In case the phases have the same pressure the compressibility of multi-phase fluid can be expressed via compressibilities of single-phase fluids as: 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) = c\sum_w {\,alpha} s_w\alpha +\cdot c_o \, s_o + c_g \, s_g_\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: _fV_w \, s_w +o \, s_o + V_g \, s_g |
where
where are volumes, occupied by individual phases.
The volume fraction of individual phase is defined as: w = \frac{V_w}{V_f}, \ s_o _o}{V_f}, \ sg = \frac{V_g_f
This leads to:
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| c_f = \frac{1}{V |
_f_f}{\partial p} =
\frac{1}{V |
_f,w+frac{1}{V_f}\,\partial o\partial p+f\,g\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 be:
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c_f = \frac{Vs_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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| anchor | cfc_w + s_o \, c_o + s_g \, c_g
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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
