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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:
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\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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ReferenceDiscussion of liquid threshold pressure gradient, 2017.pdf |