Saturation envelope

Vapor—Liquid Systems. The vapor-liquid region of a pure substance is contained within the phase or saturation envelope on a P-V diagram (see Figure 2-80), A vapor, whether it exists alone or in a mixture of gases, is said to be saturated if its partial pressure (P.) equals its equilibrium vapor pressure (P, ) at the system temperature T. This temperature is called the saturation temperature or dew point T ... 

Figure 2-10 shows a more nearly complete pressure-volume diagram.2 The dashed line shows the locus of all bubble points and dew points. The area within the dashed line indicates conditions for which liquid and gas coexist. Often this area is called the saturation envelope. The bubble-point line and dew-point line coincide at the critical point. Notice that the isotherm at the critical temperature shows a point of horizontal inflection as it passes through the critical pressure. 

The definition of the critical point as applied to a pure substance does not apply to a two-component mixture. In a two-component mixture, liquid and gas can coexist at temperatures and pressures above the critical point, Notice that the saturation envelope exists at temperatures higher than the critical temperature and at pressures higher than the critical pressure. We see now that the definition of the critical point is simply the point at which the bubble-point line and the dew-point line join. A more rigorous definition of the critical point is that it is the point at which all properties of the liquid and the gas become identical. 

Figure 2-14 shows the vapor-pressure lines of the two components of a mixture superimposed on the phase diagram of the mixture. The saturation envelope for the mixture lies between the vapor pressure lines of the two components. The critical temperature of the mixture lies between the critical temperatures of the two pure components. However, the critical pressure of the mixture is above the critical pressures of both of the components. The critical pressure of a two-component mixture usually will be higher than the critical pressure of either of the components. 

Figure 2-15 shows phase data for eight mixtures of methane and ethane, along with the vapor-pressure lines for pure methane and pure ethane.3 Again, observe that the saturation envelope of each of the mixtures lies between the vapor pressure lines of the two pure substances and that the critical pressures of the mixtures lie well above the critical pressures of the pure components. The dashed line is the locus of critical points of mixtures of methane and ethane. 

The highest temperature on the saturation envelope is called the cricondentherm. The highest pressure on the saturation envelope is called the cricondenbar. These conditions are illustrated on Figure 2-17. 

Figure 2-20 gives the pres sure-volume diagram for a mixture of n-pentane and n-heptane, showing several isotherms and the saturation envelope.4 Notice that at lower temperatures the changes in slope of the isotherms at the dew points are almost nonexistent. Also notice that the critical point is not at the top of the saturation envelope as it was for pure substances. 

Figure 2-22 gives pressure-composition diagrams for mixtures of methane and ethane.3 There are four saturation envelopes corresponding to four different temperatures. 

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. 

First, plot 70 mole percent methane and 400 psia on the — 100°F saturation envelope on Figure 2-22. Second, draw the tie-line (see Fig. 2-23) and read the composition of the equilibrium liquid on the... 

The lower line of a saturation envelope is the bubble-point line, and the upper line is the dew-point line. Composition-temperature conditions which plot below the saturation envelope indicate that the mixture is entirely liquid. 

Figure 2-27 gives the saturation envelope for mixtures of methane, propane, and n-pentane at the same temperature as Figure 2-26 but at a higher pressure. The bubble-point and dew-point lines join at a critical point. The critical point gives the composition of the mixture, which has a critical pressure of 1500 psia and a critical temperature of 160°F. 

Figure 2—28 shows the various positions the saturation envelopes of mixtures of methane, propane, and n-pentane can take at 160°F as pressure is increased from atmospheric to 2350 psia. Reference to the binary mixtures shown in Figure 2-29 will assist in understanding the reasons for the changes in the shapes of the saturation envelopes as pressure is increased. The numbered dots on Figure 2-29 correspond to the numbered diagrams of Figure 2-28. 

At the vapor pressure of propane, 380 psia at this temperature, the bubble-point and dew-point lines of the saturation envelope converge at... 

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). 

Above this pressure, dot 6, all mixtures of methane and propane are single phase. Thus only the methane-n-pentane binaries have two-phase behavior, and only the methane-n-pentane side of the ternary diagram can show a bubble point and a dew point. The bubble-point and dewpoint lines of the saturation envelope do not intercept another side of the diagram, rather the two lines join at a critical point, i.e., the composition of the three-component mixture that has a critical pressure of 1500 psia at 160°F. 

Note the wide variety of critical pressures and critical temperatures and the different positions that the critical points take on the saturation envelopes. Also note the very large separation between the critical temperature and the cricondentherm in all instances and the separation between cricondenbar and critical pressure for the lighter hydrocarbon mixtures in Figures 2-35 and 2-36. 

The Kesler-Lee correlations for liquid and vapour phase heat capacities of petroleum fluids are used for estimating the respective enthalpies at temperatures of interest. The Lee-Kesler corresponding-states method is used for obtaining estimates of the heats of vaporization and for developing the saturation envelope enthalpies. This method uses the Curl and Pitzer approach and calculates various thermodynamic properties by representing the compressibility factor of any fluid in terms of a simple fluid and a reference fluid as follows ... 

In Figure 8.12 the outer envelope is the locus of saturated equimolar liquid states and saturated equimolar vapor states. However, note that Figure 8.12 is not a phase-equilibrium diagram in Figure 8.12 every point on the two-phase line represents an equimolar mixture, but phases in vapor-liquid equilibrium generally do not have the same composition. Consequently, Figure 8.12 contains no tie lines across the two-phase region. Outside the saturation envelope, the mixtures are stable one-phase fluids. Underneath that envelope, the mixtures may be metastable one-phase fluids or they may be unstable to one phase (that is, they may exist as two-phases). 

Between the spinodal and the saturation envelope, mixtures may exist as metastable one-phase systems or as stable two-phase systems. The spinodal cannot cross the saturation envelope, but the spinodal becomes tangent to the saturation envelope at the critical point. 

These conditions identify both vapor-liquid and liquid-liquid critical points. For vapor-liquid equilibria, they are satisfied when the spinodal coincides with the vapor-liquid saturation curve. However, that point need not occur either at the maximum in the saturation envelope or at the maximum in the spinodal see Figure 8.12. Along a spinodal the one-phase metastable system is balanced on the brink of an instability at a critical point that balance coincides with a two-phase situation and the resulting fluctuations cause critical opalescence, just as they do at pure-fluid critical points. 

Volumetric Properties From an Equation of State. In general, most equations of state give relatively good predictions of volumetric properties at high temperature and low pressure. However, near the saturation envelope and especially in the critical region, volumetric predictions based on equations of state are poor, particularly for the saturated liquid. Therefore, with the exception of vapor-liquid equilibrium calculations, where internally consistent liquid densities are needed to calculate the liquid fugaclty, empirical liquid density correlations are normally used in industrial design calculations. 

Using the Steam Tables, prepare a P-V diagram for water that includes at least two isotherms as well as the saturation envelope. 

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