The pore-saturating fluid volume is related to total rock volume V_r and reservoir porosity \phi as:
| (1) | V_f = V_r \phi |
The total reservoir compressibility is going to be:
| (2) | c_t = -\frac{1}{V_r} \, \frac{\partial V_r}{\partial p} = - \frac{\phi}{V_f} \, \frac{\partial}{\partial p} \left( \frac{V_f}{\phi} \right) = - \frac{\phi}{V_f} \, \left( V_f \, \frac{\partial}{\partial p} \frac{1}{\phi} + \frac{1}{\phi} \frac{\partial V_f}{\partial p} \right) = \frac{1}{\phi} \, \frac{\partial \phi}{\partial p} - \frac{1}{V_f} \, \frac{\partial V_f}{\partial p} = c_r + c_f |