Bubble point line

The experiment could be repeated at a number of different temperatures and initial pressures to determine the shape of the two-phase envelope defined by the bubble point line and the dew point line. These two lines meet at the critical point, where it is no longer possible to distinguish between a compressed gas and a liquid. 

It is important to remember the significance of the bubble point line, the dew point line, and the two phase region, within which gas and liquid exist in equilibrium. 

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. 

The bubble-point line is also the locus of compositions of the liquid when two phases are present. The dew-point line is tire locus of compositions of the gas when gas and liquid are in equilibrium. The line which ties the composition of the liquid with the composition of gas in equilibrium is known as an equilibrium tie-line. Tie-lines are always horizontal for two-component mixtures. 

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. 

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. 

When pressure is less than the critical pressures of both components, the bubble-point and dew-point lines join at the vapor pressures of the pure components at either side of the diagram. When the pressure exceeds the critical pressure of one of the components, the bubble-point line and the dew-point line join at a critical point. For instance, a mixture of 98 mole percent methane and 2 mole percent ethane has a critical temperature of minus 110°F at a critical pressure of 700 psia. 

Tie-lines giving the compositions of the liquid and gas in equilibrium are again horizontal. The bubble-point line gives the composition of the equilibrium liquid, and the dew-point line gives the composition of the equilibrium gas. The lengths of the tie-lines represent the quantities of gas and liquid at equilibrium in the same manner as for the pressure-composition diagram. 

Third, read composition of equilibrium liquid at point where tie-line through point 1 connects with bubble-point line. See point 3. composition of liquid 13 mole percent methane... 

The critical point of a specific mixture of methane and propane occurs at 1040 psia at this temperature, dot 5. The dew-point and bubble-point lines of the ternary intersect the methane-propane side of the diagram at the composition of this critical point. 

Replot three isobars of the data given in Figure 2-37 as temperature against composition in weight percent. Use 300 psia, 600 psia, and 900 psia. This is called a temperature composition diagram. Label the bubble-point lines and dewpoint lines. 

The phase diagram for a typical volatile oil, Figure 5-2, is somewhat different from the black-oil phase diagram. The temperature range covered by the phase envelope is somewhat smaller, but of more interest is the position of the critical point. The critical temperature is much lower than for a black oil and, in fact, is close to reservoir temperature. Also, the iso-vols are not evenly spaced but are shifted upwards toward the bubble-point line. 

The concentrations of both the liquid phase, xB, and the vapor phase, yB, are determined by the pressure. The line relating vapor pressure to liquid-phase concentration is called the bubble-point line, because when the pressure on the liquid is reduced to this value, bubbles appear. The lower line, which relates vapor pressure to the vapor-phase concentration, is called the dew-point line because when vapor is compressed to give this pressure, liquid droplets appear on surfaces. 

There will be an isotherm similar to ABCD for each temperature. The complete P-V diagram for the i-pentane, w-heptane S3retem containing 52.4 weight per cent w-heptane is shown in Figure 24. The critical point is the point where the bubble-point line and dew-point line meet. This is equivalent to the statement that the intensive properties of the coexisting liquid and vapor phases are identical at the critical point. Consequently, the liquid and tiie vapor are indistinguishable at the critical pressure and temperature, The critical... 

A, B, C, and D have been calculated in the preceding example. The point A at 22.75 psia represents the computed bubble-point pressure for a solution whose mole fraction of C4H10 is 0.50. Point B represents the composition of the vapor at the bubble point. Similarly, the points C and D represent the bubble point and composition of the vapor at the bubble point for a solution whose mole fraction of C4Hio>is 0.75. The points E and jP. represent the vapor pressure of pure butane and pure propane, respectively, at 0° F. The line FACE is tile bubble-point line and the line FBDE is the dew-point line. It is obvious that a pressure-composition diagram for any ideal binary system could be calculated in this manner and would serve to describe the phase behavior quantitatively. 

It is of interest to note that the bubble-point line for an ideal binary solution is a linear function of composition. Hiis follows from Raoult s Law since in this case the bubble-point pressure is given by... 

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. 

Figure 9.4 shows another phase diagram at constant pressure. The x-axis shows the vapor-liquid mole fraction of the binary mixture. The y-axis shows temperature. The dew point line shows the temperature at which a superheated vapor mixture will begin to condense when cooled for all compositions of the mixture. The bubble point line shows the temperature at which a subcooled mixture will first begin to... 

Diagrams for systems that follow Raoult s Law are relatively "nice" it can be shown that they will never have azeotropes, which would be indicated by intersection of the bubble and dew point lines. In addition, since only one parameter in the equation depends on the temperature (the vapor pressure) and the pressure dependence is explicit, the dew and bubble point lines are relatively easy to calculate. 

III TVvo phase (wet steam) region B Bubble point line... 

At = 96 bar, the points A, and A2 are the same point for this system, therefore, the bubble point line and dew point line do not show a wet vapor region)... 

The distillation process can be discussed with the aid of a A, w or h, x diagram. The distillate vapor enthalpies are based on the dew line, and the liquid mixture enthalpies are based on the bubble point line of the binary mixture, as shown in Fig. 2-11. The specific heat requirement q is therefore the distance CD in the h, x diagram shown in Fig. 2-12. This line constructed by using Eq. (2-19), and by extrapolating the line BA back to the intercept with y, giving point... 

Fig. 2-11. h, x-Diagram of a binary mixture including liquid phase and vapor phase (a). Construction of bubble point line and dew point line in the h, x-diagram using a boiling diagram (b). A, A2 and Bj, B2 state points of liquid phase and vapor phase in equilibrium. h Enthalpy... 

A State point of feed B State point of distillation residue C State point of saturated distillate vapor Line AE specific heat requirement for heating the mixture to the bubble point Line CD specific heat requirement q... 

Consider a binary liquid mixture with the concentration zq and the temperature Tq. If the mixture is heated up, the bubble point line is reached in point A, and the first bubble is formed. When the mixture is further heated up, a further increase of temperature is obtained and more vapor is formed. At point B, the mixture consists of a liquid with the composition xq and a vapor with the composition yg. At point C, all liquid has been vaporized. Using nj as the total number of moles, the mass balance yields for point B... 

For this purpose, the values obtained from the vapor pressure equations for both components are multiplied with a factor which is specific for each dataset If the Antoine equation is used, this can be achieved by simply changing the parameter A in Eq. 3.30. The solid line in Figure F.8 shows that the correct slope of the bubble point line can be represented. The water activity coefficient at infinite... 

The effect of polymer type and polymer level on the phase boundaries can be shown on a pressure-temperature diagram by keeping the carbon dioxide level and solvent type constant. For low to medium polymer levels, experiments show that the polymer type and polymer level have little effect on the L-LV boundary (bubble-point line) (16). This is illustrated in Figure 6 for four systems having 30% carbon dioxide and tetrahydrofiiran (THF) as the solvent. The following polymers and solvent/polymer ratios were used polybutadiene (PB) at 19/1, 9/1, 5.7/1 as well as with polymethyl methacrylate (PMMA) at 5.7/1. The L-LV boundaries for each system have the same slope and nearly overlap. 

---