Ratio of field-wide cumulative oil production $\begin{array}{l}Q^{\uparrow}_O\end{array}$ to the cumulative water injection $\begin{array}{l}Q_{WI}^{\downarrow}\end{array}$ :

(1)	$\begin{array}{l}\displaystyle {\rm ΣPIR} = \frac{Q^{\uparrow}_O}{Q^{\downarrow}_{WI}}\end{array}$

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

When gas injection is not present ( $\begin{array}{l}Q^{\downarrow}_{GI} = 0\end{array}$ ) the ΣPIR can be related to the Cumulative Voidage Replacement Ratio (ΣVRR) as:

(2)

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

(see

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for derivation)

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Cumulative Production-Injection Ratio = ΣPIR

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