tion of x-y diagrams (Fig. 1.1). When bubble points and dew points can be readily calculated for a mixture of components, the saturated liquid and saturated vapor curves can be plotted for the system as in Fig. 1.5. From these data, values of x and y can be obtained for a number of temperatures and used to construct the x-y diagram. Similarly, bubble-point calculations yield the equilibrium vapor compositions, giving the values of both x andy. These can also be derived from dew-point calculations in a similar manner.
1.2.5 Calculation of bubble points and dew points
The bubble point of a mixture is calculated from
The dew point of a mixture is calculated from
The calculation method is as follows (at constant pressure): 1. Guess a temperature.
3. Calculate the sum on the lefthand side of Eq. (1.15) for bubble-point calculation. If smaller than unity, increase temperature. If greater than unity, decrease temperature. Repeat steps 2 and 3 until converged.
Alternatively, obtain the lefthand side of Eq. (1.16) for dew-point calculation. If smaller than unity, decrease temperature. If greater than unity, increase temperature. Repeat steps 2 and 3 until converged.
Figures 1.1 and 1.5 are phase diagrams for "normal" systems. In such systems, as the concentration of the less-volatile component increases, so do the dew point and the bubble point.
If the components exhibit strong physical or chemical interaction, the phase diagrams may be different from those shown in Figs. 1.1 and 1.5, and more like those shown in Fig. 1.6. In such systems there is a critical composition (the point of intersection of the equilibrium curve with the 45" diagonal) for which the vapor and liquid compositions are identical. Once this vapor and liquid composition is reached, the components cannot be separated at the given pressure. Such mixtures are called azeotropes.
A minimum-boiling azeotrope boils at a temperature lower than either of the pure components. When distilling a system made up of these components, the top product is the azeotrope. The bottom product is the high-boiling-point component when the MVC is present at low concentrations. On the other hand, when the low-boiling-point component is present at high concentrations, the bottom product is the MVC.
A maximum-boiling azeotrope boils at a temperature higher than either of the pure components and therefore always leaves at the bottom of the column. The top product is the high-boiling-point component when the MVC is present at low concentrations. The top product is the MVC when it is present at high concentrations.
If liquid phase separation occurs, the boiling temperature of the mixture as well as the vapor phase composition remain constant until one of the liquid phases disappears. Under such conditions, a mixture of the two liquids will leave the top of the column while either of the components will leave at the bottom, depending on the composition.
1.3 Nomenclature 1.3.1 English letters c Number of components f Fugacity, psia
Va urn urn Boiling 4ieotiope
"■nerogeittnus Ajeonope k and y
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