| | LaTeX Math Inline |
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| body | --uriencoded--\displaystyle q_O = q_%7BOo%7D + q_%7BOg%7D |
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| LaTeX Math Inline |
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| body | --uriencoded--\displaystyle q_G = q_%7BGg%7D + q_%7BGo%7D |
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| LaTeX Math Inline |
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| body | --uriencoded--\displaystyle q_W = q_%7BWw%7D |
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|
| LaTeX Math Inline |
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| body | --uriencoded--\displaystyle q_O = q_%7BOo%7D + q_%7BOg%7D |
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| LaTeX Math Block |
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| q_O = q_{Oo} + q_{Og} |
| | LaTeX Math Inline |
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| body | --uriencoded--\displaystyle q_O = q_%7BOo%7D + q_%7BOg%7D |
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| LaTeX Math Block |
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| q_G = q_{Gg} + q_{Go} |
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| LaTeX Math Block |
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| q_W = q_{Ww} |
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Following the definition of Solution GOR (Rs) and Vaporized Oil Ratio (Rv) :
| LaTeX Math Block |
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| R_s = q_{Go}/q_{Oo} |
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| LaTeX Math Block |
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| R_v = q_{Og}/q_{Gg} |
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so that:
| LaTeX Math Block |
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| q_O = q_{Oo} + R_v \, q_{Gg} |
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| LaTeX Math Block |
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| q_G = q_{Gg} + R_s \, q_{Oo} |
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| LaTeX Math Block |
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| q_W = q_{Ww} |
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Following the definition of Oil formation volume factor (Bo) , Gas formation volume factor (Bg) and Water formation volume factor (Bw):
| LaTeX Math Block |
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| q_{Oo}= \frac{q_o}{B_o} |
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| LaTeX Math Block |
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| q_{Gg} = \frac{q_g}{B_g} |
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| LaTeX Math Block |
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| q_{Ww} = \frac{q_w}{B_w} |
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so that:
| LaTeX Math Block |
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| q_O = \frac{q_o}{B_o} + R_v \,\frac{q_g}{B_g} |
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| LaTeX Math Block |
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| q_G = \frac{q_g}{B_g} + R_s \, \frac{q_o}{B_o} |
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| LaTeX Math Block |
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| q_W = \frac{q_w}{B_w} |
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and solving the above system of equations leads to:
| LaTeX Math Block |
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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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| LaTeX Math Block |
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| q_o = \frac{B_o \cdot (q_G - R_s \, q_O)}{1- R_v \, R_s} |
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| LaTeX Math Block |
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| q_w = B_w \cdot q_w |
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