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OILWATER
LaTeX Math Block
anchorM1AZDkrow
alignmentleft
k_{row}(s_o) = k_{rowc} \,  \bigg[  \frac{ s_o - s_{orw}   }{ 1- s_{wi} - s_{orw}  } \bigg]^{n_{ow}}
LaTeX Math Block
anchorM1AZDkrwo
alignmentleft
k_{rwo}(s_w) = k_{rwoc} \,  \bigg[ 

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

LaTeX Math Inline
bodys_o

current oil saturation,

LaTeX Math Inline
bodys_o = 1 - s_w

LaTeX Math Inline
bodys_w

current water saturation,

LaTeX Math Inline
bodys_w = 1 - s_o

LaTeX Math Inline
bodys_{orw}

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

LaTeX Math Inline
bodys_{wсo}

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

LaTeX Math Inline
bodyk_{rowc}

maximum oil relative permeability to water displacement

LaTeX Math Inline
bodyk_{rwoc}

maximum water relative permeability to oil displacement

LaTeX Math Inline
bodyn_{ow}

oil relative permeability curvature to water displacement

LaTeX Math Inline
bodyn_{wo}

water relative permeability curvature to oil displacement

...

The model assumes no gas presence in pores.


Image RemovedImage Added

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

LaTeX Math Inline
bodys
 :

LaTeX Math Block
anchor1KS5U
alignmentleft
s = \frac{s_w - s_{wi}}{1-s_{wi}-s_{orw}}

which changes between

LaTeX Math Inline
bodys = 0
 for initial water saturation 
LaTeX Math Inline
body--uriencoded--s_w = s_%7Bwi%7D
 and 
LaTeX Math Inline
bodys = 1
 for maximum water saturation 
LaTeX Math Inline
body--uriencoded--s_w = 1- s_%7Borw%7D
.


In this case equations 

LaTeX Math Block Reference
anchorkrow
 and  
LaTeX Math Block Reference
anchorkrwo
 take form:

OILWATER
LaTeX Math Block
anchorM1AZD
alignmentleft
k_{row}(s_o) = k_{rowc} \,  \bigg[  \frac{ s_o - s_{orw}   }{ 1- s_{wi} - s_{orw}  } \bigg]^{n_{ow}}
LaTeX Math Block
anchorM1AZD
alignmentleft
k_{rwo}(s_w) = k_{rwoc} \,  \bigg[ 

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


LaTeX Math Inline
bodys_o

current oil saturation,

LaTeX Math Inline
bodys_o = 1 - s_w

LaTeX Math Inline
bodys_w

current water saturation,

LaTeX Math Inline
bodys_w = 1 - s_o

LaTeX Math Inline
bodys_{orw}

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

LaTeX Math Inline
bodys_{wсo}

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

LaTeX Math Inline
bodyk_{rowc}

maximum oil relative permeability to water displacement

LaTeX Math Inline
bodyk_{rwoc}

maximum water relative permeability to oil displacement

LaTeX Math Inline
bodyn_{ow}

oil relative permeability curvature to water displacement

LaTeX Math Inline
bodyn_{wo}

water relative permeability curvature to oil displacement


See also

...

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

...