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One of the methods the method The production adjustments coefficients
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| \alpha_W(t), \ \alpha_O(t) |
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can be ...
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| WOR = \frac{\alpha_W(t) \cdot q_W^\uparrow}{\alpha_O(t) \cdot q_O^\uparrow} |
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| 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 production adjustments coefficients
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| body | \alpha_W(t), \ \alpha_O(t) |
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can be found from minimisation of the goal function:
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| 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 is the distance between each historical point and model curve on WΣW plot.
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| 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
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| body | --uriencoded--\min D \big( P_%7B\rm mod%7D%7D, P_%7B\rm hist%7D \big) |
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means minimal distance between point
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| body | --uriencoded--P_%7B\rm hist%7D = \big( ΣWOR_%7B\rm hist%7D , WOR_%7B\rm hist%7D \big) |
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and the model curve
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| body | --uriencoded--P_%7B\rm mod%7D = \big( ΣWOR_%7B\rm mod%7D , WOR_%7B\rm mod%7D \big) |
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The results of the history matching are illustrated on Fig. 1 below.
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Fig. 1.1 – WΣW plot before history matching | Fig. 1.2 – WΣW plot after history matching |
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| Fig. 1.2 – The production adjustments coefficients from history matching |
See Also
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Petroleum Industry / Upstream / Production / Subsurface Production / Field Study & Modelling / Production Analysis / Watercut Diagnostics / Watercut WΣW plot
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