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In case the phases have the same pressure the compressibility of multi-phase fluid can be expressed via compressibilities of single-phase fluids as:
| (1) |
c_f = c_w \, s_w + c_o \, s_o + c_g \, s_g |
Derivation
| (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} |
| (4) |
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} |
| (5) |
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} |
| (6) |
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
(1)
