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

#include <dune/common/fvector.hh>
#include <dumux/common/properties.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 <dumux/material/fluidstates/compositional.hh>
#include <dumux/material/spatialparams/fv.hh>
#include <dumux/material/fluidmatrixinteractions/diffusivitymillingtonquirk.hh>
#include <dumux/material/fluidmatrixinteractions/3p/thermalconductivitysomerton3p.hh>
#include "indices.hh"
#include "volumevariables.hh"
#include "iofields.hh"
#include "localresidual.hh"

Description

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

This model implements three-phase three-component flow of three fluid phases \(\alpha \in \{ water, gas, NAPL \}\) each composed of up to three components \(\kappa \in \{ water, air, contaminant \}\). The standard multiphase Darcy approach is used as the equation for the conservation of momentum:

\[ v_\alpha = - \frac{k_{r\alpha}}{\mu_\alpha} \mathbf{K} \left(\textbf{grad}\, p_\alpha - \varrho_{\alpha} \mbox{\bf g} \right) \]

By inserting this into the equations for the conservation of the components, one transport equation for each component is obtained as

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

Note that these balance equations are molar.

All equations are discretized using a vertex-centered finite volume (box) or cell-centered finite volume scheme as spatial and the implicit Euler method as time discretization.

The model uses commonly applied auxiliary conditions like \(S_w + S_n + S_g = 1\) for the saturations and \(x^w_\alpha + x^a_\alpha + x^c_\alpha = 1\) 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. The following cases can be distinguished:

All three phases are present: Primary variables are two saturations \((S_w\) and \(S_n)\), and a pressure, in this case \(p_g\).
Only the water phase is present: Primary variables are now the mole fractions of air and contaminant in the water phase \((x_w^a\) and \(x_w^c)\), as well as the gas pressure, which is, of course, in a case where only the water phase is present, just the same as the water pressure.
Gas and NAPL phases are present: Primary variables \((S_n\), \(x_g^w\), \(p_g)\).
Water and NAPL phases are present: Primary variables \((S_n\), \(x_w^a\), \(p_g)\).
Only gas phase is present: Primary variables \((x_g^w\), \(x_g^c\), \(p_g)\).
Water and gas phases are present: Primary variables \((S_w\), \(x_w^g\), \(p_g)\).

Classes
struct	Dumux::ThreePThreeCModelTraits< useCS, useMol >
	Specifies a number properties of two-phase models. More...

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

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

struct	Dumux::Properties::BaseModelTraits< TypeTag, TTag::ThreePThreeC >
	Set the model traits. More...

struct	Dumux::Properties::ModelTraits< TypeTag, TTag::ThreePThreeC >

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

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

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

struct	Dumux::Properties::PrimaryVariables< TypeTag, TTag::ThreePThreeC >
	The primary variables vector for the 3p3c model. More...

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

struct	Dumux::Properties::EffectiveDiffusivityModel< TypeTag, TTag::ThreePThreeC >
	The model after Millington (1961) is used for the effective diffusivity. More...

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

struct	Dumux::Properties::UseMoles< TypeTag, TTag::ThreePThreeC >
	Use mole fractions in the balance equations by default. More...

struct	Dumux::Properties::ModelTraits< TypeTag, TTag::ThreePThreeCNI >
	Set non-isothermal NumEq. More...

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

struct	Dumux::Properties::IOFields< TypeTag, TTag::ThreePThreeCNI >
	Set the non-isothermal vktoutputfields. More...

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

Namespaces
namespace	Dumux

namespace	Dumux::Properties

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

Include dependency graph for porousmediumflow/3p3c/model.hh:

Description

Classes

Namespaces