Residue curve analysis is quite useful in studying ternary systems. A mixture with an initial composition xi(0) and x2(o> is placed in a container at some fixed pressure. A
vapor stream is continuously removed, and the composition of the remaining liquid in the vessel is plotted on the ternary diagram.
Figure 1.21 gives an example of how the compositions of the liquid Xj and the vapor y change with time during this operation. The specific numerical example is a ternary mixture of components A, B, and C, which have constant relative volatilies of aA = 4, aB = 2, and aC = 1. The initial composition of the liquid is xA = 0.5 and xB = 0.25. The initial amount of liquid is 100 mol, and vapor is withdrawn at a rate of 1 mol per unit of time. Note that component A is quickly depleted from the liquid because it is the lightest component. The liquid concentration of component B actually increases for a while and then drops. Figure 1.22 plots the xA and xB trajectories for different initial conditions. These are the "residue curves" for this system.
Residue curves can be easily generated by using Aspen Split. Click on Tools in the upper toolbar in the Aspen Plus window and select Aspen Split and Ternary Maps. This opens the window shown in Figure 1.23, on which the three components and pressure
are selected. The numerical example is the ternary mixture of n-butane, n-pentane, and n-hexane. Clicking on Ternary Plot opens the window given in Figure 1.24. To generate a residue curve, right-click the diagram and select Add and Curve. A crosshair appears that can be moved to any location on the diagram. Clicking inserts a residue curve that passes through the selected point, as shown in Figure 1.25a. Repeating this procedure produces multiple residue curves as shown in Figure 1.25b.
Note that all the residue curves start at the lightest component (C4) and move toward the heaviest component (C6). In this sense they are similar to the compositions in a distillation column. The light components go out the top, and the heavy components, go out the bottom. We will show below that this similarity proves to be useful for the analysis of distillation systems.
The generation of residue curves is described mathematically by a dynamic molar balance of the liquid in the vessel Mliq and two dynamic component balances for
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