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The total 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_tf = c_w \, Bs_w + c_o \, Bs_o + c_g \, s_g


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titleDerivation


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V_f = V_w \, s_w + V_o \, s_o + V_g \, s_g

where 

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s_w = \frac{V_w}{V_f}, \ s_o = \frac{V_o}{V_f},
B_g
 \ s_g = \frac{V_g}{V_f}


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c_f = \frac{1}{V_f} \frac{V_f}{p} = \frac{1}{V_f} \frac{V_w}{p} + \frac{1}{V_f} \frac{V_o}{p} + \frac{1}{V_f} \frac{V_g}{p}


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c_f = \frac{V_w}{V_f} \frac{1}{V_w} \frac{V_w}{p} + \frac{V_o}{V_f} \frac{1}{V_o} \frac{V_o}{p} + \frac{V_g}{V_f} \frac{1}{V_g} \frac{V_g}{p}


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c_f = \frac{V_w}{V_f} \frac{1}{V_w} \frac{V_w}{p} + \frac{V_o}{V_f} \frac{1}{V_o} \frac{V_o}{p} + \frac{V_g}{V_f} \frac{1}{V_g} \frac{V_g}{p}

which leads to

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