Here are additional hints for the original poster once the thermo method is addressed.
One hint is to get the simulation to converge first. This may mean backing way off of your desired specs. Once you have a converged model, then gradually change the specs toward what you really want. I call this 'homotopy' but the technique may have a different name. When the model breaks, examine the trend of the converged solutions right before the break to see where the solution is heading and think of what you might do to keep it from falling off the cliff. In general, converged solutions give much more useful information than unconverged solutions. Spec'ing flow rates is often more reliable than spec'ing stream purities to get initial convergence.
Some additional suggestions for your student project: Air Sep plants are probably common simulation projects and a thorough web search might discover someone's master thesis with lots of details about how their model was specified. Another shortcut might be to contact the technical support group for Hysys and nicely ask for a working example of an Air Sep plant. Although tech support may be limited in how they are supposed to support student licenses, they are human and might show mercy to a student with a sob story.