Vapor-liquid equilibria bubble-point curve

Since the boiling point properties of the components in the mixture being separated are so critical to the distillation process, the vapor-liquid equilibrium (VLE) relationship is of importance. Specifically, it is the VLE data for a mixture which establishes the required height of a column for a desired degree of separation. Constant pressure VLE data is derived from boiling point diagrams, from which a VLE curve can be constructed like the one illustrated in Figure 9 for a binary mixture. The VLE plot shown expresses the bubble-point and the dew-point of a binary mixture at constant pressure. The curve is called the equilibrium line, and it describes the compositions of the liquid and vapor in equilibrium at a constant pressure condition. 

The pressure-temperature plot of Figure 2.1 extends all the way to the critical temperature and pressure, which has not been shown. Above the critical temperature, water strictly exists as a gas. The term saturated is used to describe the vapor-liquid portion of the curve. Basically, it implies the same thing as saying that vapor and liquid are in equilibrium with each other. The gas is said to be saturated if it is ready to condense the first drop of liquid. Conversely, the liquid is saturated if it is just about to vaporize. For the gas, this condition is called the dew point for the liquid, it is the bubble point. 

When the liquid starts to boil at temperature 7 (point B), the first vapor formed has a composition yx and is therefore at its dew point, At thia point, the vapor is as rich in the light component as it will ever be. As temperature is further raised, more of the heavier component is boiled off. The quantity of vapor formed increases, but the mole fraction of the light component in both vapor and liquid drops. At temperature T2, the liquid composition is x2 and the vapor composition is y2. Some of the initial charge is now vapor and some is liquid. A further increase in temperature to Ta will vaporize the rest of the liquid. The vapor composition will now be xlt and the last drop of liquid vaporized has a composition x3, The liquid always travels along its bubble-point curve (BEH) while the vapor always travels along the dew-point curve iDFG), Therefore, in distillation, bubble-point liquid is always in equilibrium with dew-point vapor. 

This would correspond to the bubble-point calculation as performed for vapor-liquid equilibrium, the object being to determine the temperature at a given pressure, or vice versa, whereby the first drop of vapor ensues from the vaporization of the liquid phase. That is, it would correspond to a point or locus of points on the saturated liquid curve. 

A simple case of gas-liquid equilibrium is shown in Figure 4.10. The dashed lines on the planes of Xg = 0 and Xg = 1 are the vapor pressure curves of the components A and B. The curves end up at the critical points and Cg. Two-phase border loops are shown at T, and T2. The upper branch of a loop is the bubble-point curve, upon which are the states of imminent formation of gas bubbles. Above the bubble point, only liquid exists. The lower branch is the dew-point curve, or the states of imminent formation of a liquid dew. Below the dew point, only gas exists. Enclosed within the loop are the states at heterogeneous phase coexistence. A pair of coexisting phases at equilibrium are located at the end points of a horizontal line segment in the loop. To illustrate, one such segment in the loop T, is shown to have one end point 3 on the dew-point curve and the other end point/ on the bubble-point curve. A mixture at point g is at a heterogeneous coexistence state, and is made... 

At the lowest pressure in the figure, P = 0.133 bar, the vapor-liquid equilibrium curve intersects the liquid-liquid equilibrium curve. Consequently, at this pressure, depending on the temperature and composition, we may have only a liquid, two liquids, two liquids and a vapor, a vapor and a liquid, or only a vapor in equilibrium. The equilibrium state that does exist can be found by first determining whether the composition of the liquid is such that one or two liquid phases exist at the temperature chosen. Next, the bubble point temperature of the one or either of the two liquids present is determined (for example, from experimental data or from known vapor pressures and an activity coefficient model calculation). If the liquid-phase bubble point temperature is higher than the temperature of interest, then only a liquid or two liquids are present. If the bubble point temperature is lower, then depending on the composition, either a vapor, or. a vapor and a liquid are present. However, if the temperature of interest is equal to the bubble point temperature and the composition is in the range in which two liquids are present, then a vapor and two coexisting liquids will be in equilibrium. 

