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| LaTeX Math Block |
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|
s_w + s_o + s_g =1 |
where
| share of total fluid volume occupied by water phase |
| share of total fluid volume occupied by oil phase |
| share of total fluid volume occupied by gas phase |
The accountable cross-phase exchanges are illustrated in the table below:
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| q_O = \frac { q_o/B_o + R_v \cdot q_g/B_g } {1 - R_s R_v} |
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| q_G =\frac{q_g/B_g + R_s \cdot q_o/B_o}{1-R_s R_v} |
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| q_W = \frac{q_w}{B_w} |
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| q_L = q_O + q_W |
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| q_o = B_o \cdot ( q_O - R_v \, q_G) |
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| q_g = B_g \cdot ( q_G - R_s \, q_O) |
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| q_w = B_w \cdot q_W |
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| q_t = q_o + q_g + q_w |
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In-situ oil-cut:
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| s_o = q_o/q_t |
| In-situ gas-cut:
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| s_g = q_g/q_t |
| In-situ water-cut:
| LaTeX Math Block |
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| s_w = q_w/q_t |
| | LaTeX Math Block |
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| s_o+s_g+s_w = 1 |
|
Surface oil mass rate: | LaTeX Math Block |
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| \dot m_O = \rho_O \cdot q_O
|
| Surface gas mass rate:
| LaTeX Math Block |
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| \dot m_G = \rho_G \cdot q_G
|
| Surface gas mass rate:
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| \dot m_W = \rho_W \cdot q_W
|
| Surface total fluid mass rate:
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| anchor | m_tSURF |
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| alignment | left |
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| \dot m = \dot m_O + \dot m_G + \dot m_W |
|
In-situ oil mass rate:
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| \dot m_o = \rho_O \cdot q_o/B_o = \rho_O \cdot (q_O - R_v \, q_G))
|
| In-situ gas mass rate:
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| \dot m_g = \rho_G \cdot q_g/B_g = \rho_O \cdot (q_G - R_s \, q_O) |
| In-situ water mass rate:
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| \dot m_w = \rho_W \cdot q_w/B_w |
| In-situ total fluid mass rate:
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| anchor | m_tSUB |
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| alignment | left |
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| \dot m = \dot m_o + \dot m_g + \dot m_w |
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In-situ oil density:
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| \rho_o = \rho_O/B_o |
| In-situ gas density:
| LaTeX Math Block |
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| \rho_g = \rho_G/B_g |
| In-situ water density:
| LaTeX Math Block |
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| \rho_w = \rho_W/B_w |
| In-situ Total fluid density:| LaTeX Math Block |
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| \rho_t = \dot m/q_t = s_o \, \rho_o + s_g \, \rho_g + s_w \, \rho_w |
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Total fluid compressibility: | LaTeX Math Block |
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| c = \rho_t^{-1} \cdot ( s_o \, \rho_o \, c_o + s_g \, \rho_g \, c_g + s_w \, \rho_w \, c_w ) |
|
...
