In case the fluid 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}, \ s_g = \frac{V_g_f} | are volume fractions of phases and hence This leads to:
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| c_f = \frac{1}{V | _f_f}{\partial p} =
\frac{1}{V | _f,sum_\alpha \frac{\partial V_ | w+frac{1}{V_f}\,\partial o\partial p+f\,gfrac{V_w}{V_f}sum_\alpha s_\alpha \, c_\ | 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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In most popular practical case of a 3-phase fluid model this will be:
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c_f = s_w \, c_w + s_o \, c_o + s_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