The leaving streams are usually not in equilibrium either but are much closer to being so than the entering streams are. The compositions of the phases leaving are different from the composition of the phases entering. Moreover, the compositions of the phase leaving an equilibrium stage depend on not only upon the equilibrium relationships of the system but also upon the compositions and relative quantities of the two phases entering the stage (Foust, et al., 1980). Generally, for a system of n components, n mass balances for components and total quantities are required to define the system. Solving equilibrium stage calculation can be done by numerical or by graphical method. .
In our discussion, the numerical method was discussed briefly, and we focused on the graphical method. According to Foust, et al. (1980) graphical method is more rapid in many problems than the numerical method. Graphical methods are subjected to the inherent inaccuracy of reading graphs. The most important graphical technique is determining the composition of the resultant mixture after the two entering streams are mixed. Graphical addition was introduced to us. The graphical addition rule shows that the composition of a mixture resulting from the addition of two mixtures lies on a straight line between the compositions of the original two mixtures. The inverse Lever arm rule will be used .
together with the graphical addition rule to solve the equilibrium stage calculation graphically. By substituting Equation 1 to equation 2, the equation that will result is .
L₀Xa₀ + V₂Ya₂ = (L₀ + V₂)Za .
L₀ ( Xa₀ - Za) = V₂ (Za - Ya₂).
L₀V₂ = (Za - Ya₂) (Xa₀ -Za) (Equation 7).
Same is true for component c, L₀V₂ = (Zc - Yc₂) (Xc₀ -Zc) (Equation 8).
Figure 2. A diagram showing the graphical addition rule.
These two equations relate the composition of the resultant mixture to the compositions and masses of the original two mixtures.
