HELP - Derive 2-phase 3-dimesional PD flow equation

nandz

1. The problem statement, all variables and given/known data
Hello All, I'd please like some help in deriving a 2-phase 3-dimensional partial differential flow equation from first principles.


2. Relevant equations
I know that the starting point is Darcy's flow equation.


3. The attempt at a solution
A key step is substituting the Darcy flow equation into the material balance equation, but I don't know how to get from there to the final equation for a 2-phase 3-dimensional flow.

Many thanks for helping out.