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

{\rm WOR} = \Phi \left( \frac{ \Omega_W^{\downarrow} \cdot Q_W^{\downarrow} -  \Omega_W^{\uparrow} \cdot Q_W^{\uparrow} } { EUOR - Q_O^{\uparrow} } \right)

where is some function.

For example, one can select and search for the exponent , good water percentages , and even adjust in order to achieve the best model fit to the WOR history:

\sum_t \left\| {\rm WOR}(t) - {\rm WOR}^*(t) \right\| \rightarrow 0

{\rm WOR}^*(t) =  \left[ \frac{ \Omega_W^{\downarrow} \cdot Q_W^{\downarrow}(t) -  \Omega_W^{\uparrow} \cdot Q_W^{\uparrow}(t) } { EUOR - Q_O^{\uparrow}(t) }  \right]^n

where is the norm of .

See Also