A property characterizing agility of the fluid under pressure gradient as a ratio of reservoir permeability by dynamic fluid viscosity:

(1)	$\begin{array}{l}\displaystyle M = \frac{k}{\mu}\end{array}$

where

$\begin{array}{l}k\end{array}$	formation permeability to a given fluid (which vary for different fluids)
$\begin{array}{l}\mu\end{array}$	dynamic fluid viscosity

In multiphase flow the concept of total fluid mobility is not well-defined as phases may have different mobilities and flow quite independently from each other, having different pressures, moving at different velocities and segregated in space.

In most popular case of a 3-phase Oil + Gas + Water fluid model with relatively homogeneous flow (phases may move at different velocities but occupy the same reservoir space and have the same pressure) the multi-phase mobility may be defined by Perrine model:

(2)	$\begin{array}{l}\displaystyle M = k_{air} \cdot \left[M_{rw} + \left( 1 + \frac{R_s \, B_g}{B_o} \right) \cdot M_{ro} + \left( 1 + \frac{R_v \, B_o}{B_g} \right) \cdot M_{rg} \right]\end{array}$

$\begin{array}{l}\displaystyle \Rightarrow\end{array}$

(3)	$\begin{array}{l}\displaystyle \left< \frac{k}{\mu} \right> = k_{air} \cdot \left[ \frac{k_{rw}}{\mu_w} + \left( 1 + \frac{R_s \, B_g}{B_o} \right) \cdot \frac{k_{ro}}{\mu_o} + \left( 1 + \frac{R_v \, B_o}{B_g} \right) \cdot \frac{k_{rg}}{\mu_g} \right]\end{array}$

In case of 2-phase Oil + Water fluid model with regular to small values of $\begin{array}{l}R_s\end{array}$ (when Perrine model makes the most practical sense):

(4)	$\begin{array}{l}\displaystyle M = k_{air} \cdot \left[ M_{rw} + M_{ro} \right]\end{array}$

$\begin{array}{l}\displaystyle \Rightarrow\end{array}$

(5)	$\begin{array}{l}\displaystyle \left< \frac{k}{\mu} \right> = k_{air} \cdot \left[ \frac{k_{rw}}{\mu_w} + \frac{k_{ro}}{\mu_o} \right]\end{array}$

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See also