temperature of these gases are well below ambient temperatures. For these systems, another approach is required to determine the conditions for vapor-liquid equilibrium. 

As we described in Section III.G, perturbation theories can be extended in a systematic way using cluster expansion techniques. These techniques have recently been applied to the calculation of the thermodynamic properties and vapor-liquid equilibrium of 12-6 diatomics and seem to offer a clear improvement over the first-order perturbation theories. To illustrate this point. Table I shows values of the critical density and critical temperature predicted by the ISF-ORPA theory and the first-order perturbation theory together with results recently obtained from molecular dynamics... 

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. 

The phase behavior for the polymer-solvent systems can be described using two classes of binary P-T diagrams, which originate from P—T diagrams for small molecule systems. Figure 3.24A shows the schematic P-T diagram for a type-III system where the vapor-liquid equilibrium curves for two pure components end in their respective critical points, Ci and C2. The steep dashed line in figure 3.24A at the lower temperatures is the P-T trace of the UCST... 

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. 

Using the data in Illustration 6.4-1, and the same reference state, compute the vapor pressure of oxygen over the temperature range of —200°C to the critical temperature, and also compute the specific volume, enthalpy, and entropy along the vapor-liquid equilibrium phase envelope. Add these results to Figs. 6.4-3, 6.4-4, and 6.4-5. 

Figure 103-8 Vapor-liquid equilibrium for pure ethane, pure u-heptane (solid lines), and a mixture of fixed composition of 58.71 mol % ethane (dashed curve) as a function of temperature and pressure., [Data of V B. Kay, Ind. Eng. Chem., 30, 459 (1938).] The symbols denote critical points. is the cricondenbar, and O is the cricondentherm.

In the study of the solubility of a gas in a liquid one is interested in the equilibrium when the mixture temperature T is greater than the critical temperature of at least one of the components in the mixture, the gas. If the mixture can be described by an equation of state, no special difficulties are involved, and the calculations proceed as described in Sec. 10.3. Indeed, a number of cases encountered in Sec. 10.3 were of this type (e.g., ethane in the ethane-propylene mixture at 344.3 K). Consequently, it is not necessary to consider the equation-of-state description of gas solubility, as it is another type of equation-of-state vapor-liquid equilibrium calculation, and the methods described in Sec. 10.3 can be used. 

The situation of interest here is when the mixture temperature T is greater than the critical temperature of one of the components, say component 1 (i.e., T > Tc, ), so that this species exists only as a gas in the pure component state. In this case the evaluation of the liquid-phase properties for this species, subh as / " T, P) and yi T, P, x), is not straightforward. (It is this complication that distinguishes gas solubility problems firom those of vapor-liquid equilibrium, which were considered in Chapter 10.) We will refer to species that are in the liquid phase above their critical temperatures as the solutes. For those species below their critical ternperamres. which we designate as the solvents, Eq. 11.1-2 is used just as in Sec. 10.2. 

Modern chemical processing demands much better estimates of physical properties than in previous eras because the costs of excessive design are now often too great. High-pressure systems are of particular concern, and they are becoming more prevalent as in coal gasification and liquefaction and in Fischer-Tropsch syntheses. A weak link in estimation techniques for these systems is the vapor—liquid equilibrium distribution of components at temperatures well above the critical temperature of one or more of the species present and below the critical temperature of the others. 

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