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q_t = \Big[ B_w Y_w + \left[Big( \, (B_o - R_s B_g) + GOR \cdot (B_g - R_v B_o) \cdot, GOR \right]Big) \cdot (1-Y_w) \Big] \cdot q_L |
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q_t = \Big[ B_w Y_w + \left[ (B_o - R_s B_g) + B_g \cdot GOR \right] \cdot (1-Y_w) \Big] \cdot q_L |
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q_t = B_w \, q_W + (B_o - R_s \, B_g) \, q_O + B_g \, q_G = B_w \, q_W + B_o \, q_O + B_g ( q_G - R_s \, q_O ) = B_w \, q_W + \left( 1 + \left( \frac{GOR}{R_s} -1 \right) \cdot \frac{R_s \, B_g}{B_o} \right) \cdot B_o\, q_O
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or
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q_t = B_w \, q_W + \left( 1 + \left( \frac{GOR}{R_s} -1 \right) \cdot \frac{R_s \, B_g}{B_o} \right) \cdot B_o\, q_O =
\left[
B_w \, Y_W + \left( 1 + \left( \frac{GOR}{R_s} -1 \right) \cdot \frac{R_s \, B_g}{B_o} \right) \cdot B_o\, (1- Y_w)
\rightBig( \, (B_o - R_s B_g) + GOR \cdot B_g \, \Big) \cdot (1-Y_w) \Big] \cdot q_L
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It simplifies further down to production from undersaturated reservoir as:
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