The general form of non-linear single-phase pressure diffusion @model with the finite number of sources/sinks is given by:
| LaTeX Math Block |
|---|
| \phi \cdot c_t \cdot \partial_t p + \nabla {\bf u}
+ c \cdot ( {\bf u} \, \nabla p)
= \sum_k q_k(t) \cdot \delta({\bf r}-{\bf r}_k) |
|
| LaTeX Math Block |
|---|
| {\bf u} = - M \cdot ( \nabla p - \rho \, {\bf g}) |
|
where
The alternative form is:
| LaTeX Math Block |
|---|
|
\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
