...

k_{row}(s_

...

o) = k_{rowc} \cdot  \bigg

...

[  \frac{ s_o - s_{orw}   }{ 1- s_

...

{wl} - 

...

s_

...

{orw}  } \bigg]^{n_{ow}}

k_{rwo}(s_w) = k_{

...

rwoc} \

...

cdot  \bigg[ 

 \frac{ 

...

s_w - s_{

...

wco}   }{ 1- s_{

...

wco} - s_{orw}  } \bigg]^{n_{

...

wo}}

...

where Initial water saturation 

• equal to critical 

  LaTeX Math Inline
  body s_{

...

• wсo}

   

or or

• less than critical 

  LaTeX Math Inline
  body --uriencoded--s_

...

• %7Bwl%7D < s_

...

• %7Bwco%7D

   like for example

...

• in petroleogenetic rocks

...

• .

This model assumes no free gas presence in pores.

Image Added

Image Removed

Fig. 1.

Typical Oil-Water relative permeabilities

Typical Oil+Water RPM Corey @model

The alternative form of the Oil+Water RPM Corey @model can be presented as a function of normalized water saturation

s = \frac{s_w - s_{wi}}{1-s_{wl}-s_{orw}}

which changes between

In this case equations 

k_{row}(s_o) = k_{rowc} \cdot (1-s)^{n_{ow}}

k_{rwo}(s_w) = k^*_{rwoc} \cdot (s - s^*)^{n_{wo}}

s^* = \frac{s_{wco}-s_{wi}}{1-s_{wl}-s_{orw}}

k^*_{rwoc} = k_{rwoc} \cdot \left( \frac{1-s_{wl}-s_{orw}}{1-s_{wco}-s_{orw}} \right)^{n_{wo}}

and fractional flow function is going to be:

f_w = \frac{M_{rwo}}{M_{rwo} + M_{row}} = \frac{(s-s^*)^{n_{wo}}}{(s-s^*)^{n_{wo}} + g \cdot (1-s)^{n_{ow}}}

\dot f_w = \frac{d f_w}{ds} = g \cdot (s-s^*)^{n_{wo}-1} \cdot
\frac{ n_{wo} (1-s)^{n_{ow}} + n_{ow} (s-s^*) (1-s)^{n_{ow}-1}}
{\left[ (s-s^*)^{n_{wo}} + g \cdot (1-s)^{n_{ow}} \right]^2}

where

g = \frac{M_{rowc}}{M_{rwoc}} \cdot \left( \frac{1-s_{wco}-s_{orw}}{1-s_{wl}-s_{orw}} \right)^{n_{wo}}

See also

...

Petroleum Industry / Upstream / Subsurface E&P Disciplines / Petrophysics / Relative Permeability / RPM @model

[ Permeability ] [ Absolute permeability ] [Relative permeability @model ]