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The mathematical model of the thief water production from aquifer is based on the following equation:
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| Y_W = a + b / q_L |
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| a = \frac{J_{1W} + J_{2W}}{J_{1O} + J_{1W} + J_{2W}} |
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| b = \frac{J_{1O} \cdot J_{2W}}{J_{1O} + J_{1W} + J_{2W}} \cdot (p^*_2 - p^*_1) |
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where
For the case of aquifer pressure is higher than that of petroleum reservoir:
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| body | --uriencoded--b > 0 \Leftrightarrow p%5e*_2 > p%5e*_1 |
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<q_W> = a \, \cdot <q_O> + \, b |
where
| are weighted average of and |
There are different ways to calculate weighted average of the dynamic variable, for example:
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| < A >_t \ = \frac{1}{t} \int_o^t A(t) \, dt |
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| <A>_q \ = \frac{1}{Q(t)} \int_o^t A(t) \, q(t) \, dt |
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Cases
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Case 1
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