Volumetric calculations
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body | --uriencoded--\displaystyle q_O = q_%7BOo%7D + q_%7BOg%7D |
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body | --uriencoded--\displaystyle q_G = q_%7BGg%7D + q_%7BGo%7D |
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body | --uriencoded--\displaystyle q_W = q_%7BWw%7D |
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body | --uriencoded--\displaystyle q_O = q_%7BOo%7D + q_%7BOg%7D |
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q_O = q_{Oo} + q_{Og} |
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body | --uriencoded--\displaystyle q_O = q_%7BOo%7D + q_%7BOg%7D |
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| q_G = q_{Gg} + q_{Go} |
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| q_W = q_{Ww} |
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| q_o = \frac{B_o \cdot (q_O - R_v \, q_G)}{1- R_v \, R_s} |
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| q_og = \frac{B_og \cdot (q_G - R_s \, q_O)}{1- R_v \, R_s} |
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| q_w = B_w \cdot q_w |
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Mass calculations
The oil phase
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body | --uriencoded--()_%7BOo%7D |
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and gas component LaTeX Math Inline |
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body | --uriencoded--()_%7BGo%7D |
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so that the oil phase mass flux is: LaTeX Math Block |
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m_o = m_{Oo} + m_{Go} |
The gas phase
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body | --uriencoded--()_%7BGg%7D |
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and oil component LaTeX Math Inline |
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body | --uriencoded--()_%7BOg%7D |
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so that the gas phase mass flux is: LaTeX Math Block |
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m_g = m_{Gg} + m_{Og} |
The water phase
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body | --uriencoded--()_%7BWw%7D |
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only so that the water phase mass flux is: LaTeX Math Block |
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m_w = m_{Ww} |
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| m_o = \rho_O \cdot q_{Oo} + \rho_G \cdot q_{Go} |
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| m_g = \rho_G \cdot q_{Gg} + \rho_O \cdot q_{Og} |
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| m_w = \rho_W \cdot q_{Ww} |
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| m_o = \rho_O \cdot q_{Oo} + \rho_G \cdot R_s \, q_{Oo} |
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| m_g = \rho_G \cdot q_{Gg} + \rho_O \cdot R_v \, q_{Gg} |
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| m_w = \rho_W \cdot q_{Ww} |
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| m_o = (\rho_O + \rho_G \cdot R_s) \cdot q_{Oo} |
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| m_g = (\rho_G + \rho_O \cdot R_v) \cdot q_{Gg} |
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| m_w = \rho_W \cdot q_{Ww} |
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| m_o = (\rho_O + \rho_G \cdot R_s) \cdot \frac{q_o}{B_o} |
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| m_g = (\rho_G + \rho_O \cdot R_v) \cdot \frac{q_g}{B_g} |
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| m_w = \rho_W \cdot \frac{q_w}{B_w} |
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| \rho_o = \frac{\rho_O + \rho_G \cdot R_s}{B_o} |
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| \rho_g = \frac{\rho_G + \rho_O \cdot R_v}{B_g} |
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| \rho_w = \frac{\rho_W}{B_w} |
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The total mass flow of all phases:
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\dot m = \dot m_o + \dot m_g + \dot m_w = (\rho_O + \rho_G \cdot R_s) \cdot \frac{q_o}{B_o} + (\rho_G + \rho_O \cdot R_v) \cdot \frac{q_g}{B_g} + \rho_W \cdot \frac{q_w}{B_w} |
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\dot m = (\rho_O + \rho_G \cdot R_s) \cdot \frac{q_O - R_v \, q_G}{1-R_v \, R_s} + (\rho_G + \rho_O \cdot R_v) \cdot \frac{q_G - R_s \, q_O}{1- R_v \, R_s} + \rho_W \cdot q_W |
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\dot m = \frac{ (\rho_O + \rho_G \cdot R_s)\cdot (q_O - R_v \, q_G) + (\rho_G + \rho_O \cdot R_v) \cdot (q_G - R_s \, q_O) }{1-R_v \, R_s} + \rho_W \cdot \frac{q_w}{B_w} |
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\dot m = \frac{ \rho_O \, q_O \, (1- R_v \, R_s) + \rho_G \, q_G \, (1- R_v \, R_s) }{1-R_v \, R_s} + \rho_W \cdot q_W |
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\dot m = \rho_O \cdot q_O + \rho_G \cdot q_G + \rho_W \cdot q_W = \dot m_O + \dot m_G + \dot m_W |
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\dot m = \dot m_o + \dot m_g + \dot m_w = \dot m_O + \dot m_G + \dot m_W |
which means that total mass flux of all fluid phases is equal to the total mass flux of all fluid components.
As volatile oil model does not assume water-component exchange between phases the equality
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can be broken down into two equalities: LaTeX Math Block |
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| \dot m_{HC} = \dot m_o + \dot m_g = \dot m_O + \dot m_G |
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| \dot m_w = \dot m_W |
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The total fluid density of Volatile Oil fluid @model is given by following equation (see Multiphase fluid for derivation):
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\rho = s_o \, \rho_o + s_g \, \rho_g + s_w \, \rho_w |
The total fluid compressibility of multiphase fluid is given by following equation (see Multiphase fluid for derivation):
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c = s_o \, c_o + s_g \, c_g + s_w \, c_w |
See Also
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Petroleum Industry / Upstream / Subsurface E&P Disciplines / Fluid (PVT) Analysis / Fluid @model / Volatile Oil Fluid @model