OIL

WATER

k_{row}(s_w) \bigg|_{ s_g =s_{gc}} = k_{rowc} \,  \bigg[  \frac{ 1 - s_w - s_{orw}   }{ 1- s_{wi} - s_{orw}  } \bigg]^{n_{ow}}

k_{rwo}(s_w) \bigg|_{ s_g =s_{gc}} = k_{rwoc} \,  \bigg[ 

 \frac{ s_w - s_{wi}   }{ 1- s_{wi} - s_{orw}  } \bigg]^{n_{wo}}

current oil saturation,

current water saturation

residual gas saturation to oil displacement

initial 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 during water displacement

maximum water relative permeability during oil displacement

oil relative permeability curvature to water displacement

water relative permeability curvature to oil displacement

Initial water saturation maybe equal to critical or less than critical like for example for some petroleogenetic rocks

Fig. 1. Typical Oil-Water relative permeabilities

See also