A quantity (usually denoted as ) representing the minimum pressure gradient required to initiate the reservoir flow:

\begin{equation*}
 \begin{cases}
   {\bf u}= - \frac{k}{\mu}  ( \nabla p   - G \, {\bf e}_{\nabla p} ), & |\nabla p| > G,
   \\
   {\bf u}= 0, & |\nabla p|  \leq G .
 \end{cases}
\end{equation*}

where – 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:

{\bf u}= - \frac{k(|\nabla p|)}{\mu}  \nabla p

where is defined as:

\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*}

Reference

Discussion of liquid threshold pressure gradient, 2017.pdf