Ratio of field-wide oil production rate $\begin{array}{l}q_O\end{array}$ to the water injection rate $\begin{array}{l}q_{WI}\end{array}$ :

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

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 PIR can be related to the current Instantaneous Voidage Replacement Ratio (IVRR) as:

(2)

$\begin{array}{l}\displaystyle {\rm PIR}= \frac{1}{\rm IVRR} \cdot \frac{1-Y_w}{Y_w + (1-Y_w) \, \left[ \frac{B_o}{B_w} + \frac{B_g}{B_w} \, ( {\rm GOR} - R_s) \right] } = \frac{1}{\rm IVRR} \cdot \frac{1}{{\rm WOR} + \, \left[ \frac{B_o}{B_w} + \frac{B_g}{B_w} \, ( {\rm GOR} - R_s) \right] }\end{array}$

(see (Instantaneous Voidage Replacement Ratio = IVRR:3) for derivation).

For the Balanced waterflood:

(3)	$\begin{array}{l}\displaystyle {\rm PIR}= \frac{1}{{\rm WOR} + \, \left[ \frac{B_o}{B_w} + \frac{B_g}{B_w} \, ( {\rm GOR} - R_s) \right] }\end{array}$

and for those above bubble point pressure ( $\begin{array}{l}p > p_b \Leftrightarrow GOR = R_s\end{array}$ ):

(4)	$\begin{array}{l}\displaystyle {\rm PIR}= \frac{1}{{\rm WOR} + \frac{B_o}{B_w}}\end{array}$

The equation (4) is often used for predicting the upper limit of oil production increase in response to the water injection:

(5)	$\begin{array}{l}\displaystyle q^{\uparrow}_O = {\rm PIR} \cdot q^{\downarrow}_{WI} = \frac{q^{\downarrow}_{WI}}{{\rm WOR} + \frac{B_o}{B_w}}\end{array}$

For the waterless period of Balanced waterflood project $\begin{array}{l}\textrm{WOR}= 0\end{array}$ and:

(6)	$\begin{array}{l}\displaystyle q^{\uparrow}_O = {\rm PIR} \cdot q^{\downarrow}_{WI} = \frac{B_w}{B_o} \cdot q^{\downarrow}_{WI}\end{array}$

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See Also

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Instantaneous PIR

See Also