1. Now we introduce a new concept: fugacity
When we try to model “real” systems, the expression for the chemical potential that we used for ideal systems is no longer valid
We introduce the concept of fugacity that for a pure component is the analogous (but is not equal) to the pressure

2. We showed that: Pure component i, ideal gas Component i in a mixture
of ideal gases
Let’s define:
For a real fluid, we define
Fugacity of pure species i

3. Residual Gibbs free energy
Valid for species i
in any phase and
any condition

4. Since we know how to calculate residual properties… (section 6.2)
Eqn. 6.49)
Zi from an EOS, Virial, van der Waals, etc

8. examples From Virial EOS From van der Waals EOS
General form, see eqn for cubic EOS.
First solve for Zi in the vapor or in the liquid phase

9. For cubic EOS
For the vapor phase:
3.52
For the liquid phase:
3.56
See Table 3.1 for parameters

10. Page 98

11. Fugacities of a 2-phase system
One component, two phases:
saturated liquid and saturated vapor at Pisat and Tisat
What are the equilibrium conditions for a pure component?

12. Fugacity of a pure liquid at P and T

13. Fugacity of a pure liquid at P and T

14. example
For water at 300oC and for P up to 10,000 kPa (100 bar) calculate values of fi and fi from data in the steam tables and plot them vs. P
At low P, steam is an ideal gas => fi* =P*
Get Hi* and Si* from the steam tables at 300oC and the lowest P, 1 kPa
Then get values of Hi and Si at 300oC and at other pressures P and calculate fi (P)

16. Problem
For SO2 at 600 K and 300 bar, determine good estimates of the fugacity and of GR/RT.
SO2 is a gas, what equations can we use to calculate
f = f/P
Find Tc, Pc, and acentric factor, w, Table B1, p. 680
Calculate reduced properties: Tr, Pr
Tr=1.393 and Pr=3.805

17. What equations can we use to determine fi (gas phase)

18. Generalized correlations: fugacity coefficient
Tables E13 to E16
Lee-Kessler

21. High P, high T, gas: use Lee-Kessler correlation
From tables E15 and E16 find f0 and f1
f0 = 0.672; f1 = 1.354
f = f0 f1w = 0.724
f = f P = x 300 bar = bar
GR/RT = ln f =

22. Problem
Estimate the fugacity of cyclopentane at 110oC and 275 bar. At 110 oC the vapor pressure of cyclopentane is bar.
At those conditions, cyclopentane is a high P liquid

23. Find Tc, Pc, Zc,, Vc and acentric factor, w, Table B1, p. 680
Calculate reduced properties: Tr, Prsat
Tr = and Prsat = 0.117
At P = Psat we can use the virial EOS to calculate fisat
Eqn
Eqns and 3.66

24. Get the volume of the saturated liquid phase, Rackett equation
fisat = 0.9
P-correction term:
Get the volume of the saturated liquid phase, Rackett equation
Eqn. 3.72, p. 109
Vsat = cm3/mol
f = bar