Equilibrium methods, as proposed originally by Silver [200] and extended by Bell and Ghaly [201] and others, all assume that there is local equilibrium between the vapor and the condensate throughout the condenser. Even though condensation is a nonequilibrium process, the gas temperature Tg is assumed to follow a vapor-liquid equilibrium curve at T, as the vapor mixture is cooled from the mixture dew point 7"dew to the mixture bubble temperature Tbub. These methods therefore require the generation of a cooling or condensation curve (not to be confused with the condensation curve described in Fig. 14.1), as shown in Fig. 14.25,... 

Figure 2.3-2 (a) Vapor-liquid equilibrium of the system C02-toluene at 311 K. Experimental bubble points (O) and dew points ( ) are shown as a function of the pertinent composition. The bubble and dew curves are calculated with the Peng-Robinson equation of state, (b) Percent volumetric expansion of the liquid phase in the system C02-toluene at 298 K as a function of pressure. The curve was calculated with the Peng-Robinson equation of state. 

This linear relationship between the total pressure, P, and the mole fraction, x, of the most volatile species is a characteristic of Raoult s law, as shown in Figure 7.18a for the benzene-toluene mixture at 90°C. Note that the bubble-point curve (P-x) is linear between the vapor pressures of the pure species (at x, = 0, 1), and the dew-point curve (P-yJ lies below it. When the (x, yi) points are graphed at different pressures, the familiar vapor-liquid equilibrium curve is obtained, as shown in Figure 7.18b. Using McCabe-Thiele analysis, it is shown readily that for any feed composition, there are no limitations to the values of the mole fractions of the distillate and bottoms products from a distillation tower. 

As explained in Section 1.4, the enthalpy of a mixture is a function of temperature, pressure, and composition. These parameters determine the phase, so that, in vapor-liquid equilibrium calculations, the enthalpy is also implicitly a function of the phase. For a binary mixture at constant pressure, the equilibrium vapor and liquid temperatures vary with composition as represented by the dew point and bubble point curves (Figure 2.2). The enthalpy at each point may be plotted as a function of the composition, resulting in a saturated vapor enthalpy curve and a saturated liquid enthalpy curve, as shown in Figure 5.10. The composition is plotted as the mole fraction of the lighter component. 

Also shown in Figure 2.1 is a critical point of the system, where the dew-point and bubble-point curves converge. This is known as the convergence pressure for the system. In the region above the critical temperature and pressure, the hydrocarbon mixture exists as a single phase in which the vapor and liquid phases are indistinguishable. Refer to Gas-Liquid and Liquid-Liquid Separation volume for a detailed discussion on phase equilibrium. 

A third fundamental type of laboratory distillation, which is the most tedious to perform of the three types of laboratory distillations, is equilibrium-flash distillation (EFV), for which no standard test exists. The sample is heated in such a manner that the total vapor produced remains in contact with the total remaining liquid until the desired temperature is reached at a set pressure. The volume percent vaporized at these conditions is recorded. To determine the complete flash curve, a series of runs at a fixed pressure is conducted over a range of temperature sufficient to cover the range of vaporization from 0 to 100 percent. As seen in Fig. 13-84, the component separation achieved by an EFV distillation is much less than by the ASTM or TBP distillation tests. The initial and final EFN- points are the bubble point and the dew point respectively of the sample. If desired, EFN- curves can be established at a series of pressures. 

From Table 13-5 it can be seen that the variables subject to the designer s control are C -H 3 in number. The most common way to utilize these is to specify the feed rate, composition, and pressure (C -H 1 variables) plus the drum temperature T2 and pressure P2. This operation will give one point on the equilibrium-flash curve shown in Fig. 13-26. This curve shows the relation at constant pressure between the fraction V/F of the feed flashed and the drum temperature. The temperature at V/F = 0.0 when the first bubble of vapor is about to form (saturated liquid) is the bubble-point temperature of the feed mixture, and the value at V/F = 1.0 when the first droplet of liquid is about to form (saturated liquid) is the dew-point temperature. 

Once you have a Txy diagram like that of Figure 6.4-1, bubble- and dew-point calculations become trivial. To determine a bubble-point temperature for a given liquid composition, go to the liquid curve on the Txy diagram for the system pressure and read the desired temperature from the ordinate scale. (If you are not sure why this works, go back and consider again how the curve was generated.) You can then move horizontally to the vapor curve to determine the composition of the vapor in equilibrium with the given liquid at that temperature. 

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