| (1) | \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) |
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.
| Wellbore storage model | Well model | Reservoir model | Boundary model |
|---|---|---|---|
| Constant | Skin-factor | Homogeneous | Infinite |
| Fair | Vertical well | Dual-porosity | Circle No Flow |
| Rate-dependant | Dual-permeability | Circle Constant Pi | |
| Limited entry well | Anisotropic reservoir | Single fault | |
| Horizontal well | Multi-layer reservoir | Parallel faults | |
| Slanted well | Linear-composite | Intersecting Faults | |
| Radial-composite |
See also
Pressure diffusion / Pressure Diffusion @model