version 3.9-dev

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:

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:

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...