Correlation between Water-Oil-Ratio (WOR) and Water Oil Balance Ratio (WOBR):

One of the simple way to model WOR is to build its correlation with WOBR:

$\begin{array}{l}\displaystyle {\rm WOR} = \Phi \left( \frac{ \Omega_W^{\downarrow} \cdot Q_W^{\downarrow} - \Omega_W^{\uparrow} \cdot Q_W^{\uparrow} } { EUOR - Q_O^{\uparrow} } \right)\end{array}$

For example, one can search for the $\begin{array}{l}\Omega_W^{\downarrow}\end{array}$ and $\begin{array}{l}Q_W^{\uparrow}\end{array}$ (and even adjust $\begin{array}{l}EUOR\end{array}$ ) in order to achieve the best fit the WOR history:

$\begin{array}{l}\displaystyle \sum_t {\rm WOR}(t) - {\rm WOR}_{mod}(t) \rightarrow 0\end{array}$

$\begin{array}{l}\displaystyle {\rm WOR}_{mod}(t) = \frac{ \Omega_W^{\downarrow} \cdot Q_W^{\downarrow}(t) - \Omega_W^{\uparrow} \cdot Q_W^{\uparrow}(t) } { EUOR - Q_O^{\uparrow}(t) }\end{array}$

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WOR vs WOBR

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