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

#include <dune/common/fvector.hh>
#include <dumux/common/properties.hh>
#include <dumux/material/fluidmatrixinteractions/3p/thermalconductivitysomerton3p.hh>
#include <dumux/material/fluidmatrixinteractions/diffusivitymillingtonquirk.hh>
#include <dumux/porousmediumflow/properties.hh>
#include <dumux/porousmediumflow/3p/model.hh>
#include <dumux/porousmediumflow/nonisothermal/model.hh>
#include <dumux/porousmediumflow/nonisothermal/indices.hh>
#include <dumux/porousmediumflow/nonisothermal/iofields.hh>
#include <dumux/porousmediumflow/compositional/switchableprimaryvariables.hh>
#include "indices.hh"
#include "model.hh"
#include "volumevariables.hh"
#include "localresidual.hh"
#include "iofields.hh"

Description

The model is designed for simulating three fluid phases with water, gas, and a liquid contaminant (NAPL - non-aqueous phase liquid) This model implements three-phase two-component flow of three fluid phases \(\alpha \in \{ water, gas, NAPL \}\) each composed of up to two components \(\kappa \in \{ water, contaminant \}\). 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 components, one transport equation for each component is obtained as

\begin{eqnarray*} && \frac{\partial (\sum_\alpha \phi \varrho_\alpha X_\alpha^\kappa S_\alpha )}{\partial t} - \sum\limits_\alpha \nabla \cdot \left\{ \frac{k_{r\alpha}}{\mu_\alpha} \varrho_\alpha x_\alpha^\kappa \mathbf{K} (\nabla p_\alpha - \varrho_\alpha \mathbf{g}) \right\} \nonumber \\ \nonumber \\ && - \sum\limits_\alpha \nabla \cdot \left\{ D_{\alpha, \text{pm}}^\kappa \varrho_\alpha \frac{1}{M_\kappa} \nabla X^\kappa_{\alpha} \right\} - q^\kappa = 0 \qquad \forall \kappa , \; \forall \alpha, \end{eqnarray*}

where:

\( \phi \) is the porosity of the porous medium,
\( S_\alpha \) represents the saturation of phase \( \alpha \),
\( \rho_\alpha \) is the mass density of phase \( \alpha \),
\( X_\alpha^\kappa \) is the mass fraction of component \( \kappa \) in phase \( \alpha \),
\( x_\alpha^\kappa \) is the mole fraction of component \( \kappa \) in phase \( \alpha \),
\( v_\alpha \) is the velocity of phase \( \alpha \),
\( D_{\alpha, \text{pm}}^\kappa \) is the effective diffusivity of component \( \kappa \) in phase \( \alpha \),
\( M_\kappa \) is the molar mass of component \( \kappa \)
\( q_\alpha^\kappa \) is a source or sink term.

Note that these balance equations are molar.

The model uses commonly applied auxiliary conditions like \(S_w + S_n + S_g = 1\) for the saturations and \(x^w_\alpha + x^c_\alpha = 1\) for the mole fractions. 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 dependent on the locally present fluid phases An adaptive primary variable switch is included. The phase state is stored for all nodes of the system. Different cases can be distinguished:

... to be completed ...

Classes
struct	Dumux::ThreePWaterOilModelTraits< onlyGasPhase >
	Specifies a number properties of the three-phase two-component model. More...

struct	Dumux::Properties::TTag::ThreePWaterOilNI

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

struct	Dumux::Properties::FluidState< TypeTag, TTag::ThreePWaterOilNI >
	The fluid state which is used by the volume variables to store the thermodynamic state. This should be chosen appropriately for the model ((non-)isothermal, equilibrium, ...). This can be done in the problem. More...

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

struct	Dumux::Properties::ReplaceCompEqIdx< TypeTag, TTag::ThreePWaterOilNI >
	Set as default that no component mass balance is replaced by the total mass balance. More...

struct	Dumux::Properties::PrimaryVariables< TypeTag, TTag::ThreePWaterOilNI >
	The primary variables vector for the 3p water oil non-isothermal model. More...

struct	Dumux::Properties::OnlyGasPhaseCanDisappear< TypeTag, TTag::ThreePWaterOilNI >
	Determines whether a constraint solver should be used explicitly. More...

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

struct	Dumux::Properties::EffectiveDiffusivityModel< TypeTag, TTag::ThreePWaterOilNI >
	Use the model after Millington (1961) for the effective diffusivity. More...

struct	Dumux::Properties::UseMoles< TypeTag, TTag::ThreePWaterOilNI >

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

struct	Dumux::Properties::IOFields< TypeTag, TTag::ThreePWaterOilNI >
	Set the non-isothermal vkt output fields. 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/3pwateroil/model.hh:

Description

Classes

Namespaces