Non Tie-line paths in Gas Injection (porous media)

[phil ess]

Homework Statement

I am trying to plot the non tie-line paths for the solution to 3 component injection with constant K-values.

Homework Equations

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 I am 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.

 

[NateD]

x01 = 0.6;f01 = 0.3;s01 = 0.1;K12 = 0.8;K13 = 0.6;K23 = 0.9;C1[S1_] = ((x01 - S1)*(K23 - 1))/(K12*(K13 - 1));C2[S1_] = ((x01 - S1)*(K13 - 1))/(K12*(K23 - 1));C3[S1_] = 1 - C1[S1] - C2[S1];Plot[{C1[S1], C2[S1], C3[S1]}, {S1, 0, 1}]