Fluid volume consisting of two or more contacting phases

In most practical cases in Petroleum Industry it will be a 3-phase fluid (water, oil and gas).

The total fluid density of multiphase fluid is given by following equation:

\rho = \sum_\alpha s_\alpha \, \rho_\alpha

where

Density of -phase

volumetric share of -phase

\rho = \frac{m}{V}  = \frac{1}{V} \, \sum_\alpha m_\alpha = \sum_\alpha \frac{m_\alpha}{V}= \sum_\alpha \frac{V_\alpha}{V} \cdot \frac{m_\alpha}{V_\alpha} = \sum_\alpha s_\alpha  \, \rho_\alpha

The total fluid compressibility of multiphase fluid is given by following equation:

c = \sum_\alpha s_\alpha \, c_\alpha

where

fluid compressibility of -phase

volumetric share of -phase

c = \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

See also