Compressibility of multiphase fluid in thermodynamic equilibrium at a given pressure
and temperature is a linear sum of its single-phase components: LaTeX Math Block |
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c_f(p, T) = \sum_{\alpha} s_\alpha \cdot c_\alpha(p,T) |
where
| -phase volume share, subjected to LaTeX Math Inline |
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body | \sum_{\alpha} s_\alpha = 1 |
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The total multiphase volume: LaTeX Math Block |
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| V = \sum V_\alpha |
where are volumes, occupied by individual phases.
The volume fraction of individual phase is defined as: LaTeX Math Block |
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| s_\alpha = \frac{V_\alpha}{V} |
This leads to:
LaTeX Math Block |
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| c_f = \frac{1}{V} \, \frac{\partial V}{\partial p} =
\frac{1}{V} \sum_\alpha \frac{\partial V_\alpha}{\partial p} =
\sum_\alpha \frac{V_\alpha}{V} \, \frac{1}{V_\alpha} \frac{\partial V_\alpha}{\partial p} =
\sum_\alpha s_\alpha \, c_\alpha |
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In most popular practical case of a 3-phase fluid model this will beThe total compressibility of multi-phase fluid can be expressed via compressibilities of single-phase fluids as:
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c_tf = cs_w \, Bc_w + cs_o \, Bc_o + cs_g \B_g, c_g |
where
mean water phase, oil phase and gas phase.
See also
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Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Statics / Fluid Compressibility / Fluid Compressibility @model