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The mathematical model of the thief water production from rater reservoir aquifer is based on the following equation:
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| q_W = a \, \cdot q_O + b |
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| a = J^{-1}_{1O} \cdot ( J_{1W} + J_{2W}) |
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| b = J_{2W} \cdot (p^*_2 - p^*_1) |
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where
oil pay oil & water oil pay water reservoir| in aquifer | | LaTeX Math Inline |
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| body | --uriencoded--J_%7B2W%7D |
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| water productivity index of |
water reservoir
For the case of water reservoir aquifer pressure is higher than that of oil+water petroleum reservoir:
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| body | --uriencoded--b > 0 \Leftrightarrow p%5e*_2 > p%5e*_1 |
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For the case of water reservoir aquifer pressure is lower than that of oil+water petroleum reservoir:
| LaTeX Math Inline |
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| body | --uriencoded--b < 0 \Leftrightarrow p%5e*_2 < p%5e*_1 |
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