Classes | Namespaces
pvsmodel.hh File Reference
#include <opm/material/densead/Math.hpp>
#include "pvsproperties.hh"
#include "pvslocalresidual.hh"
#include "pvsnewtonmethod.hh"
#include "pvsprimaryvariables.hh"
#include "pvsratevector.hh"
#include "pvsboundaryratevector.hh"
#include "pvsintensivequantities.hh"
#include "pvsextensivequantities.hh"
#include "pvsindices.hh"
#include <opm/common/Exceptions.hpp>
#include <opm/models/common/multiphasebasemodel.hh>
#include <opm/models/common/diffusionmodule.hh>
#include <opm/models/common/energymodule.hh>
#include <opm/models/io/vtkcompositionmodule.hh>
#include <opm/models/io/vtkenergymodule.hh>
#include <opm/models/io/vtkdiffusionmodule.hh>
#include <opm/material/fluidmatrixinteractions/NullMaterial.hpp>
#include <opm/material/fluidmatrixinteractions/MaterialTraits.hpp>
#include <iostream>
#include <sstream>
#include <string>
#include <vector>
Include dependency graph for pvsmodel.hh:

Go to the source code of this file.

Classes

struct  Opm::Properties::TTag::PvsModel
 The type tag for the isothermal single phase problems. More...
 
struct  Opm::Properties::LocalResidual< TypeTag, TTag::PvsModel >
 Use the PVS local jacobian operator for the PVS model. More...
 
struct  Opm::Properties::NewtonMethod< TypeTag, TTag::PvsModel >
 Use the PVS specific newton method for the PVS model. More...
 
struct  Opm::Properties::Model< TypeTag, TTag::PvsModel >
 the Model property More...
 
struct  Opm::Properties::PrimaryVariables< TypeTag, TTag::PvsModel >
 the PrimaryVariables property More...
 
struct  Opm::Properties::RateVector< TypeTag, TTag::PvsModel >
 the RateVector property More...
 
struct  Opm::Properties::BoundaryRateVector< TypeTag, TTag::PvsModel >
 the BoundaryRateVector property More...
 
struct  Opm::Properties::IntensiveQuantities< TypeTag, TTag::PvsModel >
 the IntensiveQuantities property More...
 
struct  Opm::Properties::ExtensiveQuantities< TypeTag, TTag::PvsModel >
 the ExtensiveQuantities property More...
 
struct  Opm::Properties::Indices< TypeTag, TTag::PvsModel >
 The indices required by the isothermal PVS model. More...
 
struct  Opm::Properties::PvsVerbosity< TypeTag, TTag::PvsModel >
 
struct  Opm::Properties::EnableEnergy< TypeTag, TTag::PvsModel >
 Disable the energy equation by default. More...
 
struct  Opm::Properties::EnableDiffusion< TypeTag, TTag::PvsModel >
 
struct  Opm::Properties::PvsPressureBaseWeight< TypeTag, TTag::PvsModel >
 The basis value for the weight of the pressure primary variable. More...
 
struct  Opm::Properties::PvsSaturationsBaseWeight< TypeTag, TTag::PvsModel >
 The basis value for the weight of the saturation primary variables. More...
 
struct  Opm::Properties::PvsMoleFractionsBaseWeight< TypeTag, TTag::PvsModel >
 The basis value for the weight of the mole fraction primary variables. More...
 
class  Opm::PvsModel< TypeTag >
 A generic compositional multi-phase model using primary-variable switching. More...
 

Namespaces

namespace  Opm
 
namespace  Opm::Properties
 
namespace  Opm::Properties::TTag
 The generic type tag for problems using the immiscible multi-phase model.
 

Detailed Description

A generic compositional multi-phase model using primary-variable switching.

This model assumes a flow of $M \geq 1$ fluid phases $\alpha$, each of which is assumed to be a mixture $N \geq M$ chemical species $\kappa$.

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

template<class TypeTag>
struct FluxModule<TypeTag, TTag::MyProblemTypeTag> { using type = Opm::ForchheimerFluxModule<TypeTag>; };
Opm::ForchheimerFluxModule
Specifies a flux module which uses the Forchheimer relation.
Definition: forchheimerfluxmodule.hh:62

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

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

To close the system mathematically, $M$ model equations are also required. This model uses the primary variable switching assumptions, which are given by:

\[ 0 \stackrel{!}{=} f_\alpha = \left\{ \begin{array}{cl} S_\alpha& \quad \text{if phase }\alpha\text{ is not present} \ \ 1 - \sum_\kappa x_\alpha^\kappa& \quad \text{else} \end{array} \right. \]

To make this approach applicable, a pseudo primary variable phase presence has to be introduced. Its purpose is to specify for each phase whether it is present or not. It is a pseudo primary variable because it is not directly considered when linearizing the system in the Newton method, but after each Newton iteration, it gets updated like the "real" primary variables. The following rules are used for this update procedure:

  • If phase $\alpha$ is present according to the pseudo primary variable, but $S_\alpha < 0$ after the Newton update, consider the phase $\alpha$ disappeared for the next iteration and use the set of primary variables which correspond to the new phase presence.
  • If phase $\alpha$ is not present according to the pseudo primary variable, but the sum of the component mole fractions in the phase is larger than 1, i.e. $\sum_\kappa x_\alpha^\kappa > 1$, consider the phase $\alpha$ present in the the next iteration and update the set of primary variables to make it consistent with the new phase presence.

  • In all other cases don't modify the phase presence for phase $\alpha$.

The model always requires $N$ primary variables, but their interpretation is dependent on the phase presence:

  • The first primary variable is always interpreted as the pressure of the phase with the lowest index $PV_0 = p_0$.

  • Then, $M - 1$ "switching primary variables" follow, which are interpreted depending in the presence of the first $M-1$ phases: If phase $\alpha$ is present, its saturation $S_\alpha = PV_i$ is used as primary variable; if it is not present, the mole fraction $PV_i = x_{\alpha^\star}^\alpha$ of the component with index $\alpha$ in the phase with the lowest index that is present $\alpha^\star$ is used instead.

  • Finally, the mole fractions of the $N-M$ components with the largest index in the phase with the lowest index that is present $x_{\alpha^\star}^\kappa$ are used as primary variables.