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LaTeX Math Block
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M_\alpha(s) = \frac{k_\alpha}{\mu_\alpha} =   \frac{k_{air} \cdot k_{r \alpha}}{\mu_\alpha} = k_{air} \cdot M_{r\alpha}(s)

where 

LaTeX Math Inline
body\displaystyle k_\alpha(s)

formation permeability to fluid 

LaTeX Math Inline
body\alpha
-phase

LaTeX Math Inline
body\displaystyle \mu_\alpha

dynamic viscosity of fluid

LaTeX Math Inline
body\alpha
-phase

LaTeX Math Inline
body\displaystyle k_{air}

absolute permeability to air

LaTeX Math Inline
body\displaystyle M_{r\alpha}(s) = \frac{k_{r \alpha}}{\mu_\alpha}

relative phase mobility

LaTeX Math Inline
body\displaystyle k_{r\alpha}(s)

relative formation permeabilityto fluid 

LaTeX Math Inline
body\alpha
-phase

LaTeX Math Inline
bodys = \{ s_{\alpha}\}

reservoir saturation

LaTeX Math Inline
body\sum_\alpha s_{\alpha} = 1
,
LaTeX Math Inline
body\alpha
-phase saturation


In most popular case of a 3-phase fluid model this will be:

LaTeX Math Inline
bodys = \{ s_w, \, s_o, \, s_g \}

LaTeX Math Inline
body s_w + s_o + s_g =1

LaTeX Math Inline
body\displaystyle M_o = \frac{k_o}{\mu_o}

oil mobility

LaTeX Math Inline
body\displaystyle M_g = \frac{k_g}{\mu_g}

gas mobility

LaTeX Math Inline
body\displaystyle M_w = \frac{k_w}{\mu_w}

water mobility

See also

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Physics /  Fluid Dynamics / Percolation

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Petrophysics ] [ Basic reservoir properties ] [ Permeability ] [ Absolute permeability ]  [Relative permeability] [ Wettability ]  [ Phase mobility ] [ Relative phase mobilities ]

[ Multihase Fluid Mobility ]