1. The problem statement, all variables and given/known data I am trying to plot the non tie-line paths for the solution to 3 component injection with constant K-values. 2. Relevant equations 3. The attempt at a solution In order to construct the paths on a ternary diagram, I need to find C1 and C2. Then C3 = 1 - C1 - C2, so I can plot the lines. In my attempt, I chose x01 f01 and s01 from a point on my initial tie-line, and then got the following plots for C1(S1) and C2(S1): But on the plot, C1 C2 and C3 all need to be positive and < 1 to be inside the composition space, and C2 and C1 are never both positive, so I can't generate the lines. I'm not sure where I've gone wrong. Here is the input for Mathematica. Hopefully someone can explain what Im missing. Thank you for any insights you have to offer! Also, if anyone knows of a resource that goes through an example of a full solution to this type of problem, it would be greatly appreciated.