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 equationqOW plotis based on the following correlation between oil production rate and water production rate:
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| q_W = a \, \cdot q_O + b |
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| a = J^{-1}_O{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 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
weighted average values:
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<q_W>\langle q_W \rangle = a \, \cdot \langle <q_O> q_O \rangle + \, b |
where
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| body | <q_W>, \ <q_O>\langle q_W \rangle, \ \langle q_O \rangle |
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| are weighted average of and |
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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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