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where 

LaTeX Math Inline
body{\bf e}_{\nabla p} = \frac{\nabla p}{|\nabla p|}
 – unit vector along the pressure gradient.


At high flow velocities and pressure gradients the model is reducing to Darcy equation.


This model can be reformulated in terms of non-linear permeability model:

...

LaTeX Math Block
anchorPIVFY
alignmentleft
\begin{equation*}
 \begin{cases}
   k(|\nabla p|) = k_0 \, ( 1 - \frac{G}{|\nabla p|} ), & |\nabla p| > G,
   \\
   k(|\nabla p|) = 0, & |\nabla p|  \leq G .
 \end{cases}
\end{equation*} 

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