The plot of water production rate(along y-axis) against the oil production rate (along x-axis).
It can be used for express Watercut Diagnostics of thief water production.
The mathematical model of the thief water production from 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}_ |
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{1O} \cdot ( J_{1W} + J_{2W}) |
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| b = 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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For the case of aquifer pressure is lower than that of petroleum reservoir:
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body | --uriencoded--b < 0 \Leftrightarrow p%5e*_2 < p%5e*_1 |
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In practical applications, the equation
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is often considered through the
averaged value weighted average values:
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<q_W>\langle q_W \rangle = a \, <q_O> + \cdot \langle q_O \rangle + \, b |
where
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body | <q_W>\langle q_W \rangle, \ <q_O>\langle q_O \rangle |
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| are weighted average of and |
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There are different ways to calculated calculate weighted average of of the dynamic variable, for example:
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| <\langle A >\rangle_t \ = \frac{1}{t} \int_o^t A(t) \, dt |
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| <A>\langle A \rangle_q \ = \frac{1}{Q(t)} \int_o^t A(t) \, q(t) \, dt |
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See Also
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Petroleum Industry / Upstream / Production / Subsurface Production / Field Study & Modelling / Production Analysis / Watercut Diagnostics
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