Can you be more specific? Which theory do yo want to apply? In early stages of my career I worked with industrial equipment simulation. Perhaps I can found some scrips for similar problems.
You are a research director, an associate professor no less , and are asking RG users to provide/write some FORTRAN for a rather straight forward problem?
You have the algorithm, what's the difficulty?
Note, the document does not describe the actual control laws that you would need - but describes the mass and energy balances - these are useful for scaling the system, but tell you nothing about how to drive it.
If you are actually building a real system then start with PID controls and then maybe move to Kalman filters to properly control the system.
I'd use LabVIEW to make a prototype, drive and sense with NI hardware (digital outputs, thermocouples, etc.), with the control laws in C.