2p2c

Two-phase, two-component Darcy flow. More...

Description

Two-phase, two-component Darcy flow.

This model implements two-phase two-component flow of two compressible and partially miscible fluids \(\alpha \in \{ w, n \}\) composed of the two components \(\kappa \in \{ w, a \}\). 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 gets one transport equation for each component

\begin{eqnarray*} && \phi \frac{\partial (\sum_\alpha \varrho_\alpha \frac{M^\kappa}{M_\alpha} x_\alpha^\kappa S_\alpha )} {\partial t} - \sum_\alpha \text{div} \left\{ \varrho_\alpha \frac{M^\kappa}{M_\alpha} x_\alpha^\kappa \frac{k_{r\alpha}}{\mu_\alpha} \mathbf{K} (\textbf{grad}\, p_\alpha - \varrho_{\alpha} \mbox{\bf g}) \right\} \nonumber \\ \nonumber \\ &-& \sum_\alpha \text{div} \left\{ D_{\alpha,\text{pm}}^\kappa \varrho_{\alpha} \textbf{grad} X^\kappa_{\alpha} \right\} - \sum_\alpha q_\alpha^\kappa = 0 \qquad \kappa \in \{w, a\} \, , \alpha \in \{w, g\} \end{eqnarray*}

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.

By using constitutive relations for the capillary pressure \(p_c = p_n - p_w\) and relative permeability \(k_{r\alpha}\) and taking advantage of the fact that \(S_w + S_n = 1\) and \(x^\kappa_w + x^\kappa_n = 1\), the number of unknowns can be reduced to two. The used primary variables are, like in the two-phase model, either \(p_w\) and \(S_n\) or \(p_n\) and \(S_w\). The formulation which ought to be used can be specified by setting the Formulation property to either TwoPTwoCFormulation::pwsn or TwoPTwoCFormulation::pnsw. By default, the model uses \(p_w\) and \(S_n\). Moreover, the second primary variable depends on the phase state, since a primary variable switch is included. The phase state is stored for all nodes of the system. The model is able to use either mole or mass fractions. The property useMoles can be set to either true or false in the problem file. Make sure that the according units are used in the problem setup. useMoles is set to true by default. Following cases can be distinguished:

• Both phases are present: The saturation is used (either \(S_n\) or \(S_w\), dependent on the chosen Formulation), as long as \( 0 < S_\alpha < 1\).
• Only wetting phase is present: The mole fraction of, e.g., air in the wetting phase \(x^a_w\) is used, as long as the maximum mole fraction is not exceeded \((x^a_w<x^a_{w,max})\)
• Only non-wetting phase is present: The mole fraction of, e.g., water in the non-wetting phase, \(x^w_n\), is used, as long as the maximum mole fraction is not exceeded \((x^w_n<x^w_{n,max})\)

Modules
	Sequential
	Sequential two-phase, two-component Darcy flow.

Files
file	porousmediumflow/2p2c/model.hh
	Adaption of the fully implicit scheme to the two-phase two-component fully implicit model.
file	porousmediumflow/2p2c/volumevariables.hh
	Contains the quantities which are constant within a finite volume in the two-phase two-component model.

Classes
class	Dumux::TwoPTwoCVolumeVariablesBase< Traits, Impl >
	Contains the quantities which are constant within a finite volume in the two-phase two-component model. This is the base class for a 2p2c model with and without chemical nonequilibrium. More...
class	Dumux::TwoPTwoCVolumeVariablesImplementation< Traits, false, useConstraintSolver >
	Contains the quantities which are constant within a finite volume in the two-phase two-component model. Specialization for chemical equilibrium. More...
class	Dumux::TwoPTwoCVolumeVariablesImplementation< Traits, true, useConstraintSolver >
	Contains the quantities which are constant within a finite volume in the two-phase two-component model. Specialization for chemical non-equilibrium. The equilibrium mole fraction is calculated using Henry's and Raoult's law. More...
class	Dumux::WaterAirProblem< TypeTag >
	Non-isothermal gas injection problem where a gas (e.g. air) is injected into a fully water saturated medium. More...
class	Dumux::WaterAirSpatialParams< GridGeometry, Scalar >
	Definition of the spatial parameters for the water-air problem. More...

Typedefs
template<class Traits , bool useConstraintSolver = true>
using	Dumux::TwoPTwoCVolumeVariables = TwoPTwoCVolumeVariablesImplementation< Traits, Traits::ModelTraits::enableChemicalNonEquilibrium(), useConstraintSolver >
	Contains the quantities which are constant within a finite volume in the two-phase two-component model. More...

Typedef Documentation

TwoPTwoCVolumeVariables

template<class Traits , bool useConstraintSolver = true>

using Dumux::TwoPTwoCVolumeVariables = typedef TwoPTwoCVolumeVariablesImplementation<Traits, Traits::ModelTraits::enableChemicalNonEquilibrium(), useConstraintSolver>

Contains the quantities which are constant within a finite volume in the two-phase two-component model.