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- \nabla p = \frac{\mu}{k} \, {\bf u} + \beta \, \rho \, | {\bf u} | \, {\bf u} |
where
Forchheimer coefficient depends on flow regime and formation permeability as:
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Forchheimer equation can be approximated by non-linear permeability model as:
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| {\bf u} = - \frac{k}{\mu} \, k_f \, \nabla p |
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| k_f(|\nabla p|) = \frac{2}{w} \big[ 1- \sqrt{1-w} \big] |
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| w = 4 \, \left(\frac{k}{\mu} \right)^2 \, \beta \, \rho \, |\nabla p| \, < \, 1 |
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See also
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Physics / Fluid Dynamics / Percolation
[ Darcy Flow Equation ]
Reference
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Philipp Forchheimer (1886). "Über die Ergiebigkeit von Brunnen-Anlagen und Sickerschlitzen". Z. Architekt. Ing.-Ver. Hannover. 32: 539–563.
