About Fracture Flow
The Fracture Flow interface uses tangential derivatives to define the flow along the interior boundaries representing fractures within a porous (or solid) block. Use this physics interface on boundaries in 3D, 2D, and axisymmetric geometries.
Fracture Flow is also available as a boundary condition in the Darcy’s Law and Richards’ Equation interfaces.
The physics interface uses the tangential version of Darcy’s law:
(4-37)
Here, qf is the volume flow rate per unit length in the fracture, κf is the fracture’s permeability, μ is the fluid dynamic viscosity, df is the aperture or fracture thickness, ∇T denotes the gradient operator restricted to the fracture’s tangential plane, p is the pressure, ρ is the fluid density, g is the acceleration of gravity, and D represents the vertical coordinate.
Gravity effects are not active by default. Select the check box Include gravity to activate the acceleration of gravity. Setting the elevation D to zero also turns off gravity effects.
The variable qf gives the volume flow rate per unit length of the fracture. The mean fluid velocity within the fracture is uf = qf/df.
It is also possible to use the hydraulic conductivity of the fracture, Kf (SI unit: m/s), to define the capacity to transmit flow instead of using the fracture’s permeability κf and fluid viscosity μ. These quantities are related by
The hydraulic conductivity represents properties of both fluid and porous matrix. If the model is defined using the hydraulic conductivity, Equation 4-37 changes to
(4-38)
The Cubic law equation describes the permeability of the fracture from the aperture or fracture’s thickness df and the roughness factor ff
If the model is defined using the Cubic law equation, the expression for flow rate per unit length in the fracture in Equation 4-37 changes to
(4-39)
Together with the material properties, Equation 4-37 above, in combination with the continuity equation integrated over the fracture cross section, produces a single equation for the pressure.
(4-40)
where εf is the fracture porosity, and Qm is the mass source term (SI unit: kg/(m3·s)). The aperture or fracture thickness df can vary along the fracture and therefore appears on both sides of the equation.
The physics interface solves for the same dependent variable as for the equation in the porous medium, the pressure p.