For multiphase fluid in thermodynamic equilibrium at a given pressure $\begin{array}{l}p\end{array}$ and temperature $\begin{array}{l}T\end{array}$ the compressibility is:

(1)	$\begin{array}{l}\displaystyle c_f(p, T) = \sum_{\alpha} s_\alpha c_\alpha\end{array}$

where

$\begin{array}{l}s_\alpha\end{array}$	$\begin{array}{l}\alpha\end{array}$ -phase saturation, subjected to $\begin{array}{l}\sum_{\alpha} s_\alpha = 1\end{array}$
$\begin{array}{l}c_\alpha = c_\alpha(p, T)\end{array}$	$\begin{array}{l}\alpha\end{array}$ -phase compressibility as function of pressure $\begin{array}{l}p\end{array}$ and temperature $\begin{array}{l}T\end{array}$

In most popular practical case of a 3-phase fluid model this will be:

(2)	$\begin{array}{l}\displaystyle c_f = c_w \, s_w + c_o \, s_o + c_g \, s_g\end{array}$

where $\begin{array}{l}{w, \, o, \, g}\end{array}$ mean water phase, oil phase and gas phase.

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See also