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(1) |
WOR = \frac{\alpha_W(t) \cdot q_W^\uparrow}{\alpha_O(t) \cdot q_O^\uparrow} |
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(2) |
ΣWOR = \frac{ \int\limits_0^t \alpha_W(t) \cdot q_W^\uparrow \, dt}{ \int\limits_0^t \alpha_O(t) \cdot q_O^\uparrow \, dt} |
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The history matching coefficients
\alpha_W(t), \ \alpha_O(t) can be found from minimisation of the goal function:
(3) |
E[\alpha_W(t), \alpha_O(t)] = \sum_t \ \min D \big( P_{\rm mod}(t), P_{\rm hist}(t) \big) \rightarrow 0 |
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where
D is the distance between each historical point and model curve on WΣW plot.
(4) |
D \big( P_{\rm mod}}(t), P_{\rm hist}(t) \big) = \sqrt{ \big( WOR_{\rm mod} - WOR_{\rm hist} \big)^2 + \big( ΣWOR_{\rm mod} - ΣWOR_{\rm hist} \big)^2 } |
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and
\min D \big( P_{\rm mod}}, P_{\rm hist} \big) means minimal distance between point
P_{\rm hist} = \big( ΣWOR_{\rm hist} , WOR_{\rm hist} \big) and the model curve
P_{\rm mod} = \big( ΣWOR_{\rm mod} , WOR_{\rm mod} \big)
See Also
Petroleum Industry / Upstream / Production / Subsurface Production / Field Study & Modelling / Production Analysis / Watercut Diagnostics / Watercut WΣW plot