physical chemistry - When fugacity and z-compressability equations instead of Gibbs free energy equations?

In very high pressure environments such as mud circulating systems, conditions for polymers contain fugacity/z-compressability criteria instead of Gibbs free energy, more in the answer. So

When fugacity and z-compressability equations instead of Gibbs free energy equations?

and helper questions to the latter

1. 
   

   when are fugacity and z-compressability equations used?

   
   


2. 
   

   When are Gibbs free energy equations used?

   
   
   


3. 
   

   By which criteria can you justify your decision to choose between Gibbs free energy criterion and fugacity/compressability criterion?