The general form of the watercut YW regression is:
| (1) | Y_W^{-1} = Y_{W0}^{-1} + \mbox{Regression}(\{q_k\}), \quad k=[1..N] |
where
(\{q_k\} = \{ q_1, \, q_2, \, ... q_N \} | sandface flowrates |
One can build various types of regression including the Artificial Neural Network or the closed-form regressions.
The simplest form of the linear closed-form regression is:
| (2) | 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:
| (3) | Y_W^{-1} = Y_{W0}^{-1} + \sum_{k=1}^N w_k \cdot q_k ^ {n_k} |
The more general of the non-linear closed-form regression is rational:
| (4) | 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 |