Bubble point curve

More than one phase border loop exists at one temperature for some mixtures of components of greater disparity. Figure 4.11 shows the isothermal gle of n-heptane + ethanol at 313° and 333°K. Two connected loops occur at each temperature. Both branches of the lower curves are dew-point states the upper curve, bubble-point states. The dew state and bubble state on the same branch of the saturation loop and at the same T and p are at phase equilibrium. To illustrate, two phases are at equilibrium at 313°K and 20 kPa and also at 333° and 50 kPa. All four pairs are shown with dashed line segments. 

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. 

The calculation for a point on the flash curve that is intermediate between the bubble point and the dew point is referred to as an isothermal-flash calculation because To is specified. Except for an ideal binary mixture, procedures for calculating an isothermal flash are iterative. A popular method is the following due to Rachford and Rice [I. Pet. Technol, 4(10), sec. 1, p. 19, and sec. 2, p. 3 (October 1952)]. The component mole balance (FZi = Vy, + LXi), phase-distribution relation (K = yJXi), and total mole balance (F = V + L) can be combined to give... 

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. 

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. 

Alternately, use the slope of the e versus T 1 curve between the bubble point and a second, lower pressure at e2, rp< to evaluate CO, or... 

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. 

Again, this seems to be a rather nice application for computer technology. Even a good-quality programmable calculator can store a number of vapor-pressure curves. At least for hydrocarbons, equations for these curves can be extracted from the API (American Petroleum Institute) data book. Also, a programmable calculator can perform bubble-point and dew-point calculations, with over 10 components, without difficulty. 

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. 

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. 

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,... 

Consider the enlarged nose section of a single PT loop shown in Fig. 12.5. The critical point is at C. The points of maximum pressure and maximum temperature are identified as MP and MT. The dashed curves of Fig. 12.5 indicate the fraction of the overall system that is liquid in a two-phase mixture of liquid and vapor. To the left of the critical point C a reduction in pressure along a line such as BD is accompanied by vaporization from the bubble point to the dew Point, as would be expected. However, if the original condition corresponds to Point F, a state of saturated vapor, liquefaction occurs upon reduction of the pressure and reaches a maximum at G, after which vaporization takes place until the dew point is reached at H. This phenomenon is called retrograde condensation. It is of considerable importance in the operation of certain deep natural-gas wells where the pressure and temperature in the underground forma-... 

Data for tetrahydrofuran/ carbon tetrachloride at 30°C are shown in 12.9a. Here, the Px or bubble-point curve on a Pxy diagram lies below the ltn... 

With reference to the txy diagram, we describe the course of a constant-pressure heating process leading from a state of subcooled liquid at point a to a state of superheated vapor at point d. The path shown on the figure is for a constant composition of 60 mole percent acetonitrile. The temperature of the liquid increases as the result of heating from point a to point b, where the first bubble of vapor appears. Thus point b is a bubble point, and the t - x, curve is the locus of bubble points. 

Px relation of Raoult s law, and the system therefore exhibits negative deviations. When the deviations become sufficiently large relative to the difference between the two pure-species vapor pressures, the Px curve exhibits a minimum, as illustrated in Fig. 12.96 for the chloroform/tetrahydrofuran system at 30°C. This figure shows that the Py curve also has a minimum at the same point. Thus at this point where x - y the dew-point and bubble-point curves are tangent to the same horizontal line. A boiling liquid of this composition produces a vapor of exactly the same composition, and the liquid therefore does not change in composition as it evaporates. No separation of such a constant-boiling solution is possible by distillation. The term azeotrope is used to describe this state. 

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. 

Figures 3.6 and 3.7 have shapes that are characteristic for ideal systems. Certain nonideal systems deviate so much from these as to form maxima or minima at an intermediate composition rather than at one end or the other of the diagram. Thus the dew-point and bubble-point curves meet at this intermediate composition as well as at the ends. Such a composition is called an azeotropic composition. ...

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