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A generalization of Darcy equation for the flow with account for inertial (kinetic) effects at high velocity reservoir flow:

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-  \nabla p = \frac{\mu}{k} \, {\bf u} + \beta \, \rho \,  | {\bf u} | \, {\bf u}

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 is small for the small flow velocities (reducing Forchheimer equation t to Darcy equation) and grows quickly for high flow velocities.

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