1. Generalized Correlations for Gases (Lee-Kesler)
By: Santosh Koirala
Manoj Joshi
Lauren Billings
Cory Klemashevich

2. The Generalized Correlation for Gases
The generalized Pitzer’s correlation is a three-parameter corresponding states method for estimating thermodynamic properties of pure, nonpolar fluids . For the compressibility factor Z, it takes the form
Z = Z0 + ω Z1
where,
Z0 = Compressibility factor for fluids of nearly spherical molecules,
ω = Pitzer's acentric factor, and
Z1 = Corrects for nonspherical intermolecular forces.
Appendix E provides values of Z0 and Z1 (Lee-Kessler correlations), from which Z can be calculated and, hence, the molar volume can be computed.

3. Virial equations
The Virial equation (up to the second Virial coefficient) provides an approximation of Z and the equation is:

4. Cont……
The virial equation (up to the Third coefficient) also provides an approximation of Z. Such virial equation is:

5. Example Problem
Determine the molar volume of n-butane at 510 K and 25 bar by each of the following:
a) The ideal-gas equation,
b) The generalized compressibility-factor correlation,
c) Generalized correlation for using eq. 3.61,
d) Equation 3.68 the third virial coefficient equation.

6. A. By the Ideal Gas equation:

7. B. From the values of Tc and Pc given in Table B.1 of App. B

8. C. Using the Second Virial EquationP 25
bar T
510 K Pc
37.96 Tc
425.1 Pr Tr ω
0.2 B0 B1 Z R
83.14
cm3bar/molK V
cm3/mol
Here, Excel was used to calculate the volume using second virial coefficient equation.

9. D. Using Second and Third Virial coefficientP 25
bar T
510 K Pc
37.96 Tc
425.1 Pr
Z (Guess)
Z (Calculated) Tr 1 ω
0.2 B0 B1 C0 C1 R
83.14
cm3bar/molK V
cm3/mol
This is the third coefficient virial equation for the same problem. Again Excel was used to obtain the solution. The solution is again very close to the value obtained by the Lee-Kesler method.

10. Where the Virial Equation Applies
The second coefficient virial equation works at low pressures where Z is a linear function. It is used when an approximation of a non ideal gas is needed, but at non extreme temperatures and pressures.
The third virial coefficient equation provides another correction to the virial equation.
This graph shows the difference obtained for the Z0 value for the Lee/Kesler correlation vs. the virial coefficient equation.