...
A quantity (usually denoted as
) representing the minimum pressure gradient required to initiate the reservoir flow
.: LaTeX Math Block |
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|
\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
LaTeX Math Inline |
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body | {\bf e}_{\nabla p} = \frac{\nabla p}{|\nabla p|} |
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– 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:
...
where
os is defined as:
LaTeX Math Block |
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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*} |