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 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
and is threshold pressure gradient (TPG) and represents the minimum pressure gradient required to initiate the reservoir flow.
This model can be reformulated in terms of non-linear permeability model:
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