co2injectionproblem.hh

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// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
// vi: set et ts=4 sw=4 sts=4:
/*
  This file is part of the Open Porous Media project (OPM).
 
  OPM is free software: you can redistribute it and/or modify
  it under the terms of the GNU General Public License as published by
  the Free Software Foundation, either version 2 of the License, or
  (at your option) any later version.
 
  OPM is distributed in the hope that it will be useful,
  but WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  GNU General Public License for more details.
 
  You should have received a copy of the GNU General Public License
  along with OPM.  If not, see <http://www.gnu.org/licenses/>.
 
  Consult the COPYING file in the top-level source directory of this
  module for the precise wording of the license and the list of
  copyright holders.
*/
#ifndef EWOMS_CO2_INJECTION_PROBLEM_HH
#define EWOMS_CO2_INJECTION_PROBLEM_HH
 
#include <opm/models/immiscible/immisciblemodel.hh>
#include <opm/simulators/linalg/parallelamgbackend.hh>
 
#include <opm/material/fluidsystems/H2ON2FluidSystem.hpp>
#include <opm/material/fluidsystems/BrineCO2FluidSystem.hpp>
#include <opm/material/fluidstates/CompositionalFluidState.hpp>
#include <opm/material/fluidstates/ImmiscibleFluidState.hpp>
#include <opm/material/constraintsolvers/ComputeFromReferencePhase.hpp>
#include <opm/material/fluidmatrixinteractions/LinearMaterial.hpp>
#include <opm/material/fluidmatrixinteractions/RegularizedBrooksCorey.hpp>
#include <opm/material/fluidmatrixinteractions/EffToAbsLaw.hpp>
#include <opm/material/fluidmatrixinteractions/MaterialTraits.hpp>
#include <opm/material/thermal/SomertonThermalConductionLaw.hpp>
#include <opm/material/thermal/ConstantSolidHeatCapLaw.hpp>
#include <opm/material/binarycoefficients/Brine_CO2.hpp>
#include <opm/material/common/UniformTabulated2DFunction.hpp>
 
#include <dune/grid/yaspgrid.hh>
#include <dune/grid/io/file/dgfparser/dgfyasp.hh>
 
#include <dune/common/version.hh>
#include <dune/common/fvector.hh>
#include <dune/common/fmatrix.hh>
 
#include <sstream>
#include <iostream>
#include <string>
 
namespace Opm {
 
template <class TypeTag>
class Co2InjectionProblem;
 
}
 
namespace Opm::Properties {
 
namespace TTag {
struct Co2InjectionBaseProblem {};
}
 
// Set the grid type
template<class TypeTag>
struct Grid<TypeTag, TTag::Co2InjectionBaseProblem> { using type = Dune::YaspGrid<2>; };
 
// Set the problem property
template<class TypeTag>
struct Problem<TypeTag, TTag::Co2InjectionBaseProblem>
{ using type = Opm::Co2InjectionProblem<TypeTag>; };
 
// Set fluid configuration
template<class TypeTag>
struct FluidSystem<TypeTag, TTag::Co2InjectionBaseProblem>
{
private:
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
 
public:
    using type = Opm::BrineCO2FluidSystem<Scalar>;
    //using type = Opm::H2ON2FluidSystem<Scalar, /*useComplexRelations=*/false>;
};
 
// Set the material Law
template<class TypeTag>
struct MaterialLaw<TypeTag, TTag::Co2InjectionBaseProblem>
{
private:
    using FluidSystem = GetPropType<TypeTag, Properties::FluidSystem>;
    enum { liquidPhaseIdx = FluidSystem::liquidPhaseIdx };
    enum { gasPhaseIdx = FluidSystem::gasPhaseIdx };
 
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using Traits = Opm::TwoPhaseMaterialTraits<Scalar,
                                               /*wettingPhaseIdx=*/FluidSystem::liquidPhaseIdx,
                                               /*nonWettingPhaseIdx=*/FluidSystem::gasPhaseIdx>;
 
    // define the material law which is parameterized by effective
    // saturations
    using EffMaterialLaw = Opm::RegularizedBrooksCorey<Traits>;
 
public:
    // define the material law parameterized by absolute saturations
    using type = Opm::EffToAbsLaw<EffMaterialLaw>;
};
 
// Set the thermal conduction law
template<class TypeTag>
struct ThermalConductionLaw<TypeTag, TTag::Co2InjectionBaseProblem>
{
private:
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using FluidSystem = GetPropType<TypeTag, Properties::FluidSystem>;
 
public:
    // define the material law parameterized by absolute saturations
    using type = Opm::SomertonThermalConductionLaw<FluidSystem, Scalar>;
};
 
