OPM - Reference Documentation for ewoms

A compositional multi-phase model based on non-linear complementarity functions. More...

#include <opm/material/localad/Math.hpp>
#include "ncpproperties.hh"
#include "ncplocalresidual.hh"
#include "ncpextensivequantities.hh"
#include "ncpprimaryvariables.hh"
#include "ncpboundaryratevector.hh"
#include "ncpratevector.hh"
#include "ncpintensivequantities.hh"
#include "ncpnewtonmethod.hh"
#include "ncpindices.hh"
#include <ewoms/models/common/multiphasebasemodel.hh>
#include <ewoms/models/common/energymodule.hh>
#include <ewoms/models/common/diffusionmodule.hh>
#include <ewoms/io/vtkcompositionmodule.hh>
#include <ewoms/io/vtkenergymodule.hh>
#include <ewoms/io/vtkdiffusionmodule.hh>
#include <opm/common/ErrorMacros.hpp>
#include <opm/common/Exceptions.hpp>
#include <dune/common/fvector.hh>
#include <dune/common/unused.hh>
#include <sstream>
#include <string>
#include <vector>
#include <array>

Include dependency graph for ncpmodel.hh:

Go to the source code of this file.

Classes
class	Ewoms::NcpModel< TypeTag >
	A compositional multi-phase model based on non-linear complementarity functions. More...

class	Ewoms::NcpModel< TypeTag >
	A compositional multi-phase model based on non-linear complementarity functions. More...

Namespaces
	Ewoms

	Ewoms::Properties

Functions
	Ewoms::Properties::NEW_TYPE_TAG (NcpModel, INHERITS_FROM(MultiPhaseBaseModel, VtkComposition, VtkEnergy, VtkDiffusion))
	Define the type tag for the compositional NCP model. More...

	Ewoms::Properties::SET_TYPE_PROP (NcpModel, LocalResidual, Ewoms::NcpLocalResidual< TypeTag >)
	Use the Ncp local jacobian operator for the compositional NCP model. More...

	Ewoms::Properties::SET_TYPE_PROP (NcpModel, NewtonMethod, Ewoms::NcpNewtonMethod< TypeTag >)
	Use the Ncp specific newton method for the compositional NCP model. More...

	Ewoms::Properties::SET_TYPE_PROP (NcpModel, Model, Ewoms::NcpModel< TypeTag >)
	the Model property More...

	Ewoms::Properties::SET_TYPE_PROP (NcpModel, BaseProblem, Ewoms::MultiPhaseBaseProblem< TypeTag >)
	The type of the base base class for actual problems. More...

	Ewoms::Properties::SET_BOOL_PROP (NcpModel, EnableEnergy, false)
	Disable the energy equation by default. More...

	Ewoms::Properties::SET_BOOL_PROP (NcpModel, EnableDiffusion, false)
	disable diffusion by default More...

	Ewoms::Properties::SET_TYPE_PROP (NcpModel, RateVector, Ewoms::NcpRateVector< TypeTag >)
	the RateVector property More...

	Ewoms::Properties::SET_TYPE_PROP (NcpModel, BoundaryRateVector, Ewoms::NcpBoundaryRateVector< TypeTag >)
	the BoundaryRateVector property More...

	Ewoms::Properties::SET_TYPE_PROP (NcpModel, PrimaryVariables, Ewoms::NcpPrimaryVariables< TypeTag >)
	the PrimaryVariables property More...

	Ewoms::Properties::SET_TYPE_PROP (NcpModel, IntensiveQuantities, Ewoms::NcpIntensiveQuantities< TypeTag >)
	the IntensiveQuantities property More...

	Ewoms::Properties::SET_TYPE_PROP (NcpModel, ExtensiveQuantities, Ewoms::NcpExtensiveQuantities< TypeTag >)
	the ExtensiveQuantities property More...

	Ewoms::Properties::SET_INT_PROP (NcpModel, NcpNewtonNumChoppedIterations, 3)
	truncate the newton update for the first 3 iterations of a time step More...

	Ewoms::Properties::SET_TYPE_PROP (NcpModel, Indices, Ewoms::NcpIndices< TypeTag, 0 >)
	The indices required by the compositional NCP model. More...

	Ewoms::Properties::SET_SCALAR_PROP (NcpModel, NcpPressureBaseWeight, 1.0)
	The unmodified weight for the pressure primary variable. More...

	Ewoms::Properties::SET_SCALAR_PROP (NcpModel, NcpSaturationsBaseWeight, 1.0)
	The weight for the saturation primary variables. More...

	Ewoms::Properties::SET_SCALAR_PROP (NcpModel, NcpFugacitiesBaseWeight, 1.0)
	The unmodified weight for the fugacity primary variables. More...

Detailed Description

A compositional multi-phase model based on non-linear complementarity functions.

This model implements a $M$ -phase flow of a fluid mixture composed of $N$ chemical species. The phases are denoted by lower index $\alpha \in \{ 1, \dots, M \}$ . All fluid phases are mixtures of $N \geq M - 1$ chemical species which are denoted by the upper index $\kappa \in \{ 1, \dots, N \}$ .

By default, the standard multi-phase Darcy approach is used to determine the velocity, i.e.

$\mathbf{v}_\alpha = - \frac{k_{r\alpha}}{\mu_\alpha} \mathbf{K} \left(\mathbf{grad}\, p_\alpha - \varrho_{\alpha} \mathbf{g} \right) \;,$

although the actual approach which is used can be specified via the FluxModule property. For example, the velocity model can by changed to the Forchheimer approach by

SET_TYPE_PROP(MyProblemTypeTag, FluxModule, Ewoms::ForchheimerFluxModule<TypeTag>);

The core of the model is the conservation mass of each component by means of the equation

$\sum_\alpha \frac{\partial\;\phi c_\alpha^\kappa S_\alpha }{\partial t} - \sum_\alpha \mathrm{div} \left\{ c_\alpha^\kappa \mathbf{v}_\alpha \right\} - q^\kappa = 0 \;.$

For the missing $M$ model assumptions, the model uses non-linear complementarity functions. These are based on the observation that if a fluid phase is not present, the sum of the mole fractions of this fluid phase is smaller than $1$ , i.e.

$\forall \alpha: S_\alpha = 0 \implies \sum_\kappa x_\alpha^\kappa \leq 1$

Also, if a fluid phase may be present at a given spatial location its saturation must be non-negative:

$\forall \alpha: \sum_\kappa x_\alpha^\kappa = 1 \implies S_\alpha \geq 0 *$

Since at any given spatial location, a phase is always either present or not present, one of the strict equalities on the right hand side is always true, i.e.

$\forall \alpha: S_\alpha \left( \sum_\kappa x_\alpha^\kappa - 1 \right) = 0$

always holds.

These three equations constitute a non-linear complementarity problem, which can be solved using so-called non-linear complementarity functions $\Phi(a, b)$ . Such functions have the property