Pressure-composition vapor-liquid diagrams

The curves given in Figs. 2-1 and 2-2 are termed the normal type. However, there are several other common types of curves. In Fig. 2-3 temperature-composition diagrams for constant total pressure are given for four different types of binary mixtures, and in Fig. 2-4 the corresponding vapor-liquid diagrams are given for the four same mixtures. 

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. 

Figure 13.4. Some vapor-liquid composition diagrams at essentially atmospheric pressure. This is one of four such diagrams in the original reference (Kirschbaum, Destillier und Rektifiziertechnik, Springer, Berlin, 1969). Compositions are in weight fractions of the first-named.

Pressure has a marked effect on the azeotropic composition and vapor-liquid equilibrium diagrams of alcohol-ketone systems (J). This is due to the fact that the slopes of the vapor pressure curves of alcohols are appreciably greater than for ketones it results in an unusually larger change in the relative boiling points of the components of an alcohol-ketone system with change in pressure. 

Given in the literature are vapor pressure data for acetaldehyde and its aqueous solutions (1—3) vapor—liquid equilibria data for acetaldehyde—ethylene oxide [75-21-8] (1), acetaldehyde—methanol [67-56-1] (4), sulfur dioxide [7446-09-5]— acetaldehyde—water (5), acetaldehyde—water—methanol (6) the azeotropes of acetaldehyde—butane [106-97-8] and acetaldehyde—ethyl ether (7) solubility data for acetaldehyde—water—methane [74-82-8] (8), acetaldehyde—methane (9) densities and refractive indexes of acetaldehyde for temperatures 0—20°C (2) compressibility and viscosity at high pressure (10) thermodynamic data (11—13) pressure—enthalpy diagram for acetaldehyde (14) specific gravities of acetaldehyde—paraldehyde and acetaldehyde—acetaldol mixtures at 20/20°C vs composition (7) boiling point vs composition of acetaldehyde—water at 101.3 kPa (1 atm) and integral heat of solution of acetaldehyde in water at 11°C (7). 

The phase behavior of multicomponent hydrocarbon systems in the liquid-vapor region is very similar to that of binary systems. However, it is obvious that two-dimensional pressure-composition and temperature-composition diagrams no longer suffice to describe the behavior of multicomponent systems. For a multicomponent system with a given overall composition, the characteristics of the P-T and P-V diagrams are very similar to those of a two-component system. For systems involving crude oils which usually contain appreciable amounts of relatively r on-volatile constituents, the dew points may occur at such low pressures that they are practically unattainable. This fact will modify the behavior of these systems to some extent. 

Figure 14.18 is the phase diagram drawn at constant T corresponding to the constant-P diagram of Fig. 14.16. On it we identity the three-phase-equihbrium pressure as P, the tliree-phase-equihbrium vapor composition as and the compositions of the two liquid phases that contribute to the vapor/liquid/liquid equihbrium state as jc" and xf. The phase boimdaries separating the three liquid-phase regions are nearly vertical, because pressure has only a weak influence on liquid solubilities.

The mutual solubility of ozone and oxygen at —183° and —195.5° C. has been determined by measuring the magnetic susceptibility and vapor pressure (4) of solutions, and a critical solution temperature of —180° C is indicated. The vapor pressure-composition data, combined with vapor pressure data for liquid ozone (1), were used to interpret the phase diagram of the system ( ). Measurements of the density and viscosity of solutions and the surface tension of liquid ozone are reported. 

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. 

The separation process depends on the nature of the vapor-liquid equilibrium relationships of the system, which can be represented on a ternary diagram. Figure 10.3a shows a ternary diagram at some fixed system pressure. Components A and B are close boilers, and A forms an azeotrope with the entrainer E. The curves in the triangle represent liquid isotherms. A corresponding vapor isotherm (not shown) could be drawn to represent the vapor at equilibrium with each liquid curve with tie lines joining vapor and liquid compositions at equilibrium. The temperature of the isotherms reaches a minimum at point Z that corresponds to the composition of the azeotrope formed between A and E. 

The computer-aided procedure, unless automated by the program, requires running a series of liquid-liquid equilibrium calculations (the equivalent of vapor-hquid flash calculations) at constant temperature and pressure. The composition is varied around the equilibrium curve, and the transition points from one phase to two, or vice versa, are noted. As many points as needed are obtained this way to generate the entire equilibrium curve. Also, each time an equilibrium calculation is done in the two-phase region, the compositions of the two phases are recorded. Each pair of data points thus obtained defines a tie line. The data obtained at one temperature and pressure generate one triangular diagram. If so desired, the procedure is repeated at other temperatures and pressures to determine the effect of these variables. 

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... 

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. 

If the temperature is raised to Tj, the phase behavior shown in figure 3.7e occurs. This temperature is greater than the UCEP temperature, therefore two phases exist as the pressure is increased as long as the critical mixture curve is not intersected. The two branches of the vapor-liquid phase envelope approach each other in composition at an intermediate pressure and it appears that a mixture critical point may occur. But as the pressure is further increased, a mixture critical point is not observed and the two curves begin to diverge. To avoid confusion, the phase behavior shown in figure 3.7e is not included in the P-T-x diagram. 

Consider first the schematic P-T and P-x diagrams for the naphthalene-ethylene system. Figure 3.18b depicts the solubility behavior of naphthalene in supercritical ethylene at a temperature greater than the UCEP temperature. Solid-gas equilibria exist at low pressures until the three-phase SLV line is intersected. The equilibrium vapor, liquid, and solid phases are depicted as points on the horizontal tie line at pressure Pj. As the pressure is further increased a vapor-liquid envelope is observed for overall mixture concentrations less than Xl- A mixture critical point is observed for this vapor-liquid envelope, as described earlier. If the overall mixture composition is greater than Xl, then solid-gas equilibria are observed as the pressure is increased above Pj. 

Example 18.1. A mixture of 50 mole percent benzene and 50 mole percent toluene is subjected to flash distillation at a separator pressure of 1 atm. The vapor-liquid equilibrium curve and boiling-point diagram are shown in Figs. 18.2 and 18.3. Plot the following quantities, all as functions of f, the fractional vaporization (n) the temperature in the separator, b) the composition of the liquid leaving the separator, and (c) the composition of the vapor leaving the separator. 

---