Ratio of Cumulative Intakes to Cumulative Offtakes:
| (1) | {\rm ΣVRR} = \frac{\rm Cumulative \ Intakes}{\rm Cumulative \ Offtakes} = \frac{Q^{\downarrow}_t}{Q^{\uparrow}_t} |
It is normally calculated for the whole field or its sector and represents one of the key Production Analysis metrics.
The most popular case of using ΣVRR metrics is waterflood FDP in Black Oil reservoir where ΣVRR takes form:
| (2) | {\rm ΣVRR} = \frac{B_w \, Q^{\downarrow}_{WI}+B_g \, Q^{\downarrow}_{GI}}{B_w \, Q^{\uparrow}_W + B_o \, Q^{\uparrow}_O + B_g \, [ Q^{\uparrow}_G - R_s \, Q^{\uparrow}_O] } = \frac{B_w \, Q^{\downarrow}_{WI}+B_g \, Q^{\downarrow}_{GI}}{B_w \, Q^{\uparrow}_W + [ B_o + B_g \, ( {\rm ΣGOR} - R_s) ] \, Q^{\uparrow}_O } |
where
Q^{\downarrow}_{WI}, \ Q^{\downarrow}_G | cumulative water injection and cumulative gas injection |
Q^{\uparrow}_W, \, Q^{\uparrow}_O, \, Q^{\uparrow}_G | water, oil, gas surface flowrates |
B_w, \, B_o, \, B_g | formation volume factors between separator and sandface pressure/temperature conditions |
| GOR | production Gas-Oil Ratio |
R_s | solution GOR at sandface pressure/temperature conditions |
When production and injection is happening in/from the same reservoir the high ΣVRR values will result in high formation pressure.
The key waterflood strategy is to maintain ΣVRR > 1.0.
Most waterflood projects maintain ΣVRR within 1.05 ÷ 1.07 range to account for thief injection.
In case of efficient Aquifer or Gas Cap support the ΣVRR can be maintained at less than 1.0 value.
When gas injection is not present ( Q^{\downarrow}_{GI} = 0) the alternative form of ΣVRR equation can be derived from (2):
| (3) | {\rm ΣVRR} = \frac{Q^{\downarrow}_{WI}}{Q^{\uparrow}_W + \left[ \frac{B_o}{B_w} + \frac{B_g}{B_w} \, ( {\rm ΣGOR} - R_s) \right] \, Q^{\uparrow}_O } = \frac{Q^{\downarrow}_{WI}}{Q^{\uparrow}_O} \cdot \frac{1}{{\rm ΣWOR} + \left[ \frac{B_o}{B_w} + \frac{B_g}{B_w} \, ( {\rm ΣGOR} - R_s) \right] } = \frac{1}{\rm ΣPIR} \cdot \frac{1}{\frac{ΣY_w}{1-ΣY_w} + \left[ \frac{B_o}{B_w} + \frac{B_g}{B_w} \, ( {\rm ΣGOR} - R_s) \right] } |
where
See Also
Petroleum Industry / Upstream / Production / Subsurface Production / Field Study & Modelling / Production Analysis
[ Cumulative Offtakes] [Cumulative Intakes ] [ Instantaneous Voidage Replacement Ratio (IVRR) ]