Ratio of field-wide cumulative oil production to the cumulative water injection :

{\rm ΣPIR} = \frac{Q^{\uparrow}_O}{Q^{\downarrow}_{WI}}

It measures how efficiently waterflood supports the oil production and represent one of the key Waterflood Diagnostics.

When gas injection is not present () the ΣPIR can be related to the Cumulative Voidage Replacement Ratio (ΣVRR) as:

{\rm ΣPIR}= \frac{1}{\rm ΣVRR} \cdot \frac{1-ΣY_w}{ΣY_w  + (1-ΣY_w) \, \left[ \frac{B_o}{B_w}  + \frac{B_g}{B_w} \, ( {\rm ΣGOR} - R_s) \right] } = 
\frac{1}{\rm ΣVRR} \cdot \frac{1}{{\rm ΣWOR}  + \, \left[ \frac{B_o}{B_w}  + \frac{B_g}{B_w} \, ( {\rm ΣGOR} - R_s) \right] }

(see for derivation)

See Also