Derivation of the Fugacity Expression

The Trebble-Bishnoi EoS (Trebble and Bishnoi, I988a b) for a fluid mixture is given by equation 14.6. The fugacity, (j, of component j in a mixture is given by the following expression for case 1 (t 0) 

A number of partial derivatives are needed and they are given next. 

If t is negative then X is given by equation A.l, 6b and the derivative is given by 

---