Synonym: Waterflood Recovery (WF) = Waterflooding

The Expected Ultimate Recovery during the waterflood sweep can be assessed with the following formula:

(1)	$\begin{array}{l}\displaystyle EUR_{WF} = E_S \, E_D + (1-E_S) \cdot EUR_{ND}\end{array}$

where $\begin{array}{l}E_D\end{array}$ – displacement efficiency, $\begin{array}{l}E_S\end{array}$ – sweep efficiency.

Voidage Replacement

One of the key principle of Waterflooding is to maintain Instantaneous Voidage Replacement Ratio (IVRR) above unit value at all times:

(2)	$\begin{array}{l}\displaystyle {\rm IVRR} = \frac{B_w \, q^{\downarrow}_{WI}}{B_w \, q^{uparrow}_W + [ B_o + B_g \, ( {\rm GOR} - R_s) ] \, q^{uparrow}_O } \geq 1\end{array}$

which is equivalent to maintainign the surface water injection to liquid production ratio as:

(3)	$\begin{array}{l}\displaystyle \frac{q^{\downarrow}_{WI}}{q^{\uparrow}_L} \geq Y_W +(1-Y_W) \cdot \left[ \frac{B_o}{B_w} + \frac{B_g}{B_w} (GOR - R_s) \right]\end{array}$

This ensures maintaining the formation pressure at initial value.

Due to numerous reasons this condition is very difficult to implement in practise.

Sweep efficiency

A part of the reservoir pore volume subjected to displacement by invaded fluid (aquifer, injected water, injected gas or injected chemicals):

Total sweep

Areal sweep

Vertical sweep

(4)	$\begin{array}{l}\displaystyle E_S = \frac{V_{sweep}}{V_\phi}\end{array}$

(5)	$\begin{array}{l}\displaystyle E_{SA} = \frac{A_{sweep}}{A_\phi}\end{array}$

(6)	$\begin{array}{l}\displaystyle E_{SV} = \frac{h_{sweep}}{h_\phi}\end{array}$

$\begin{array}{l}V_{sweep}\end{array}$ – sweep volume

$\begin{array}{l}V_\phi\end{array}$ – pore volume

$\begin{array}{l}A_{sweep}\end{array}$ – sweep area

$\begin{array}{l}A_\phi\end{array}$ – pore area

$\begin{array}{l}h_{sweep}\end{array}$ – sweep thickness

$\begin{array}{l}h_\phi\end{array}$ – pore thickness

The total sweep efficiency is a product of areal and vertical sweep efficiencies:

(7)	$\begin{array}{l}\displaystyle E_S = E_{SV} \, E_{SA}\end{array}$

$\begin{array}{l}\displaystyle E_{Dow} = 1- \frac{V_{o, \ LEFT}}{V_{o, \ INITITAL}} = \frac{1-s_{wi}-s_{orw}}{1-s_{wi}}\end{array}$

where $\begin{array}{l}s_{wi}\end{array}$ – initial water in oil pay, $\begin{array}{l}s_{orw}\end{array}$ – residual oil to water sweep.

James T. Smith, Wiliam M. Cobb, Waterflooding (2010)