Three-phase, two-component Darcy flow with water (liquid & gas) and oil. More...

Description

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

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 ...

Files
file	porousmediumflow/3pwateroil/indices.hh
	Defines the indices required for the 3p2cni model.

file	porousmediumflow/3pwateroil/iofields.hh
	Adds I/O fields specific to the three-phase three-component model.

file	porousmediumflow/3pwateroil/localresidual.hh
	Element-wise calculation of the Jacobian matrix for problems using the three-phase three-component fully implicit model.

file	porousmediumflow/3pwateroil/model.hh
	Adaption of the fully implicit scheme to the three-phase water oil flow model.

file	3pwateroil/primaryvariableswitch.hh
	The primary variable switch for the 3p3c model.

file	porousmediumflow/3pwateroil/volumevariables.hh
	Contains the quantities which are constant within a finite volume in the three-phase, two-component model.

Classes
class	Dumux::ThreePWaterOilIndices
	The indices for the isothermal 3p2cni model. More...

class	Dumux::ThreePWaterOilIOFields
	Adds I/O fields specific to the three-phase three-component model. More...

class	Dumux::ThreePWaterOilLocalResidual< TypeTag >
	Element-wise calculation of the local residual for problems using the ThreePWaterOil fully implicit model. More...

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

class	Dumux::ThreePWaterOilPrimaryVariableSwitch
	The primary variable switch controlling the phase presence state variable. More...

class	Dumux::ThreePWaterOilVolumeVariables< Traits >
	Contains the quantities which are are constant within a finite volume in the three-phase, two-component model. More...

Description

Files

Classes