Lever rule ternary system

This problem is concerned with the properties of the triangular diagram used for representing ternary systems. Use the lever rule and notice that if the residue were mixed with the distillate at any moment it would give a mixture represented by point A, Note also that the composition of the distillate is alwa3rs somewhere on XF because Z is not volatile. 

Assuming that the composition of the top vapor stream reaches the ternary azeotrope (with the minimum temperature of the whole system), the compositions of both the AO and the OR can be estimated. With the known fresh-feed flowrate and the lever rule, the flowrate of the OR and the makeup flowrate can be estimated by the inner and outer material balance envelopes, respectively. Second, from the tie-line information and the lever rule, the flowrate of the AO stream can also be estimated. Thirdly, by using the outer material balance envelop and the lever mle, the bottom flowrate can further be estimated. Finally by using the inner material balance envelop and the lever mle, the top vapor flowrate can be estimated. 

From Figure 8.14 one would immediately see that, because the fresh feed is more diluted, the material balance line drawn from the point of FF + D2 to the point of OR is very close to the point of ternary azeotrope. From the lever rule, the top vapor flowrate can be estimated to be much greater than the flowrate of the bottom IPA product, thus requiring a large recycle flowrate in the overall system (large OR and large AO as feed to the recovery column). 

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