Sequential

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

Description

Sequential two-phase, two-component Darcy flow.

Pressure

Provides a Finite Volume implementation for the pressure equation of a compressible system with two components. An IMPES-like method is used for the sequential solution of the problem. Diffusion is neglected, capillarity can be regarded. Isothermal conditions and local thermodynamic equilibrium are assumed. Gravity is included.

\[ c_{total}\frac{\partial p}{\partial t} + \sum_{\kappa} \frac{\partial v_{total}}{\partial C^{\kappa}} \nabla \cdot \left( \sum_{\alpha} X^{\kappa}_{\alpha} \varrho_{\alpha} \bf{v}_{\alpha}\right) = \sum_{\kappa} \frac{\partial v_{total}}{\partial C^{\kappa}} q^{\kappa}, \]

where \(\bf{v}_{\alpha} = - \lambda_{\alpha} \bf{K} \left(\nabla p_{\alpha} + \rho_{\alpha} \bf{g} \right) \). \( c_{total} \) represents the total compressibility, for constant porosity this yields \( - \frac{\partial V_{total}}{\partial p_{\alpha}} \), \(p_{\alpha} \) denotes the phase pressure, \( \bf{K} \) the absolute permeability, \( \lambda_{\alpha} \) the phase mobility, \( \rho_{\alpha} \) the phase density and \( \bf{g} \) the gravity constant and \( C^{\kappa} \) the total Component concentration. See paper SPE 99619 or "Analysis of a Compositional Model for Fluid Flow in Porous Media" by Chen, Qin and Ewing for derivation.

The pressure base class FVPressure assembles the matrix and right-hand-side vector and solves for the pressure vector, whereas this class provides the actual entries for the matrix and RHS vector. The partial derivatives of the actual fluid volume \( v_{total} \) are gained by using a secant method.

Velocity

The finite volume model for the solution of the transport equation for compositional two-phase flow.

\[ \frac{\partial C^\kappa}{\partial t} = - \nabla \cdot \left( \sum_{\alpha} X^{\kappa}_{\alpha} \varrho_{alpha} \bf{v}_{\alpha}\right) + q^{\kappa}, \]

where \( \bf{v}_{\alpha} = - \lambda_{\alpha} \bf{K} \left(\nabla p_{\alpha} + \rho_{\alpha} \bf{g} \right) \). \( p_{\alpha} \) denotes the phase pressure, \( \bf{K} \) the absolute permeability, \( \lambda_{\alpha} \) the phase mobility, \( \rho_{\alpha} \) the phase density and \( \bf{g} \) the gravity constant and \( C^{\kappa} \) the total Component concentration. The whole flux contribution for each cell is subdivided into a storage term, a flux term and a source term. Corresponding functions (getFlux() and getFluxOnBoundary()) are provided, internal sources are directly treated.

Template Parameters

TypeTag

The Type Tag

Files
file	adaptiveproperties.hh
	Defines the properties required for the adaptive sequential 2p2c models.
file	2p2c/sequential/celldata.hh
	Storage container for discretized data of the constitutive relations for one element.
file	c/sequential/celldataadaptive.hh
	Class including the variables and data of discretized data of the constitutive relations for one element.
file	celldatamultiphysics.hh
	Storage container for discretized data for multi-physics models.
file	2p2c/sequential/fluxdata.hh
	Class including the variables and data of discretized data of the constitutive relations.
file	fv2dpressureadaptive.hh
	Finite Volume Diffusion Model.
file	fv2dtransportadaptive.hh
	Finite volume discretization of the component transport equation.
file	fv3dpressureadaptive.hh
	Finite volume diffusion model.
file	fv3dtransportadaptive.hh
	Finite volume discretization of the component transport equation.
file	fvmpfal3dinteractionvolumecontaineradaptive.hh
	Interaction volume container for compositional adaptive 3-d (using MPFA L-method).
file	fvpressure.hh
	Finite volume 2p2c pressure model.
file	fvpressurecompositional.hh
	Base class for compositional pressure equations.
file	fvpressuremultiphysics.hh
	Finite volume 2p2c pressure model with multi-physics.
file	fvtransport.hh
	Finite volume discretization of the component transport equation.
file	fvtransportmultiphysics.hh
	Finite volume discretization of the component transport equation.
file	porousmediumflow/2p2c/sequential/problem.hh
	Base class for sequential 2p2c compositional problems.
file	porousmediumflow/2p2c/sequential/properties.hh
	Defines the properties required for the sequential 2p2c models.
file	2p2c/sequential/variableclassadaptive.hh
	Base class holding the variables for sequential models.

Classes
struct	Dumux::SequentialTwoPTwoCIndicesAdaptive< TypeTag >
	Missing indices to the mpfa2p model. More...
class	Dumux::CellData2P2C< TypeTag >
	Storage container for discretized data of the constitutive relations for one element. More...
class	Dumux::CellData2P2CAdaptive< TypeTag >
	Class including the data of a grid cell needed if an adaptive grid is used. More...
class	Dumux::CellData2P2CMultiPhysics< TypeTag >
	Storage container for discretized data for multiphysics models. More...
class	Dumux::FluxData2P2C< TypeTag >
	Class including the variables and data of discretized data of the constitutive relations. More...
class	Dumux::FV2dPressure2P2CAdaptive< TypeTag >
	The finite volume model for the solution of the compositional pressure equation. More...
class	Dumux::FV2dTransport2P2CAdaptive< TypeTag >
	Compositional Transport step in a Finite Volume discretization for a adaptive 2D-grid. More...
class	Dumux::FV3dPressure2P2CAdaptive< TypeTag >
	The finite volume model for the solution of the compositional pressure equation. More...
class	Dumux::FV3dTransport2P2CAdaptive< TypeTag >
	Compositional transport step in a finite volume discretization. More...
class	Dumux::FvMpfaL3d2P2CInteractionVolumeContainerAdaptive< TypeTag >
	Interaction volume container for compositional adaptive 3-d (using MPFA L-method) Model. More...
class	Dumux::FVPressure2P2C< TypeTag >
	The finite volume model for the solution of the compositional pressure equation. More...
class	Dumux::FVPressureCompositional< TypeTag >
	The finite volume model for the solution of the compositional pressure equation. More...
class	Dumux::FVPressure2P2CMultiPhysics< TypeTag >
	The finite volume model for the solution of the compositional pressure equation. More...
class	Dumux::FVTransport2P2C< TypeTag >
	Compositional transport step in a Finite Volume discretization. More...
class	Dumux::FVTransport2P2CMultiPhysics< TypeTag >
	Compositional transport step in a finite volume discretization. More...
class	Dumux::IMPETProblem2P2C< TypeTag >
	Base class for all compositional 2-phase problems which use an impet algorithm. More...
class	Dumux::VariableClass2P2CAdaptive< TypeTag >
	Class holding additionally mpfa data of adaptive compositional models. More...