OIL

WATER

(1)	$\begin{array}{l}\displaystyle k_{row}(s_o) = k_{rowc} \, \bigg[ \frac{ s_o - s_{orw} }{ 1- s_{wi} - s_{orw} } \bigg]^{n_{ow}}\end{array}$

(2)	$\begin{array}{l}\displaystyle k_{rwo}(s_w) = k_{rwoc} \, \bigg[ \frac{ s_w - s_{wc} }{ 1- s_{wc} - s_{orw} } \bigg]^{n_{wo}}\end{array}$

$\begin{array}{l}s_o\end{array}$

current oil saturation, $\begin{array}{l}s_o = 1 - s_w\end{array}$

$\begin{array}{l}s_w\end{array}$

current water saturation, $\begin{array}{l}s_w = 1 - s_o\end{array}$

$\begin{array}{l}s_{orw}\end{array}$

residual oil saturation to water displacement, below which oil is immobile

$\begin{array}{l}s_{wс}\end{array}$

critical water saturation to oil displacement, below which water is immobile

$\begin{array}{l}k_{rowc}\end{array}$

maximum oil relative permeability during water displacement

$\begin{array}{l}k_{rwoc}\end{array}$

maximum water relative permeability during oil displacement

$\begin{array}{l}n_{ow}\end{array}$

oil relative permeability curvature to water displacement

$\begin{array}{l}n_{wo}\end{array}$

water relative permeability curvature to oil displacement

where $\begin{array}{l}s_{wi}\end{array}$ is initial water saturation which maybe equal to critical $\begin{array}{l}s_{wс}\end{array}$ or less than critical $\begin{array}{l}s_{wi} < s_{wc}\end{array}$ like for example in petroleogenetic rocks.

The model assumes no gas presence in pores.

Fig. 1. Typical Oil-Water relative permeability

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See also

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Oil-Water relative permeability Corey @model

See also