Real Gas Modeling

Overview

Since version 2022, Flow Simulator has used the compressibility factor, z, to adjust the ideal gas relationship for density. The compressibility factor improves the accuracy for fluids that are at pressures and temperatures where they do not behave like an ideal gas.

$ρ = \frac{P}{z R T}$

In version 2025, Flow Simulator has an improved accuracy option for fluids that do not behave as an ideal gas. This new approach uses modified exponents for the isentropic equations, reference 1. It still uses the compressibility factor as before. As before, only fluids using Coolprop can model the real gas effects.

From the Material Editor, select the Real Gas Gamma option.

Equations

The two new “gammas” used for real gas:

$γ_{P v} = \frac{C_{p}}{P C_{v} β} = \frac{γ_{i d e a l}}{P β}$

$γ_{T v} = 1 + \frac{v α}{C_{v} β}$

$α = \frac{1}{v {(\frac{\partial v}{\partial T})}_{P}} = i s o b a r i c e x p a n s i o n c o e f f i c i e n t$

$β = \frac{- 1}{v {(\frac{\partial v}{\partial p})}_{T}} = i s o t h e r m a l c o m p r e s s i b i l i t y f a c t o r$

For a fluid near the ideal gas conditions, the two new gammas are equivalent to the ideal gas gamma.

$γ = γ_{P v} = γ_{T v} = \frac{C_{p}}{C_{v}}, for ideal gas conditions$

The isentropic relations and the flow function equations can be rewritten using the new “gammas”.

$\frac{P_{o}}{P} = {(1 + \frac{γ_{P v} - 1}{2} M^{2})}^{\frac{γ_{P v}}{γ_{P v} - 1}}$

$\frac{T_{o}}{T} = {(1 + \frac{γ_{P v} - 1}{2} M^{2})}^{\frac{γ_{T v} - 1}{γ_{P v} - 1}}$

$\frac{\dot{m} \sqrt{T_{o}}}{P_{o} A} = \frac{\sqrt{\frac{γ_{P v}}{z_{o} R}} M}{{(1 + \frac{γ_{P v} - 1}{2} M^{2})}^{\frac{γ_{P v} + 1}{2 (γ_{P v} - 1)}}}$

For a fluid near the ideal gas conditions, these equations are equivalent to the ideal gas equations.

Output

The *.prop file has a column for these two new “gammas”. The “RG” at the end of “COOLPROPRG” in the output files also denotes the real gas gammas that were used in the analysis.

References

Nederstigt, P., Pecnik, R., “Generalised Isentropic Relations in Thermodynamics”, Energies 2023, 16, 2281.
https://doi.org/10.3390/en16052281.