Chapter 1
Fundamentals of VaporâLiquid 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 equilibriumâspecifically, vaporâliquid equilibrium (VLE) and in some cases vaporâliquidâliquid 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.
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 âlighterâ 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 âlower-boilingâ 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 âtemperature versus x and yâ 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. Be...