Compressibility of multiphase fluid in thermodynamic equilibrium at a given pressure and temperature is a linear sum of its single-phase components:

c_f(p, T) = \sum_{\alpha} s_\alpha \cdot c_\alpha(p,T)

where

	-phase volume share, subjected to
	-phase compressibility as function of pressure and temperature

The total multiphase volume:

V = \sum V_\alpha

where are volumes, occupied by individual phases.

The volume fraction of individual phase is defined as:

s_\alpha = \frac{V_\alpha}{V}

This leads to:

c_f = \frac{1}{V} \, \frac{\partial V}{\partial p} = 
\frac{1}{V} \sum_\alpha \frac{\partial V_\alpha}{\partial p} = 
 \sum_\alpha \frac{V_\alpha}{V} \, \frac{1}{V_\alpha} \frac{\partial V_\alpha}{\partial p} =
 \sum_\alpha s_\alpha \, c_\alpha

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

c_f = s_w \, c_w + s_o \, c_o + s_g \, c_g

where mean water phase, oil phase and gas phase.

See also