2p1c

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

Description

A two-phase one-component flow model using the fully implicit scheme.

Note

The 2p1c model requires the use of the non-isothermal extension found in dumux/porousmediumflow/nonisothermal.

This model is designed for simulating two fluid phases with water as the only component. It is particularly suitable for the simulation of steam injection in saturated conditions.

The model implements the flow of two phases and one component, i.e. a pure liquid (e.g. water) and its vapor (e.g. steam), $\alpha \in \{w,n\}$ using a standard multi-phase Darcy approach 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 phase mass, one gets

$$\begin{gathered} \frac{\partial \sum _{\alpha }(\varphi {\rho }_{\alpha }{S}_{\alpha })}{\partial t} \\ -\sum _{\alpha }\mathrm{\nabla }\cdot \{{\rho }_{\alpha }\frac{k_{r\alpha }}{{\mu }_{\alpha }}\mathbf{K}(\mathrm{\nabla }{p}_{\alpha }-{\rho }_{\alpha }\mathbf{g})\}-q^w=0, \end{gathered}$$

where:

• $\varphi$ is the porosity of the porous medium,
• $S_{\alpha }$ represents the saturation of phase $\alpha$,
• ${\rho }_{\alpha }$ is the mass density of phase $\alpha$,
• $k_{r\alpha }$ is the relative permeability of phase $\alpha$,
• ${\mu }_{\alpha }$ is the dynamic viscosity of phase $\alpha$,
• $\mathbf{K}$ is the intrinsic permeability tensor,
• $p_{\alpha }$ is the pressure of phase $\alpha$,
• $\mathbf{g}$ is the gravitational acceleration vector,
• $q^w$ is a source or sink term.

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 $S_w+S_n=1$, the number of unknowns can be reduced to two. The model features a primary variable switch. If only one phase is present, $p_n$ and $T$ are the primary variables. In the presence of two phases, $p_n$ and $S_w$ become the new primary variables.

Files
file	porousmediumflow/2p1c/darcyslaw.hh
file	porousmediumflow/2p1c/indices.hh
file	porousmediumflow/2p1c/iofields.hh
file	porousmediumflow/2p1c/localresidual.hh
file	porousmediumflow/2p1c/model.hh
	A two-phase one-component flow model using the fully implicit scheme.
file	2p1c/primaryvariableswitch.hh
file	porousmediumflow/2p1c/volumevariables.hh

Classes
class	Dumux::TwoPOneCDarcysLaw< TypeTag >
	Specialization of Darcy's Law for the two-phase one-component model, including a the possibility to block spurious fluxes of cold water into the steam zone, which can improve the model's convergence behavior (Gudbjerg et al., 2005) [45]. More...
class	Dumux::TwoPOneCIndices
	The indices for the two-phase one-component model. More...
class	Dumux::TwoPOneCIOFields
	Adds I/O fields specific to two-phase one-component model. More...
class	Dumux::TwoPOneCLocalResidual< TypeTag >
	Element-wise calculation of the residual for the fully implicit two-phase one-component flow model. More...
struct	Dumux::TwoPOneCNIModelTraits< f >
	Specifies a number properties of models considering two phases with water as a single component. More...
struct	Dumux::TwoPOneCVolumeVariablesTraits< PV, FSY, FST, SSY, SST, PT, MT >
	Traits class for the two-phase model. More...
class	Dumux::TwoPOneCPrimaryVariableSwitch
	The primary variable switch for the two-phase one-component model. More...
class	Dumux::TwoPOneCVolumeVariables< Traits >
	The volume variables (i.e. secondary variables) for the two-phase one-component model. More...