Ternary azeotropes finding

Suppose we have a mixture of water, pyridine, and toluene. We set the pressure to 1 atm and attempt to solve the above equations. Lacking any further insight, we set all the vapor and liquid compositions equal to 0.33333 and then attempt a solution using a Newton-based method. The problem with finding azeotropes becomes immediately evident. There are six solutions to these equations the three binary azeotropes and the three pure species. There is no ternary azeotrope. To find all azeotropes for a mixture, we must find all solutions to the above equations. Finding multiple solutions to a set of highly nonlinear equations like these is usually a very difficult task. 

Figure 43 shows these azeotropes as well as a ternary one we now wish to find. Starting at the ethanol/water binary azeotrope, the infinite-dilution f-value for toluene is 2.78. Allowing for two liquid phases, the above algorithm locates the ternary azeotrope without difficulty. If we do not allow for two liquid phases, computations indicate there is no ternary azeotrope. 

Assuming perfect distillation, with pure ethanol in the bottoms product and only the ternary azeotrope in the distillate, find the entrainer to feed flow rate ratio if the ethanol solution feed stream contains 90 mole% ethanol and 10 mole% water. 

Repeat the second step above to find the remaining binary azeotropes. If more than a single binary, ternary, or higher-order azeotrope is suspected, march away from each of lower-order azeotropes toward it, as is done in the third and fourth steps above. 

Stored in the DDB. For three binary systems, azeotropic behavior is calculated. No ternary or quaternary azeotropic point is found using the group contribution equation of state VTPR. A comparison with the experimental data stored in the DDB shows that this is in agreement with the experimental findings. 

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