Pressure Diffusion @model

There is a large number of various pressure diffusion models.

The popular classifications are summarized below:

Number of phases	Number of wells	Equation Linearity	Computational Scheme	Spatial dimension
Single-phase	Single-well	Linear	Analytical	0D
Multi-phase	Multi-well	Pseudo-Linear	Numerical	1D
		Non-linear		2D
				3D

The usual combinations are:

Linear Analytical 1D	Pseudo-Linear Analytical 1D	Non-Linear Numerical 2D/3D
Single-phase Linear Analytical 1D	Single-phase Pseudo-Linear Analytical 1D	Single-phase Non-Linear Numerical 1D/2D/3D
Multi-phase Linear Analytical 1D	Multi-phase Pseudo-Linear Analytical 1D	Multi-phase Non-Linear Numerical 1D/2D/3D

In many practical cases a pressure diffusion process is honouring some PDE with constant coefficients availing a number of very efficient computational and diagnostic techniques:

Time Convolution	Spatial Superposition
Pressure convolution model	Pressure superposition model
Pressure deconvolution model	Pressure decomposition model

In some cases a pressure diffusion process can be fairly approximated by a hybrid model based on PDE with constant coefficients and PseudoPressure and PseudoTime.

There is a number of specific pressure diffusion models which represent the key practical scenarios of pressure diffusion and play important academical and practical role:

	Transient flow	Steady-State (SS) flow	Pseudo-Steady State (PSS) flow
Radial flow	Radial Flow Pressure Diffusion @model	Steady State Radial Flow Pressure Diffusion @model	Pseudo-Steady State Radial Flow Pressure Diffusion @model
Linear flow	Linear Flow Pressure Diffusion @model	Steady State Linear Pressure Diffusion @model	Pseudo-Steady State Linear Pressure Diffusion @model

The Pressure Diffusion @model consists of the following system components:

Pressure Diffusion Wellbore Storage @model

Pressure Diffusion Well Trajectory @model

Pressure Diffusion Well-Reservoir Contact @ model

Pressure Diffusion Reservoir @model

Pressure Diffusion Boundary @model

The table below shows a list of popular well and reservoir pressure diffusion models which in some cases maybe simulated with analytical methods to speed up the calculations.

Wellbore storage model	Well model	Reservoir model	Boundary model
Constant	Skin-factor	Homogeneous	Unconstrained
Fair	Vertical well	Dual-porosity		Infinite
Rate-dependant	Fractured vertical well	Dual-permeability	Fully constrained
	Limited entry well	Anisotropic reservoir		Circle No Flow / Circle Constant P_i
	Slanted well	Multi-layer reservoir		Rectangular No Flow / Rectangular Constant P_i
	Horizontal well	Linear-composite	Partially constrained
	Multifrac horizontal well	Radial-composite		Single fault
				Parallel faults
				Intersecting Faults

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Pressure Diffusion @model