A property characterising agility of the multi-phase fluid under pressure gradient with account of relative permeability and dynamic fluid viscosity:

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

where

$\begin{array}{l}M\end{array}$	total fluid mobility
$\begin{array}{l}M_{r, \alpha}\end{array}$	relative phase mobility of $\begin{array}{l}\alpha\end{array}$ -phase
$\begin{array}{l}k_{air}\end{array}$	absolute permeability to air
$\begin{array}{l}s\end{array}$	reservoir saturation $\begin{array}{l}\{ s_w, \, s_o, \, s_g \}\end{array}$

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

(2)	$\begin{array}{l}\displaystyle M_{r}(s) = M_{r o}(s) + M_{r g}(s) + M_{r g}(s)\end{array}$


$\begin{array}{l}\displaystyle M_{ro} = \frac{k_{ro}}{\mu_o}\end{array}$	relative oil mobility
$\begin{array}{l}\displaystyle M_{rg} = \frac{k_{rg}}{\mu_g}\end{array}$	relative gas mobility
$\begin{array}{l}\displaystyle M_{rw} = \frac{k_{rw}}{\mu_w}\end{array}$	relative water mobility

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See also