Local volume and time averaging is used to derive rigorously energy eq
uations for multi-phase flows in heterogeneous porous media. The flow
is conditionally divided into three velocity fields. Each of the field
s consists of several chemical components. Using the conservation equa
tions for mass and momentum and the Gibbs equation, entropy equations
are rigorously derived It is shown that the use of the specific entrop
y as one of the dependent variables leads to the simplest way of-descr
ibing and modeling such a complicated thermodynamic system, A working
form of the final entropy equation is recommended for general use in m
ulti-phase flow dynamics.