Published on *PNG 520: Phase Behavior of Natural Gas and Condensate Fluids* (https://www.e-education.psu.edu/png520)

Expressions (16.34) and (16.40) are particularly suitable for the calculation of fugacity with P-explicit equations of state, which cubic equations of state are. One can take every cubic EOS we have presented and proceed with the integration, coming up with the expression for fugacity for that particular equation of state. We will spare the reader these derivations. The fugacity expressions for the cubic EOS of most interest to us (SRK and PR EOS) are presented below:

$$ln\text{}\varphi =Z-1-\mathrm{ln}(Z-B)-\frac{A}{B}\mathrm{ln}\left(1+\frac{B}{Z}\right)$$

$$ln\text{}{\varphi}_{i}={(BB)}_{i}(Z-1)-\mathrm{ln}(Z-B)-\frac{A}{B}{({(AA)}_{i}-BB)}_{i})\mathrm{ln}\left[1+\frac{B}{Z}\right]$$

$$ln\text{}\varphi =Z-1-\mathrm{ln}(Z-B)-\frac{A}{2\sqrt{2}B}\mathrm{ln}\frac{Z+(1+\sqrt{2})B}{Z+(1-\sqrt{2})B}$$

$$ln\text{}{\varphi}_{i}={(BB)}_{i}(Z-1)-\mathrm{ln}(Z-B)-\frac{A}{2\sqrt{2}B}({(AA)}_{i}-{(BB)}_{i})\mathrm{ln}\left[\frac{Z+(\sqrt{2}+1)B}{Z-(\sqrt{2}-1)B}\right]$$

The expressions for $A\text{,}B\text{,}{b}_{i},\text{}{b}_{m},\text{(a}\alpha {\text{)}}_{m},\text{(a}\alpha {\text{)}}_{ij}$
are the same as given before in the previous modules. (AA)_{i} and (BB)_{i} are calculated as:

$${(AA)}_{i}=\frac{2}{{(a\alpha )}_{m}}\left[{\displaystyle \sum _{j}^{{n}_{c}}{(a\alpha )}_{ij}}\right]$$

$${(BB)}_{i}=\frac{{b}_{i}}{{b}_{m}}$$

A and B parameters and the Z-factor of each phase are needed in order to calculate the corresponding fugacity coefficients. Now that we know how to calculate fugacity via EOS, and how this concept can be applied for equilibrium calculations (Section 16.2), we are ready to resume our discussion on Vapor-Liquid Equilibrium as we left it in Module 13. In our next module, we will concentrate on Vapor-Liquid Equilibrium via EOS.