The general form of the watercut YWWater-Oil Ratio (WOR) regression is:
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Y_W^{-1}WOR = Y_{W0}^{-1} + \WOR_0 + Q_O \cdot \mbox{Regression}(\{q_k\}, \{Q_k\}), \quad k=[1..N] |
where
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Watercut Power Regression
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WOR = WOR_0 + Q_{O} \cdot \sum_{k=1..N} \big[ a_{O,k} \, Q_{O,k}^{gQ_{O,k}} + a_{W,k} \, Q_{W,k}^{gQ_{W,k}} + b_{O,k} \, q_{O,k}^{gq_{O,k}} + b_{W,k} \, q_{W,k}^{gq_{W,k}} \big] |
Watercut Rational Regression
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WOR = WOR_0 + \frac {Q_{O} \cdot \sum_{k=1..N} \big[ a_{O,k} \, Q_{O,k}^{gQ_{O,k}} + a_{W,k} \, Q_{W,k}^{gQ_{W,k}} + b_{O,k} \, q_{O,k}^{gq_{O,k}} + b_{W,k} \, q_{W,k}^{gq_{W,k}} \big] }{1 + \sum_{k=1..N} \big[ c_{O,k} \, Q_{O,k}^{hQ_{O,k}} + c_{W,k} \, Q_{W,k}^{hQ_{W,k}} + d_{O,k} \, q_{O,k}^{hq_{O,k}} + d_{W,k} \, q_{W,k}^{hq_{W,k}} \big] } |
Watercut Neural Network Regression
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WOR = WOR_0 + Q_O \cdot \mbox{ANN}(\{Q_{O,k}\}, \{Q_{W,k}\},\{q_{O,k}\},\{q_{W,k}\}), \quad k=[1..N] |
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The simplest form of the linear closed-form regression is:
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Y_W^{-1} = Y_{W0}^{-1} + \sum_{k=1}^N w_k \cdot q_k, \quad k=[1..N] |
The simplest form of the non-linear closed-form regression is polynomial:
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Y_W^{-1} = Y_{W0}^{-1} + \sum_{k=1}^N w_k \cdot q_k ^ {n_k} |
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Y_W^{-1} = Y_{W0}^{-1} + \frac{\sum_{k=1}^N w_k \cdot q_k ^ {n_k} }{\sum_{k=1}^N z_k \cdot q_k ^ {m_k} }, \quad |z| = \sqrt{\sum_k z_k} >0 |
See Also
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Petroleum Industry / Upstream / Subsurface E&P Disciplines / Well Testing (WT) / Flowrate Testing / Flowrate / Production Water cut (Yw)
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