PNG 520
Phase Relations in Reservoir Engineering

Cubic EOS Fugacity Expressions

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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:

SRK EOS

Pure Substance

ln ϕ=Z−1−ln(Z−B)− A B ln( 1+ B Z ) This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers.
(16.42)
 

Mixtures

ln  ϕ i = (BB) i (Z−1)−ln(Z−B)− A B ( (AA) i −BB) i )ln[ 1+ B Z ] This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers.
(16.43)
 

PR EOS

Pure Substance

ln ϕ=Z−1−ln(Z−B)− A 2 2 B ln Z+(1+ 2 )B Z+(1− 2 )B This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers.
(16.44)
 

Mixtures

ln  ϕ i = (BB) i (Z−1)−ln(Z−B)− A 2 2 B ( (AA) i − (BB) i )ln[ Z+( 2 +1)B Z−( 2 −1)B ] This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers.
(16.45)
 

The expressions for A, B,  b i ,  b m , (aα ) m , (aα ) ij This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers. are the same as given before in the previous modules. (AA)i and (BB)i are calculated as:

(AA) i = 2 (aα) m [ ∑ j n c (aα) ij ] This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers.
(16.46a)
 
(BB) i = b i b m This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers.
(16.47b)
 

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.