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titleDerivation


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



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

where

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body\rho_\alpha

fluid compressibility  of 

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body\alpha
-phase

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bodys_\alpha

volumetric share of 

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body\alpha
-phase


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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



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