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

\phi \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)

The alternative form is:

\phi \cdot c_t \cdot \mu \cdot \partial_t \Psi -   
 \nabla \cdot \left( k \cdot  \Big( \vec \nabla \Psi  - \frac{\rho^2}{\mu}  \, {\bf g} \Big)  \right) 
  = \sum_k q({\bf r}) \cdot \delta({\bf r}-{\bf r}_k)

where

Physical models of pressure diffusion can be split into two categories: Newtonian and Rheological (non-Newtonian) based on the fluid stress model.

Mathematical models of pressure diffusion can be split into three categories: Linear, Pseudo-linear and Non-linear. 

These models are built using Numerical, Analytical or Hybrid pressure diffusion solvers.

Many popular 1DR solutions can be approximated by Radial Flow Pressure Diffusion @model which has a big methodological value.

The simplest analytical solutions for pressure diffusion are given by 1DL Linear-Drive Solution (LDS) and 1DR Line Source Solution (LSS)

The table below shows a list of popular well and reservoir pressure diffusion models.

See also

Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Dynamics / Pressure Diffusion / Pressure Diffusion @model