7.16.1.6. Darcy

Syntax

Ic For DofName ([{of} SpeciesName] | [{in} MaterialPhaseName] | [{ls} {a | b | c}]) {@ | at | for | on | over} MeshExtent = Darcy ([Gx = gx] | [Gy = gy] | [Gz = gz] | [Relative_To = relative_to])

Summary

Provides the Darcy velocity model.

Description

For phase $p$ , the velocity provided is

$\mathbf{u}_{p} = \phi S_p \mathbf{u}_{matrix} - \dfrac{k_{r,p}}{\mu_p} \mathbf{K}_s\left(\nabla P_p - \rho_p \mathbf{g}\right),$

where $\mathbf{u}_{matrix}$ is the optional matrix velocity as specified in the relative to parameter, $\phi$ is the porosity, $S_p$ is the optional phase saturation, $k_{r,p}$ is the relative permeability of the phase, $\mu_p$ is the dynamic viscosity of the phase, $\mathbf{K}_s$ is the intrinsic permeability tensor, $P_p$ is the phase pressure, $\rho_p$ is the density of the phase, and $\mathbf{g}$ is the gravitational acceleration vector.

If the optional phase saturation $S_p$ is provided, the pore volume is assumed to be occupied by multiple phases (e.g., liquid / gas) in accordance to their saturations, otherwise it is occupied fully by a single phase. Note, the sum of phase saturation should equal to one i.e., individual phase volumes should sum to the total pore volume.

Additionally, if the matrix is deforming, the optional relative to parameter should specify which phase should be used as the matrix velocity. For instance, relative to = solid_phase would ensure the velocity due to the pressure gradient is relative to the deforming solid matrix.

Lastly, note the Darcy velocity is the superficial velocity and is related to the pore scale velocity through the product of porosity and optional phase saturation.

Parameter	Value	Default
DofName	string	–
{of}	{of \| species \| subindex}	–
SpeciesName	string	–
{in}	{in \| material_phase}	–
MaterialPhaseName	string	–
{ls}	{levelset_phase \| ls}	–
MeshExtent	string	–
gx	real	0
gy	real	0
gz	real	0
relative_to	“string”	–