Calculating Mixture Critical Temperature and Pressure using Equation of State?

[Suman Chakraborty]

Hello Everyone,

 

I am trying to calculate critical Temperature and Pressure of binary and ternary mixtures using equation of state. In particular, I am using Peng-Robinson Equation of State. I combined this with Van-der Waals critical criterion to get my result, but am way off experimental data.

 

Vander Waals criteria states: dP/dv = 0 and d2P/dv2=0

 

My steps:

1. I solve the two partial derivative equations mentioned above to end up with a cubic equation in 'v' (molar volume). Solving this I get the critical molar volume

 

2. I put this back in either of the partial derivative conditions and calculate Temperature using iteration.

 

3. Now I know Tc and Vc. I put these values back in the equation of state to get my pressure.

 

Problem:

My Tc values are still within range or close to experimental data but the Pc values are way off.

 

Attached Plot:

Attached plot is of a binary mixture of methane(C1) and propane(C3). Tc and Pc plots are attached vs mole fraction of C1