Bubble-point temperature curve

Example 1.9 shows that, for certain systems, deviations from Raoult s law can cause a maximum or a minimum in the vapor pressure to exist at a certain temperature and composition. At constant pressure, the boiling point or bubble point temperature curve could have a maximum or a minimum. Liquid mixtures whose vapor pressure curve or surface exhibits a maximum or a minimum are said to form azeotropes. The composition at which the azeotrope occurs is the azeotropic composition. Binaries are likely to form azeotropes if they deviate from Raoult s law and if their boiling points are not too far apart (within about 8°C). Azeotropes caused by positive deviations from Raoult s law are minimum boiling, that is, the azeotrope boils at a... 

Note that this equation is not easily integrated, for two reasons. First, the activity coefficient is a function of the liquid-phase composition, which continually changes as additional liquid is vaporized. Second, differential distillations are usually done at constant pressure (in particular, open to the atmosphere), so that as the composition changes, the equilibrium temperature of the liquid changes (following the bubble point temperature curve), and the pure component vapor pressures are a function of temperature. 

Equilibrium curves. To establish the equilibrium curve for the key components, Hengstebeck (15) recommends that the relative volatilities of the key components be determined at tbe bottom product bubble-point temperature and at the overhead product dew-point temperature. If these top and bottom values differ by less than 10 percent, the equilibrium curve is drawn from Eq. (1.4), that is,... 

The condition at which the liquid just begins to form is called the dew point. The condition at which the vapor just begins to form is called the bubble point. A curve can be plotted showing the temperature and pressure at which a mixture just begins to liquefy. Such a curve is called a dew-point curve or dew-point locus. A similar curve can be constructed for the bubble point. The phase envelope is the combined loci of the bubble and dew points, which intersect at a critical point. The phase envelope maps out the regions where the various phases exist. 

A degrees-of-freedom analysis indicates that the variables subject to the designer s control are C -H 3 in number. The most common way to use 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 equU rium flash curve shown in Fig. 13-17. 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 v ue at V/F = 1.0 when the first droplet of liquid is about to form (saturated vapor) 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. 

In the systems that we have examined so far, the bubble point and the dew point of the mixture vary monotonically with the composition. This is the case for ideal systems. However, for very non-ideal systems, there may be a maximum or a minimum in the bubble and dew point curves. This is the case for azeotropic systems. An example of a system that exhibits a low-boiling azeotrope is a mixture of 77-heptane and ethanol, which is shown in Figure 3.5. For this type of system, both the bubble and dew point temperature curves have a local minimum at the same composition. At this composition, these two curves meet. This point is known as the azeotrope. At the azeotrope, the composition of the coexisting liquid and vapor phases are identical. In this case at the azeotrope, the boiling temperature... 

For a high boiling azeotropic system, the bubble and dew point temperature curves meet at a maximum in the Txy diagram. Mixtures of nitric acid and water form exhibit a high boiling azeotrope this system is shown in Fig. 3.6. 

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. 

Figures 6.7a and b and 6.8a and b plot the experimentally obtained bubble point pressure as a function of the liquid screen side temperature and bulk liquid temperature, respectively for the 200 x 1400 and 325 x 2300 screens. The room temperature bubble point prediction curve is also plotted in these figures. The 200 x 1400 room temperature pore diameter is taken from Table 3.2. The results from Jurns and McQuillen (2008) are plotted in Figures 6.7b and 6.8b for comparison to the current data.

FIGURE 8.17 Temperature-composition diagram for ethanol-water at 1 atm, using data points from [1]. The curves are simple smooth interpolations. The arrows show the graphical solution for the bubble point (temperature-specified) and vapor composition. 

With reference to Fig. 6.11, assume that this binary feed mixture enters the column as saturated vapor on the fourth plate. Ideally, the liquid on the plate above the feed inlet (point L5) has the same composition as the feed, but is at a lower temperature since the latter is at the bubble-point temperature rather than at the dew-point temperature. Within the column, vapor flows upward through the liquid layer on each plate, while the liquid flows across each plate and down to the next plate by means of a downcomer. The vapor transfers heat to the liquid on each plate as it bubbles through the liquid. This heat transfer results in the evaporation of a small amount of the more volatile component from the liquid layer and correspondingly in the condensation of a small amount of the less volatile component in the vapor. Thus, the vapor becomes richer in nitrogen as the vapor comes in contact with the liquid layer and the liquid layer becomes richer in oxygen as the liquid contacts the vapor and flows downward from plate to plate. This is illustrated in Fig. 6.12, which shows the ideal temperature-composition of the vapor and liquid above and below the feed entry. As the saturated liquid moves down the column, its composition moves to the left along the bubble-point curve (points L4, L3,... 

