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

#include <dumux/common/properties.hh>
#include <dumux/material/fluidstates/immiscible.hh>
#include <dumux/material/fluidmatrixinteractions/3p/thermalconductivitysomerton3p.hh>
#include <dumux/porousmediumflow/properties.hh>
#include <dumux/porousmediumflow/immiscible/localresidual.hh>
#include <dumux/porousmediumflow/nonisothermal/model.hh>
#include <dumux/porousmediumflow/nonisothermal/indices.hh>
#include <dumux/porousmediumflow/nonisothermal/iofields.hh>
#include "indices.hh"
#include "volumevariables.hh"
#include "iofields.hh"

Description

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 \(S_n\).

Classes
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...

struct	Dumux::Properties::TTag::ThreeP
	The type tags for the isothermal three-phase model. More...

struct	Dumux::Properties::TTag::ThreePNI
	The type tags for the non-isothermal three-phase model. More...

struct	Dumux::Properties::ModelTraits< TypeTag, TTag::ThreeP >
	Set the model traits. More...

struct	Dumux::Properties::LocalResidual< TypeTag, TTag::ThreeP >
	The local residual function of the conservation equations. More...

struct	Dumux::Properties::VolumeVariables< TypeTag, TTag::ThreeP >
	Set the volume variables property. More...

struct	Dumux::Properties::FluidState< TypeTag, TTag::ThreeP >
	The fluid state which is used by the volume variables to store the thermodynamic state. More...

struct	Dumux::Properties::IOFields< TypeTag, TTag::ThreeP >
	Set the vtk output fields specific to this model. More...

struct	Dumux::Properties::ThermalConductivityModel< TypeTag, TTag::ThreePNI >
	Somerton is used as default model to compute the effective thermal heat conductivity. More...

struct	Dumux::Properties::IOFields< TypeTag, TTag::ThreePNI >
	Set non-isothermal output fields. More...

struct	Dumux::Properties::ModelTraits< TypeTag, TTag::ThreePNI >
	Set non-isothermal model traits. More...

struct	Dumux::Properties::VolumeVariables< TypeTag, TTag::ThreePNI >
	Set the volume variables property. More...

Namespaces
namespace	Dumux

namespace	Dumux::Properties
	The energy balance equation for a porous solid.

namespace	Dumux::Properties::TTag
	Type tag for numeric models.

Include dependency graph for porousmediumflow/3p/model.hh:

Description

Classes

Namespaces