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 fluid
$\begin{array}{l}\mu\end{array}$	dynamic viscosity of fluid

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.

But in most popular case of a 3-phase 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)	$\begin{array}{l}\displaystyle M = k_{air} \left[M_{rw} + \left( 1 + \frac{R_s \, B_g}{B_o} \right) \cdot M_{ro} + \left( 1 + \frac{R_v \, B_o}{B_g} \right) \cdot M_{rg} \right]\end{array}$

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

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

For the case of 2-phase Oil + Water fluid model (when Perrine model makes the most practical sense):

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

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

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

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See also