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| q_O = \frac{q_o}{B_o} + R_v \,\frac{q_g}{B_g} |
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| q_G = \frac{q_g}{B_g} + R_s \, \frac{q_o}{B_o} |
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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 = \frac{B_o \cdot (q_O - R_v \, q_G)}{1- R_v \, R_s} |
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| q_g = \frac{B_g \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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| 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:
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| s_w = q_w/q_t |
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| s_o+s_g+s_w = 1 |
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Surface oil mass rate: LaTeX Math Block |
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| \dot m_O = \rho_O \cdot q_O
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| Surface gas mass rate:
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| \dot m_G = \rho_G \cdot q_G
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| Surface gas mass rate:
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| \dot m_W = \rho_W \cdot q_W
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| 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 |
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In-situ oil mass rate:
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| \dot m_o = (\rho_O \cdot q_o/B_o =+ \rho_OG \cdot (q_O - R_vs) \,cdot \frac{q_G))
o}{B_o} |
| 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_sv) \,cdot \frac{q_O)_g}{B_g} |
| 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 = \frac{\rho_O/ + \rho_G \cdot R_s}{B_o} |
| In-situ gas density:
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| \rho_g = \frac{\rho_G/ + \rho_O \cdot R_v}{B_g} |
| In-situ water density:
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| \rho_w = \frac{\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 ) |
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