A property characterizing agility of the fluid $\begin{array}{l}\alpha\end{array}$ -phase under pressure gradient with account of reservoir permeability and dynamic fluid viscosity:

(1)	$\begin{array}{l}\displaystyle M_\alpha(s) = \frac{k_\alpha}{\mu_\alpha} = \frac{k_{air} \cdot k_{r \alpha}}{\mu_\alpha} = k_{air} \cdot M_{r\alpha}(s)\end{array}$

where

$\begin{array}{l}\displaystyle k_\alpha(s)\end{array}$	formation permeability to fluid $\begin{array}{l}\alpha\end{array}$ -phase
$\begin{array}{l}\displaystyle \mu_\alpha\end{array}$	dynamic viscosity of fluid $\begin{array}{l}\alpha\end{array}$ -phase
$\begin{array}{l}\displaystyle k_{air}\end{array}$	absolute permeability to air
$\begin{array}{l}\displaystyle M_{r\alpha}(s) = \frac{k_{r \alpha}}{\mu_\alpha}\end{array}$	relative phase mobility
$\begin{array}{l}\displaystyle k_{r\alpha}(s)\end{array}$	relative formation permeability to fluid $\begin{array}{l}\alpha\end{array}$ -phase
$\begin{array}{l}s = \{ s_{\alpha}\}\end{array}$	reservoir saturation $\begin{array}{l}\sum_\alpha s_{\alpha} = 1\end{array}$ , $\begin{array}{l}\alpha\end{array}$ -phase saturation

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

$\begin{array}{l}s = \{ s_w, \, s_o, \, s_g \}\end{array}$	$\begin{array}{l}s_w + s_o + s_g =1\end{array}$
$\begin{array}{l}\displaystyle M_o = \frac{k_o}{\mu_o}\end{array}$	oil mobility
$\begin{array}{l}\displaystyle M_g = \frac{k_g}{\mu_g}\end{array}$	gas mobility
$\begin{array}{l}\displaystyle M_w = \frac{k_w}{\mu_w}\end{array}$	water mobility

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See also