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| \delta \left[ \phi \cdot \left( \xi_{O,o} \, s_o + \xi_{O,g} \, s_g \right) \right] = V^{-1} \, \delta Q_O |
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| \delta \left[ \phi \cdot \left( \xi_{G,o} \, s_o + \xi_{G,g} \, s_g \right) \right] = V^{-1} \, \delta Q_G |
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| \delta \left[ \phi \cdot \xi_{W,w} \, s_w \right] = V^{-1} \, \delta Q_W |
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| \phi \cdot \left[ \frac{1}{B_o} \, s_o + \frac{R_v}{B_g} \, s_g \right] = V^{-1} \, \delta qQ_O + \phi_i \cdot \left[ \frac{1}{B_{oi}} \, s_o + \frac{R_{vi}}{B_{gi}} \, s_{gi} \right] |
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| \phi \cdot \left[ \frac{R_s}{B_o} \, s_o + \frac{1}{B_g} \, s_g \right] = V^{-1} \, \delta qQ_G + \phi_i \cdot \left[ \frac{R_{si}}{B_{oi}} \, s_o + \frac{1}{B_{gi}} \, s_{gi} \right] |
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| \phi \cdot \frac{1}{B_w} \, s_w = V^{-1} \, \delta qQ_W + \phi_i \cdot \frac{1}{B_{wi}} \, s_{wi} |
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| \phi_n \cdot \left[ \frac{1}{B_o} \, s_o + \frac{R_v}{B_g} \, s_g \right] = V_e^{-1} \, \delta qQ_O + \left[ \frac{1}{B_{oi}} \, s_o + \frac{R_{vi}}{B_{gi}} \, s_{gi} \right] |
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| \phi_n \cdot \left[ \frac{R_s}{B_o} \, s_o + \frac{1}{B_g} \, s_g \right] = V_e^{-1} \, \delta qQ_G + \left[ \frac{R_{si}}{B_{oi}} \, s_o + \frac{1}{B_{gi}} \, s_{gi} \right] |
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| \phi_n \cdot \frac{1}{B_w} \, s_w = V_e^{-1} \, \delta qQ_W + \frac{1}{B_{wi}} \, s_{wi} |
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| \phi_n(p) = \phi(p) / \phi_i |
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| \frac{1}{B_o} \, s_o + \frac{R_v}{B_g} \, s_g = F_O/\phi_n |
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| F_O = V_e^{-1} \, \delta qQ_O + \left[ \frac{1}{B_{oi}} \, s_o + \frac{R_{vi}}{B_{gi}} \, s_{gi} \right] |
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| \frac{R_s}{B_o} \, s_o + \frac{1}{B_g} \, s_g = F_G/\phi_n |
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| F_G = V_e^{-1} \, \delta qQ_G + \left[ \frac{R_{si}}{B_{oi}} \, s_o + \frac{1}{B_{gi}} \, s_{gi} \right] |
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| \frac{1}{B_w} \, s_w = F_W/\phi_n |
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| F_W = V_e^{-1} \, \delta qQ_W + \frac{1}{B_{wi}} \, s_{wi} |
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| \frac{B_o \, (F_O - R_v \, F_G)}{\phi_n \, (1- R_s \, R_v)} + \frac{B_g \, (F_G - R_s \, F_O)}{\phi_n \, (1- R_s \, R_v)} + \frac{B_w \, F_W}{\phi_n} =1 |
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| B_o \, (F_O - R_v \, F_G) + B_g \, (F_G - R_s \, F_O) + B_w \, F_W \, (1- R_s \, R_v) = \phi_n \, (1- R_s \, R_v) |
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alignment | left |
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| (B_o - R_s \, B_g) \, F_O +(B_g - R_V \, B_o) \, F_G + (B_w \, F_W - \phi_n )\, (1- R_s \, R_v) = 0 |
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See Also
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Petroleum Industry / Upstream / Production / Subsurface Production / Field Study & Modelling / Production Analysis / Material Balance Analysis (MatBal) / Material Balance Pressure @model