3p

Three-phase (immiscible) Darcy flow. More...

Description

Adaption of the fully implicit scheme to the three-phase flow model.

This model implements three-phase flow of three fluid phases \(\alpha \in \{ water, gas, NAPL \}\). The standard multiphase Darcy approach is used as the equation for the conservation of momentum. For details on Darcy's law see dumux/flux/darcyslaw.hh.

By inserting Darcy's law into the equations for the conservation of the phase mass, one gets

\[ \frac{\partial (\phi \varrho_\alpha S_\alpha )}{\partial t} - \nabla \cdot \left\{ \varrho_\alpha \frac{k_{r\alpha}}{\mu_\alpha} \mathbf{K} \left(\nabla p_\alpha - \varrho_{\alpha} \mathbf{g} \right) \right\} - q_\alpha = 0, \]

where:

• \( \phi \) is the porosity of the porous medium,
• \( S_\alpha \) represents the saturation of phase \( \alpha \),
• \( \varrho_\alpha \) is the mass density of phase \( \alpha \),
• \( k_{r\alpha} \) is the relative permeability of phase \( \alpha \),
• \( \mu_\alpha \) is the dynamic viscosity of phase \( \alpha \),
• \( \mathbf{K} \) is the intrinsic permeability tensor,
• \( p_\alpha \) is the pressure of phase \( \alpha \),
• \( \mathbf{g} \) is the gravitational acceleration vector,
• \( q_\alpha \) is a source or sink term.

The model uses commonly applied auxiliary conditions like \(S_w + S_n + S_g = 1\) for the saturations. Furthermore, the phase pressures are related to each other via capillary pressures between the fluid phases, which are functions of the saturation, e.g. according to the approach of Parker et al.

The used primary variables are gas phase pressure \(p_g\), water saturation \(S_w\) and NAPL saturation \(S_n\).

Files
file	porousmediumflow/3p/indices.hh
	Defines the indices for the three-phase model.
file	porousmediumflow/3p/iofields.hh
	Adds I/O fields specific to the three-phase model.
file	porousmediumflow/3p/model.hh
	Adaption of the fully implicit scheme to the three-phase flow model.
file	porousmediumflow/3p/volumevariables.hh
	Contains the quantities which are constant within a finite volume in the three-phase model.

Classes
class	Dumux::ThreePIndices
	The common indices for the isothermal three-phase model. More...
class	Dumux::ThreePIOFields
	Adds I/O fields specific to the three-phase model. More...
struct	Dumux::ThreePModelTraits
	Specifies a number properties of three-phase models. More...
struct	Dumux::ThreePVolumeVariablesTraits< PV, FSY, FST, SSY, SST, PT, MT >
	Traits class for the two-phase model. More...
class	Dumux::ThreePVolumeVariables< Traits >
	Contains the quantities which are constant within a finite volume in the three-phase model. More...