Determine the roots of a virial equation of state with cubic order dependency on specific volume.
The project will involve determining the roots of a virial equation of state with cubic order dependency on specific volume. This program can be used in the future for helping to determine phase transition on the PVT surface for any PEOS.
We want to do this in an object-oriented way, where the specific parameters will be supplied in separate functions apart from the main program.
Any PEOS can be put into virial form, so this program can be used for any specific PEOS, including RK, van der Walls, Peng Robinson, etc.
We will use the Peng Robinson parameters which will be supplied as a separate function.
Matlab or Python is permitted.
The virial EOS is discussed in Chapter 6 of your book, so you can begin reading about it as you read through Chapter 6. You are responsible for all of Chapter 6 reading and the final exam will focus on that material, albeit in an energy balance way. The virial EOS is also discussed in detail in Chapter 5 of Felder and Rousseau.
I will be giving formal,written guidance on what you should calculate and what the project report format should be. But, you have a heads up. The program is pretty simple to write and you can use supplied root finding methods in Matlab and Numpy in python. There are also analytical expression for roots of a cubic equation. I prefer the root finding schemes since it gives you the ability to go to fourth order, if you know the fourth order parameters.
The project will involve determining the roots of a virial equation of state with cubic order dependency on specific volume. This program can be used in the future for helping to determine phase transition on the PVT surface for any PEOS.
We want to do this in an object-oriented way, where the specific parameters will be supplied in separate functions apart from the main program.
Any PEOS can be put into virial form, so this program can be used for any specific PEOS, including RK, van der Walls, Peng Robinson, etc.
We will use the Redlich-Kwong parameters which will be supplied as separate functions.
Matlab or Python is permitted. NO EXCEL OR VBA allowed.
RK EOS: See Handout from class.
B(T) = b – a(T) / RT
C(T) =b2 + b a(T) / RT
where
a(T) = 0.472 R2 Tc2.5 / (T1/2 Pc)
and
b = 0.867 RTc / Pc
Program:
Main Program has the virial EOS in cubic form. B and C are provided as separate functions or modules.
Main program gives the roots across a range of temperatures and pressures corresponding to the saturated steam tables. Minimum root is the liquid and the maximum root is the vapor. The middle root is a metastable value that is not used here.
Show plots of computed values of Vhat versus T for vapor and liquid under the Results section of your report.
Report format is given in a separate document on Bb.
