Bubble point locus

A simple pressure-temperature projection of the pressure-temperature-composition diagram for a mixture is given in Figure 2. It is necessary to define the terms bubble point, dew point, maxcondentherm, and maxcondenbar. A bubble point is a state of liquid mixture at which, if the pressure is decreased slightly, a second phase, a vapour, appears. Similarly, a dew point is a state of a vapour at which, if the pressure is increased slightly, a liquid phase appears. The dew point locus and the bubble point locus are continuous curves meeting at the critical point. The maxcondentherm and maxcondenbar are the maximum temperature and maximum pressure respectively on the bubble point-dew point... 

The apparatus can be also used to establish the dew point-bubble point locus. The great advantage of Kay s apparatus over most types of apparatus for determining critical properties is that it is relatively simple to operate. However, it does have the disadvantage that the samples are not degassed. This could lead to errors of 0.01 to 0.06 MPa in the critical pressure and up to 1 K in the critical temperature. 

Figure 6 shows the experimental and predicted phase envelope and critical point for a four-component lean gas mixture. Although the agreement along the bubble point locus is good, the agreement... 

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 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. 

The substitution of v, = xu-Kvu in the numerator of Equation 4.3a suggests that this equation applies at the bubble point, or the quadruple point (Lw-H-V-Lhc) that marks the lowest pressure of a three-phase (Lw-H-Lhc) region (point C in Figure 4.2c). The P-T locus of the three-phase (Lw-H-Lhc) line is almost vertical, so Equation 4.3a is an approximation of both the lowest pressure and the highest temperature for the three phases in equilibrium. Katz noted that Scauzillo (1956) had measured systems that did not appear to conform to the above equation. Later measurements by Verma (1974) and Holder (1976) confirmed Katz s analysis for hydrate formation from crude oil reservoirs. 

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. 

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. 

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. 

The points Ci and are the critical points of pure methane and ethane, respectively. The line connecting these two points, which is the intersection of the bubble point and dew point surfaces, is the critical locus. This is the set of critical points for the various mixtures of methane and ethane. The black curve connecting points A and Ci is the vapor pressure curve of pure methane, and the violet curve connecting points B and C2 is the vapor pressure curve of pure ethane. 

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. 

As the pressure is further increased at this fixed overall composition, the amount of the liquid phase increases while the amount of the vapor phase shrinks until only a small bubble of vapor remains. If the pressure is still further increased, the bubble of vapor finally disappears, then a single liquid phase exists. The locus of points that separates the two-phase vapor-liquid region from the one-phase liquid region is called the bubble point curve. This vapor-liquid envelope can now be inserted into the three-dimensional P-T-x diagram in figure 3.2a. 

Figure 10.3-2 The bubble point, dew point, and critical locus for the ethane-propylene system.

Figure 2 Bubble-point dew-point locus of a mixture of constant composition. AA and BB are paths along which retrograde condensation and retrograde evaporation take place respectively, C, critical point, D, maxcondentherm-, andE, maxcondenbar...

The region in which vapor and liquid may coexist in a binary system is limited by the vapor pressure curves of the pure components and the critical line. In Figure 5.9 the vapor pressure curves of the pure compounds of the system ethane-heptane are shown together with the PT-curves of different fixed compositions of the liquid and the vapor phase. The intersections of the dew point and the bubble point curve for a given temperature and pressure mark the VLE for the chosen compositions in the liquid and the vapor phase. The critical points of a binary system can be found where a loop in Figure 5.9 is tangential to the envelope critical curve, also called critical locus. 

In Class B1 systems branch II of the critical locus spans the entire temperature range from the critical temperature of the heavy component (if this is accessible without decomposition) down to and below the critical temperature of the solvent, as in curves (a) and (b) in Figure 1.9. On raising the pressure at a constant temperature which is above the solvent critical temperature, complete miscibility between the liquid and supercritical fluid phases occurs at the pressure (the critical pressure) corresponding to this temperature on the locus curve. The dew- and bubble-point curves then merge giving a closed loop pressure/composition diagram. 

In P-T projections, the composition axis is collapsed into the pressure-temperature plane. The vapor pressure curve for component A is labeled LV(A) and that for component B is labeled LV(B). These curves terminate at the component critical points (L = V) designated as hollow circles. In Fig. 2, dew pressure and bubble pressure curves for an intermediate composition x intersect at a point on the (L = V) critical locus where the liquid and vapor phases become critically identical. Normally, dew and bubble pressure curves are not shown in projections. They are shown here so that the construction of the related P-x at fixed T, and T-x at fixed P, phase diagrams is clearly illustrated. Each critical point on the critical locus corresponds to a fixed composition. Points close to the critical point of component A are critical points for mixtures with high concentrations of A, whereas points closer to the critical point of... 

In Fig. 10.3-2 we have plotted, for various fixed compositions, the bubble and dew point pressures of this mixture as a function of temperature. The leftmost curve in this figure is the vapor pressure of pure ethane as a function of temperature, terminating in the critical point of ethane (for a pure component, the coexisting vapor and liquid are necessarily of the same composition, so the bubble and dew pressures are identical and equal to the vapor pressure). Similarly, the rightmost curve is the vapor pressure of pure propylene, terminating at the propylene critical point. The intermediate curves (loops) are the bubble and dew point curves relating temperature and pressure for various fixed compositions. Finally, there is aline in Fig. 10.3-2 connecting the critical points of the mixtures of various compositions this line is the critical locus of ethane-propylene mixtures. 

Hence, for each component the concentration of a vapour rising from the tray ( +l) equals the concentration of the liquid flowing from the tray n. This relation defines a distillation curve as the locus of the tray compositions at total reflux. A distillation curve map (DCM) can be generated easily by choosing a tray liquid composition , and stepping up and down by a series of bubble and dew points. 

Figure 6. Solution of bubble growth model for water superheated to 600 K at 2.89 MPa (on spinodal). Curve AB is the locus of liquid states just upstream of the bubble (evaporation wave). Curve A B is the locus of states for the liquid-vapor mixture within the bubble. CJ indicates the Chapman-Jouguet point. The inset shows the distinction between the maximum velocity point B and the satturation curve

The above discussion identifies predicted values of Smb as a measure of relative instability, and hence of fluidization quality, in bubbling systems. In the following section the significance of this relation to perturbation propagation in fluidized beds will be examined. For the moment it is sufficient to point out that predicted Smb values lower than about 0.1 correspond approximately to the Group D powders of the Geldart map the predicted B/D boundary, shown in Figure 10.1, represents the locus of dp, Pp) combinations which result in computed values of Smb of exactly 0.1. 

Between the bubble and dew point curves we have, of course, mixtures of liquid and vapor in equilibrium with each other. The dashed line in Figure 14.2, for example, represents the locus of such mixtures, where the liquid phase is 20% of the total. 

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