In case the phases have the same pressure the compressibility of multi-phase fluid can be expressed via compressibilities of single-phase fluids as:
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c_f = c_w \, s_w + c_o \, s_o + c_g \, s_g |
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| V_f = V_w \, s_w + V_o \, s_o + V_g \, s_g |
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| s_w = \frac{V_w}{V_f}, \ s_o = \frac{V_o}{V_f}, \ s_g = \frac{V_g}{V_f} |
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| 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} |
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| c_f = \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 | LaTeX Math Block Reference |
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