Chapter 1

Fundamentals of Vapor–Liquid Equilibrium (VLE)

Distillation occupies a very important position in chemical engineering. Distillation and chemical reactors represent the backbone of what distinguishes chemical engineering from other engineering disciplines. Operations involving heat transfer and fluid mechanics are common to several disciplines. But distillation is uniquely under the purview of chemical engineers.

The basis of distillation is phase equilibrium—specifically, vapor–liquid equilibrium (VLE) and in some cases vapor–liquid–liquid equilibrium (VLLE). Distillation can only effect a separation among chemical components if the compositions of the vapor and liquid phases that are in phase equilibrium with each other are different. A reasonable understanding of VLE is essential for the analysis, design, and control of distillation columns.

The fundamentals of VLE are briefly reviewed in this chapter.

1.1 Vapor Pressure

Vapor pressure is a physical property of a pure chemical component. It is the pressure that a pure component exerts at a given temperature when there are both liquid and vapor phases present. Laboratory vapor pressure data, usually generated by chemists, are available for most of the chemical components of importance in industry.

Vapor pressure depends only on temperature. It does not depend on composition because it is a pure component property. This dependence is normally a strong one, with an exponential increase in vapor pressure with increasing temperature. Figure 1.1 gives two typical vapor pressure curves, one for benzene and one for toluene. The natural log of the vapor pressures of the two components is plotted against the reciprocal of the absolute temperature. As temperature increases, we move to the left in the figure, which means a higher vapor pressure. In this particular figure, the vapor pressure PS of each component is given in units of mmHg. The temperature is given in kelvin.

Figure 1.1 Vapor pressures of pure benzene and toluene.

Looking at a vertical constant-temperature line shows that benzene has a higher vapor pressure than toluene at a given temperature. Therefore, benzene is the “lighter” component from the standpoint of volatility (not density). Looking at a constant-pressure horizontal line shows that benzene boils at a lower temperature than toluene. Therefore, benzene is the “lower-boiling” component. Notice that the vapor pressure lines for benzene and toluene are fairly parallel. This means that the ratio of the vapor pressures does not change much with temperature (or pressure). As discussed in a later section, this means that the ease or difficulty of the benzene/toluene separation (the energy required to make a specified separation) does not change much with the operating pressure of the column. Other chemical components can have temperature dependences that are quite different.

If we have a vessel containing a mixture of these two components with liquid and vapor phases present, the vapor phase will contain a higher concentration of benzene than will the liquid phase. The reverse is true for the heavier, higher-boiling toluene. Therefore, benzene and toluene can be separated in a distillation column into an overhead distillate stream that is fairly pure benzene and a bottoms stream that is fairly pure toluene.

Equations can be fitted to the experimental vapor pressure data for each component using two, three, or more parameters. For example, the two-parameter version is

The Cj and Dj are constants for each pure chemical component. Their numerical values depend on the units used for vapor pressure (mmHg, kPa, psia, atm, etc.) and on the units used for temperature (K or °R).

1.2 Binary VLE Phase Diagrams

There are two types of VLE diagrams that are widely used to represent data for two-component (binary) systems. The first is a “temperature versus x and y” diagram (Txy). The x term represents the liquid composition, usually in terms of mole fraction. The y term represents the vapor composition. The second diagram is a plot of x versus y.

These types of diagrams are generated at a constant pressure. Because the pressure in a distillation column is relatively constant in most column (the exception is vacuum distillation in which the pressure at the top and bottom are significantly different in terms of absolute pressure level), a Txy diagram and an xy diagram are convenient for the analysis of binary distillation systems.

Figure 1.2 gives the Txy diagram for the benzene/toluene system at a pressure of 1 atm. The abscissa is the mole fraction of benzene. The ordinate is temperature. The lower curve is the “saturated liquid” line that gives the mole fraction of benzene in the liquid phase x. The upper curve is the “saturated vapor” line that gives the mole fraction of benzene in the vapor phase y. Drawing a horizontal line at some temperature and reading off the intersection of this line with the two curves give the compositions of the two phases. For example, at 370 K, the value of x is 0.375 mol fraction benzene, and the value of y is 0.586 mol fraction benzene. As expected, the vapor is richer in the lighter component.

Figure 1.2 Txy diagram for benzene and toluene at 1 atm.

At the leftmost point, we have pure toluene (0 mol fraction benzene), so the boiling point of toluene at 1 atm can be read from the diagram (384.7 K). At the rightmost point, we have pure benzene (1 mol fraction benzene), so the boiling point of benzene at 1 atm can be read from the diagram (353.0 K). The region between the curves is where there are two phases. The region above the saturated vapor curve is where there is only a single “superheated” vapor phase. The region below the saturated liquid curve is where there is only a single “subcooled” liquid phase.

The diagram is easily generated in Aspen Plus by going to Tools on the upper tool bar and selecting Analysis, Property, and Binary. The window shown in Figure 1.3 opens on which the type of diagram and the pressure are specified. Then click the Go button.

Figure 1.3 Specifying Txy diagram parameters.

The pressure in the Txy diagram given in Figure 1.2 is 1 atm. Results at several pressures can also be generated as illustrated in Figure 1.4. The higher the pressure, the higher the temperature.

Figure 1.4 Txy diagrams at two pressures.

The other type of diagram, an xy diagram, is generated in Aspen Plus by clicking the Plot Wizard button at the bottom of the Binary Analysis Results window that also opens when the Go button is clicked to generate the Txy diagram. As shown in Figure 1.5, this window also gives a table of detailed information. The window shown in Figure 1.6 opens, and xy picture is selected. Clicking the Next and Finish button generates the xy diagram shown in Figure 1.7. Figure 1.8 gives an xy diagram for the system propylene/propane. These components have boiling points that are quite close, which leads to a very difficult separation.

Figure 1.5 Using Plot Wizard to generate xy diagram.

Figure 1.6 Using Plot Wizard to generate xy diagram.

Figure 1.7 xy diagram for benzene/toluene.

Figure 1.8 xy diagram for propylene/propane.

These diagrams provide valuable insight about the VLE of binary systems. They can be used for quantitative analysis of distillation columns, as we will demonstrate in Chapter 2. Three-component ternary systems can also be represented graphically, as discussed in Section 1.6.

1.3 Physical Property Methods

The observant reader may have noticed in Figure 1.3 that the physical property method specified for the VLE calculations in the benzene/toluene example was “Chao–Seader.” This method works well for most hydrocarbon systems.

One of the most important issues involved in distillation calculations is the selection of an appropriate physical property method that will accurately describe the phase equilibrium of the chemical component system. The Aspen Plus library has a large number of alternative methods. Some of the most commonly used methods are Chao–Seader, van Laar, Wilson, Unifac, and NRTL.

In most design situations, there is some type of data that can be used to select the most appropriate physical property method. Often VLE data can be found in the literature. The multivolume DECHEMA data books1 provide an extensive source of data.

If operating data from a laboratory, pilot-plant, or plant column are available, it can be used to determine what physical property method fits the column data. There could be a problem in using column data because the tray efficiency is also not known, and the VLE parameters cannot be...