The plot of WOR (along y-axis) against the inverse oil production rate (along x-axis) (see Fig. 1).

GLOSSARY > WOIL plot > image2023-7-5_18-14-51.png

Fig. 1. WOR (logarithmic vertical axis) vs inverse oil production rate (linear horizontal axis)

It can be used for express Watercut Diagnostics of thief water production.

The mathematical model of the thief water production from aquifer is based on the following equation:

WOR = \frac{q_W}{q_O} = a  + b \, \cdot q^{-1}_O

a = J^{-1}_{1O} \cdot ( J_{1W} + J_{2W})

b = J_{2W} \cdot (p^*_2 - p^*_1)

where

	water production rate	oil production rate
formation pressure in petroleum reservoir	water productivity index of petroleum reservoir	oil productivity index of petroleum reservoir
formation pressure in aquifer	water productivity index of aquifer

For the case of aquifer pressure is higher than that of petroleum reservoir:

For the case of aquifer pressure is lower than that of petroleum reservoir:

In practical applications, the equation is often considered through the weighted average values:

\langle WOR \rangle =\frac{\langle q_W \rangle}{\langle q_O \rangle}  = a  + b \cdot \langle q_O^{-1} \rangle

where

are weighted average of and

There are different ways to calculate weighted average of the dynamic variable, for example:

\langle A \rangle_t \ = \frac{1}{t} \int_o^t A(t) \, dt

\langle A\rangle_q \ = \frac{1}{Q(t)} \int_o^t A(t) \, q(t) \, dt

References

Fig. 1 – Instantaneous watercut Yw vs cumulative watercut

Based on the context it may mean:

Single-well watercut history WΣW plot	Multi-well watercut history WΣW plot	Pivot watercut WΣW plot

See Also