3p3c

Three-phase, three-component Darcy flow. More...

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. 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,mol} x_\alpha^\kappa S_\alpha )}{\partial t} - \sum\limits_\alpha \nabla \cdot \left\{ \frac{k_{r\alpha}}{\mu_\alpha} \varrho_{\alpha,mol} x_\alpha^\kappa \mathbf{K} (\nabla p_\alpha - \varrho_{\alpha,mass} \mathbf{g}) \right\} \nonumber \\ \nonumber \\ && - \sum\limits_\alpha \nabla \cdot \left\{ D_{\alpha, \text{pm}}^\kappa \frac{1}{M_{\kappa}} \varrho_{\alpha} \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 \(x^w_\alpha + x^a_\alpha + x^c_\alpha = 1\) 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 \((S_w\), \(x_w^g\), \(p_g)\).

Files
file	porousmediumflow/3p3c/indices.hh
	Defines the indices required for the three-phase three-component fully implicit model.
file	porousmediumflow/3p3c/iofields.hh
	Adds I/O fields specific to the three-phase three-component model.
file	porousmediumflow/3p3c/localresidual.hh
	Element-wise calculation of the Jacobian matrix for problems using the three-phase three-component fully implicit model.
file	porousmediumflow/3p3c/model.hh
	Adaption of the fully implicit scheme to the three-phase three-component flow model.
file	3p3c/primaryvariableswitch.hh
	The primary variable switch for the 3p3c model.
file	porousmediumflow/3p3c/volumevariables.hh
	Contains the quantities which are constant within a finite volume in the three-phase three-component model.

Classes
class	Dumux::ThreePThreeCIndices
	The indices for the isothermal three-phase three-component model. More...
class	Dumux::ThreePThreeCIOFields
	Adds I/O fields specific to the three-phase three-component model. More...
class	Dumux::ThreePThreeCLocalResidual< TypeTag >
	Element-wise calculation of the Jacobian matrix for problems using the three-phase three-component fully implicit model. More...
struct	Dumux::ThreePThreeCModelTraits< useCS, useMol >
	Specifies a number properties of two-phase models. More...
class	Dumux::ThreePThreeCPrimaryVariableSwitch
	The primary variable switch controlling the phase presence state variable. More...
class	Dumux::ThreePThreeCVolumeVariables< Traits >
	Contains the quantities which are are constant within a finite volume in the three-phase three-component model. More...