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The plot of water production rate

LaTeX Math Inline
bodyq_W
(along y-axis) against the oil production rate
LaTeX Math Inline
bodyq_O
 (along x-axis).

It can be used in express water cut diagnostics of thief water production.

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

...


LaTeX Math Inline
bodyq_W

water production rate

LaTeX Math Inline
bodyq_O

oil production rate

LaTeX Math Inline
body--uriencoded--p%5e*_1

formation pressure in petroleum reservoir

LaTeX Math Inline
body--uriencoded--J_%7B1W%7D

water productivity index of petroleum reservoir

LaTeX Math Inline
body--uriencoded--J_%7B1O%7D

oil productivity index of petroleum reservoir

LaTeX Math Inline
body--uriencoded--p%5e*_2

formation pressure in aquifer

LaTeX Math Inline
body--uriencoded--J_%7B2W%7D

water productivity index of aquifer



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

LaTeX Math Inline
body--uriencoded--b > 0 \Leftrightarrow p%5e*_2 > p%5e*_1

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

LaTeX Math Inline
body--uriencoded--b < 0 \Leftrightarrow p%5e*_2 < p%5e*_1

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