Dispersion Tensors

Dispersion tensor models characterising mechanical dispersion in porous media. More...

Description

Mechanical dispersion is caused by particles traveling at different velocities through the porous medium [45]. A particle in the middle of a pore has a higher velocity than a particle close to a grain. Due to the tortuosity of the porous medium, particles take different paths through it. Given the existence of an REV, mechanical dispersion typically leads to increased Fickian diffusion on the Darcy scale [15]. The magnitude and directionality of the increase diffusive transport depends on the size of the averaging volumes and characteristics of the flow such as average velocity magnitude and direction. The following classes can be implemented.

Full dispersion tensor

The full dispersion tensor is given by the spatial parameters.

Scheidegger's dispersion tensor

This class calculates the dispersion tensor for compositional and thermal models using Scheidegger's model. The dispersion tensor is given by:

\[D = \frac{\mathbf{v} \mathbf{v}^T}{\|\mathbf{v}\|} \cdot (\alpha_L - \alpha_T) + \|\mathbf{v}\| \cdot \alpha_T \cdot \mathbf{I} \]

where \(\mathbf{v}\) is the velocity vector, \(\alpha_L\) and \(\alpha_T\) are the longitudinal and transverse dispersivities, respectively, and \(\mathbf{I}\) is the identity matrix. The velocity is either taken from the spatial parameters or, for the box method, evaluated with the potential gradient of the advection type (AdvectionType::potentialGradient), i.e. with the same density in the gravity term as the advective flux. The dispersivities are taken from the spatial parameters.

Classes
class	Dumux::FullDispersionTensor< TypeTag >
	Full dispersion tensor. More...
class	Dumux::ScheideggersDispersionTensor< TypeTag >
	Scheidegger's dispersion tensor. More...

Files
file	fulltensor.hh
	Full dispersion tensor.
file	scheidegger.hh
	Scheidegger's dispersion tensor.