(1)	$\begin{array}{l}\displaystyle k_{rog}(s_o) \bigg\|_{ s_w =s_{wi}} = k_{rogc} \, \bigg[ \frac{ s_o - s_{wi} - s_{org} }{ 1 - s_{wi} - s_{org} } \bigg]^{n_{og}}\end{array}$

(2)	$\begin{array}{l}\displaystyle k_{rgo}(s_g) \bigg\|_{ s_w =s_{wi}} = k_{rgoc} \, \bigg[ \frac{ s_g - s_{goc} }{ 1 - s_{goc} - s_{wi} - s_{org} } \bigg]^{n_{go}}\end{array}$

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

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

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

current gas saturation, $\begin{array}{l}s_g = 1 - s_o - s_{wi}\end{array}$

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

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

$\begin{array}{l}s_{goс}\end{array}$

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

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

maximum oil relative permeability to gas displacement

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

maximum gas relative permeability to oil displacement

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

oil relative permeability curvature to gas displacement

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

gas 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 that water presence in pores is limited to $\begin{array}{l}s_{wi}\end{array}$ only.

Fig. 1. Typical Oil+Gas RPM Corey @model

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See also