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The general form of non-linear single-phase pressure diffusion model@model is given by:
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\beta({\bf r},p) \, \frac{\partial p}{\partial t} =phi \cdot c_t \cdot \partial_t p - \nabla \Bigleft( M \cdot ({ \bfnabla r},p, \nabla p) \cdot \nabla p \Bigp - \rho \cdot \mathbf{g} ) \right) - c \cdot M \cdot (\nabla p)^2 = \sum_k q({\bf r}) \cdot \delta({\bf r}-{\bf r}_k) |
with non-linear dependence of fluid mobility
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Below is the list of popular physical phenomena and their mathematical models which can be covered by
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Forchheimer Equation
Pressure diffusion equation is going to be:
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с_t \phi_e \frac{\partial p}{\partial t} = \nabla ( \frac{k(\nabla p)}{\mu} \nabla p) |
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Pressure diffusion / Pressure Diffusion @model / Single-phase pressure diffusion model / Non-linear single-phase pressure diffusion @model
Reference
Philipp Forchheimer (1886). "Über die Ergiebigkeit von Brunnen-Anlagen und Sickerschlitzen". Z. Architekt. Ing.-Ver. Hannover. 32: 539–563.