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s_o + = 1 - s_{gc}{gc}
OILWATER


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



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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}}


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bodys_o

current oil saturation,

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body

s_w

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body
s_w

current water saturation,

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bodys_

w = 1 - s_o

residual gas saturation to oil displacement

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bodys_{wi}

initial water saturation

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bodys_{orw}

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

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bodys_{wс}

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

LaTeX Math Inline
bodyk_{rowc}

maximum oil relative permeability during water displacement

LaTeX Math Inline
bodyk_{rwoc}

maximum water relative permeability during oil displacement

LaTeX Math Inline
bodyn_{ow}

oil relative permeability curvature to water displacement

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bodyn_{wo}

water relative permeability curvature to oil displacement


where Initial water saturation 

LaTeX Math Inline
bodys_{wi}
 is initial water saturation which maybe equal to critical 
LaTeX Math Inline
bodys_{wс}
 or less than critical 
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bodys_{wi} < s_{wc}
 like for example for some in petroleogenetic rocks.


Fig. 1. Typical Oil-Water relative permeability

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