Final temperature of an O-G mixture undergoing compression

[Fausto]

Hi,

A question to this forum.

I have a liquid-gas (oil+gas) mixture at (p1, T1), and
this mixture shall be compressed to (p2, T2). p2 is known
and I want to compute/estimate/calculate T2. All fluids'
properties at inlet (specific heats, densities, whatever)
are also available. Since it is a mixture, the polytropic
expansion equation,

(T2/T1) = (p2/p1)**(1 - 1/n)

(or something like that, where "n" is some exponent which
equals Cp/Cv for an isentropic expansion) cannot be used
as this formula does not apply to 2-phase mixtures.

Any hints? I am not using any commercial package,
all I need is a quick-&-dirty approach to compute the
final temperature for an expansion like that.

Thanks in advance!

---Fausto