OIL

WATER

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}}

current oil saturation,

current water saturation,

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

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

maximum oil relative permeability to water displacement

maximum water relative permeability to oil displacement

oil relative permeability curvature to water displacement

water relative permeability curvature to oil displacement

where is connate water saturation which maybe

equal to critical

or

less than critical like for example in petroleogenetic rocks.

This model assumes no free gas presence in pores.

GLOSSARY > Oil+Water RPM Corey @model > image2021-6-17_15-11-32.png

Fig. 1. 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 for initial water saturation and for maximum water saturation .

In this case equations and take form:

OIL

WATER

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