When the two components are mixed together (say in a mixture of 10% ethane, 90% n-heptane) the bubble point curve and the dew point curve no longer coincide, and a two-phase envelope appears. Within this two-phase region, a mixture of liquid and gas exist, with both components being present in each phase in proportions dictated by the exact temperature and pressure, i.e. the composition of the liquid and gas phases within the two-phase envelope are not constant. The mixture has its own critical point C g. 

With a further increase in the temperature the gas composition moves to the right until it reaches v = 1/2 at the phase boundary, at which point all the liquid is gone. (This is called the dew point because, when the gas is cooled, this is the first point at which drops of liquid appear.) An unportant feature of this behaviour is that the transition from liquid to gas occurs gradually over a nonzero range of temperature, unlike the situation shown for a one-component system in figure A2.5.1. Thus the two-phase region is bounded by a dew-point curve and a bubble-point curve. 

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 the three distinct 2D cross-sectional views (7.41a), (7.42), (7.43) of the P-T-x surface, we can now visualize the full 3D form of the surface as shown in Fig. 7.8. The surface is seen to resemble a curved envelope, clipped at each end to reveal the inside of the envelope through the hatched holes. Viewed toward the P—T plane, only the curved edge of the envelope is seen, as in (7.41a). However, viewed toward the P-xB plane or the T-xB plane, the inside of the envelope is seen as the hatch marks in (7.42) or (7.43), respectively. The upper P-T-x surface of the envelope is called the bubble-point surface, in reference to the first vapor bubbles that are seen as the liquid is heated to its boiling point. The P-T-xBap underside of the envelope is correspondingly called the dew-point surface, in reference to the first dewy droplets of liquid as the vapor is cooled to its condensation temperature. Although we normally see only the flat P-T, P-xB, or T-xb projections on the blackboard or book page, it is useful to keep in mind the full 3D form of the P-T-xB surface that underlies these 2D projections of the / = 3 system. 

Figure 7.8 Three-dimensional curved envelope of the binary fluid P-T-xB surface (left), showing the upper bubble-point (liquid) surface, the lower dew-point (vapor) surface, and the hatched inside of the envelope, together with the three 2D projections (right) that result from slicing the envelope through the plane of constant temperature (upper), pressure (middle), or composition (lower).

Since in the critical point the bubble point curve (l+g—tf) and the dew-point curve (l+g-+g) merge at temperatures between 7C and 7 , an isotherm will intersect the dew-point curve twice. If we lower the pressure on this isotherm we will pass the first dew-point and with decreasing pressure the amount of liquid will increase. Then the amount of liquid will reach a maximum and upon a further decrease of the pressure the amount of liquid will decrease until is becomes zero at the second dew-point. The phenomenon is called retrograde condensation and is of importance for natural gas pipe lines. In supercritical extraction use is made of the opposite effect. With increasing pressure a non-volatile liquid will dissolve in a dense supercritical gas phase at the first dew point. 

In Figure 2.2-7a the bubble-point curve shows a horizontal point of inflection at the critical point l2=h and in Figure 2.2-7d the binodal shows a horizontal point of inflection at the critical point lj-g. At temperatures lower than TLcep and temperatures higher than Tucep the P c-sections are the same as for type I systems. 

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. 

Figure 10 shows the relationship between yx and xx for different values of an calculated from Eq. (8). When two components have close boiling points, by implication they have similar vapor pressures, so that an is close to unity. Separation of mixtures by distillation becomes more difficult as an approaches unity. Figure 11 indicates some of the x, y diagrams that can be obtained for distillation systems. Also shown are corresponding temperature-composition diagrams. The saturated vapor or dewpoint curve is determined by finding the temperature at which liquid starts to condense from a vapor mixture. Similarly, the saturated liquid or bubble-point curve corresponds to the temperature at which a liquid mixture starts to boil. For ideal mixtures, the dewpoint and bubble-point curves can be calculated as follows. From Eq. (3), at the dew point, since... 

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. 

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