The total multiphase volume:
| (2) |
V_f = V_w \, s_w + V_o \, s_o + V_g \, s_g |
where
| (3) |
s_w = \frac{V_w}{V_f}, \ s_o = \frac{V_o}{V_f}, \ s_g = \frac{V_g}{V_f} |
are volume fractions of phases and hence
| (4) |
c_f = \frac{1}{V_f} \, \frac{\partial V_f}{\partial p} = \frac{1}{V_f} \, \frac{\partial V_w}{\partial p} + \frac{1}{V_f}\, \frac{\partial V_o}{\partial p} + \frac{1}{V_f}\, \frac{\partial V_g}{\partial p} = \frac{V_w}{V_f} \, \left( \frac{1}{V_w} \, \frac{\partial V_w}{\partial p} \right) + \frac{V_o}{V_f} \, \left( \frac{1}{V_o} \, \frac{\partial V_o}{\partial p} \right) + \frac{V_g}{V_f} \, \left( \frac{1}{V_g} \, \frac{\partial V_g}{\partial p} \right) |
which leads to
(1)
