Dew point curves

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. 

If a mixture of benzene and toluene is heated in a vessel, closed in such a way that the pressure remains atmospheric and no material can escape and the mole fraction of the more volatile component in the liquid, that is benzene, is plotted as abscissa, and the temperature at which the mixture boils as ordinate, then the boiling curve is obtained as shown by ABCJ in Figure 11.5. The corresponding dew point curve ADEJ shows the temperature at which a vapour of composition y starts to condense. 

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. 

The area bounded by the bubble point and dew point curves on the phase diagram of a multicomponent mixture defines the conditions for gas and liquid to exist in equilibrium. This was discussed in Chapter 2. The quantities and compositions of the two phases vary at different points within the limits of this phase envelope. 

In conventional vapor phase molecular sieve operations, the operating temperature must be even higher and the operating pressure must be even lower than that required by the dew point curve for the high boiling constituents. These extra requirements are needed to prevent capillary condensation. Condensa-... 

Referring to Fig. 2.1, at any point on the dew point curve the summation of each component divided by its respective K value at that point is equal to 1.0. Putting this statement in a mathematical term,... 

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. 

Curve ABC in each figure represents the states of saturated-liquid mixtures it is called the bubble-point curve because it is the locus of bubble points in the temperature-composition diagram. Curve ADC represents the states of saturated vapor it is called the dewpoint curve because it is the locus of the dew points. The bubble- and dew-point curves converge at the two ends, which represent the saturation points of the two pure components. Thus in Fig. 3.6, point A corresponds to the boiling point of toluene at 133.3 kPa, and point C corresponds to the boiling point of benzene. Similarly, in Fig. 3.7, point A corresponds to the vapor pressure of toluene at 100°C, and point C corresponds to the vapor pressure of benzene. 

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. 

Figure 3.2 shows a phase envelope for an acid gas mixture. Note that the locus at lower pressure is the dew-point curve, whereas the one at higher pressure is the bubble-point curve. In fact, any point inside the phase envelope is a two-phase point. 

Sometimes the liquid-vapor volume distribution in the two-pbaae region is also indicated on P-T diagrams. This can be accomplished by a series of curves each of which represents a certain percentage by volume of liquid. Thus the dotted curves XC, YC, and ZC represent 25%, 50%, and 75% by volume of liquid, respectively. In the isothermal compression described above, the point K would represent 50% liquid and 50% vapor by volume. Obviously, the dew-point curve and the bubble-point curve represent 0% and 100% liquid, respectively. 

Figure 10. Phase Diagram for Explaining the Difference between Analytical and Industrial Furfural Processes D and D Dew Point Curves E and E Boiling Point Curves...

Draw a p-T chart for water. Label the following clearly vapor-pressure curve, dew-point curve, saturated region, superheated region, subcooled region, and triple point. Show where evaporation, condensation, and sublimation take place by arrows. 

Figure 3.23 represents a two-component system with a fixed overall composition. You might wonder what a diagram would look like if we were to try to show systems of several compositions on one page. This has been done in Fig. 3.24. Here we have a composite p-T diagram, which is somewhat awkward to visualize, but represents the bubble-point and dew-point curves for various mixtures of ethane and heptane. These curves in essence are intersections of surfeces in the composition coordinate sliced out of a three-dimensional system and are stacked one in front of the other, although in two dimensions it appears that they intersect one another. The vapor-pressure curves for the two pure components are at the extreme sides of the diagrams as single curves (as you might expect). Each of the loops represents the two-phase area for a system of a specific composition. An infinite number of these surfaces are possible, of course. The dashed line indicates the envelope of the critical points for each possible composition. Although this line appears to be two-dimensional in Fig. 3.24, it actually is a three-dimensional line of which only the projection is shown in the figure.

Figure 3.2 Generic pressure-temperature diagram for binary mixtures of methane and ethane (i) pure methane (black line), (ii) I5mol% ethane (red lines), (iii) 5()mol% ethane (green lines), (iv) 70mol% ethane (blue lines), and (v) pure ethane (violet line). The solid lines and filled symbols denote the bubble point curves (saturated liquid), and the dashed lines and open symbols denote the dew point curves (saturated vapor). Data taken from RT Ellington et al.. Pap. Symp. Thermophys. Prop. 1, 180 (1959).

In Fig. 3.3a, we present the Txy diagram for binary mixtures of cyclohexane and toluene at a pressure of 1 atm, which is below the critical pressure of both pure species. Point A denotes the boiling temperature of pure toluene, and point C is the boiling temperature of pure cyclohexane. Connecting these two points are two curves that form the two-phase envelope. The upper curve (with the open symbols) is the dew point curve, and the lower curve (with the filled symbols) is the bubble point line. 

Above the two-phase envelope, the system is a vapor, and below the envelope, the system is a liquid. Witliin the envelope, the system separates into a coexisting vapor and liquid phase. The composition of tlie phases is given by the dew point curve and the bubble point curve. For example at point E (mole fraction Za), the system splits into a vapor phase with a composition corresponding to point D (mole fraction / ) and a liquid phase with a composition corresponding to point B (mole fraction Xa The ratio of the total moles of the liquid phase to the total moles of the vapor phase is... 

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... 

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. 

Bubble points and dew points may be generated as described above for a given mixture over ranges of temperature and pressure. The locus of bubble points is the bubble point curve and the locus of dew points is the dew point curve. The two curves together define the phase envelope. In addition to the bubble point curve (total liquid saturated) and the dew point curve (total vapor saturated), other curves may be drawn representing constant vapor mole fraction. All these curves meet at one point, the critical point, where the vapor and liquid phases lose their distinctive characteristics and merge into a single, dense phase. 

In areas surrounding the phase envelope, the system exists as a single phase. Below the dew point curve and at higher temperatures, it is a superheated vapor, while areas above the bubble point curve and to the left of it represent a sub-cooled liquid. In areas above the phase envelope between the sub-cooled liquid and the superheated vapor, the mixture is a dense or supercritical fluid, with properties changing gradually from those typical of a liquid to those typical of a vapor. 

In this diagram, applicable mainly to binary systems, the temperature, pressure, and overall composition are the independent variables, with the pressure held constant. The diagram, shown schematically in Figure 2.2, consists of an upper curve representing dew points and a lower curve representing bubble points. The Z coordinate represents overall mole fraction of component 1, usually chosen as the more volatile component. A vertical line at Z = 0 corresponds to pure component 2, and point A represents its boiling point at the fixed system pressure. Similarly, pure component 1 is represented by a vertical line at Z = 1, and its boiling point by point B. Points above the dew point curve are in the vapor phase, and those below the bubble point curve are in the liquid phase, while the area between the two curves corresponds to the mixed phase. 

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