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The general form of non-linear single-phase pressure diffusion model@model is given by: 

\beta({\bf r},p) \, \frac{\partial p}{\partial t} = \nabla \Big( M({\bf r},p, \nabla p) \cdot \nabla p \Bigphi \cdot c_t \cdot \partial_t p -   \nabla  \left( M \cdot ( \nabla p - \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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c_t({\bf r},p)  = c_r({\bf r},p) + \sum_\alpha s_\alpha({\bf r}) c_\alpha(p) 

where

The same account for non-linearity can be applied for non-linear multi-phase pressure diffusion when Pressure Diffusion Model Validity Scope is met and multi-phase pressure dynamics can be modeled as effective single-phase pressure dynamics.

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:

\с_t \phi_e \frac{\partial p}{\partial t} = \nabla ( \frac{k(\nabla p)}{\mu} \nabla p)

where

See also

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Pressure diffusion / Pressure Diffusion @model /  Single-phase pressure diffusion model  / Non-linear single-phase pressure diffusion @model

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