// set the energy storage law for the solid phase
template<class TypeTag>
struct SolidEnergyLaw<TypeTag, TTag::Co2InjectionBaseProblem>
{ using type = Opm::ConstantSolidHeatCapLaw<GetPropType<TypeTag, Properties::Scalar>>; };
 
// Use the algebraic multi-grid linear solver for this problem
template<class TypeTag>
struct LinearSolverSplice<TypeTag, TTag::Co2InjectionBaseProblem> { using type = TTag::ParallelAmgLinearSolver; };
 
} // namespace Opm::Properties
 
namespace Opm::Parameters {
 
struct FluidSystemNumPressure { static constexpr unsigned value = 100; };
struct FluidSystemNumTemperature { static constexpr unsigned value = 100; };
 
template<class Scalar>
struct FluidSystemPressureHigh { static constexpr Scalar value = 4e7; };
 
template<class Scalar>
struct FluidSystemPressureLow { static constexpr Scalar value = 3e7; };
 
template<class Scalar>
struct FluidSystemTemperatureHigh { static constexpr Scalar value = 500.0; };
 
template<class Scalar>
struct FluidSystemTemperatureLow { static constexpr Scalar value = 290.0; };
 
template<class Scalar>
struct MaxDepth { static constexpr Scalar value = 2500.0; };
 
struct SimulationName { static constexpr auto value = "co2injection"; };
 
template<class Scalar>
struct Temperature { static constexpr Scalar value = 293.15; };
 
} // namespace Opm::Parameters
 
namespace Opm {
 
double Co2InjectionTolerance = 1e-8;
 
template <class TypeTag>
class Co2InjectionProblem : public GetPropType<TypeTag, Properties::BaseProblem>
{
    using ParentType = GetPropType<TypeTag, Properties::BaseProblem>;
 
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using Evaluation = GetPropType<TypeTag, Properties::Evaluation>;
    using GridView = GetPropType<TypeTag, Properties::GridView>;
    using FluidSystem = GetPropType<TypeTag, Properties::FluidSystem>;
 
    enum { dim = GridView::dimension };
    enum { dimWorld = GridView::dimensionworld };
 
    // copy some indices for convenience
    using Indices = GetPropType<TypeTag, Properties::Indices>;
    enum { numPhases = FluidSystem::numPhases };
    enum { gasPhaseIdx = FluidSystem::gasPhaseIdx };
    enum { liquidPhaseIdx = FluidSystem::liquidPhaseIdx };
    enum { CO2Idx = FluidSystem::CO2Idx };
    enum { BrineIdx = FluidSystem::BrineIdx };
    enum { conti0EqIdx = Indices::conti0EqIdx };
    enum { contiCO2EqIdx = conti0EqIdx + CO2Idx };
 
    using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>;
    using RateVector = GetPropType<TypeTag, Properties::RateVector>;
    using BoundaryRateVector = GetPropType<TypeTag, Properties::BoundaryRateVector>;
    using MaterialLaw = GetPropType<TypeTag, Properties::MaterialLaw>;
    using Simulator = GetPropType<TypeTag, Properties::Simulator>;
    using Model = GetPropType<TypeTag, Properties::Model>;
    using MaterialLawParams = GetPropType<TypeTag, Properties::MaterialLawParams>;
    using ThermalConductionLaw = GetPropType<TypeTag, Properties::ThermalConductionLaw>;
    using SolidEnergyLawParams = GetPropType<TypeTag, Properties::SolidEnergyLawParams>;
    using ThermalConductionLawParams = typename ThermalConductionLaw::Params;
 
    using Toolbox = Opm::MathToolbox<Evaluation>;
    using CoordScalar = typename GridView::ctype;
    using GlobalPosition = Dune::FieldVector<CoordScalar, dimWorld>;
    using DimMatrix = Dune::FieldMatrix<Scalar, dimWorld, dimWorld>;
 
public:
    Co2InjectionProblem(Simulator& simulator)
        : ParentType(simulator)
    { }
 
    void finishInit()
    {
        ParentType::finishInit();
 
        eps_ = 1e-6;
 
        temperatureLow_ = Parameters::Get<Parameters::FluidSystemTemperatureLow<Scalar>>();
        temperatureHigh_ = Parameters::Get<Parameters::FluidSystemTemperatureHigh<Scalar>>();
        nTemperature_ = Parameters::Get<Parameters::FluidSystemNumTemperature>();
 
        pressureLow_ = Parameters::Get<Parameters::FluidSystemPressureLow<Scalar>>();
        pressureHigh_ = Parameters::Get<Parameters::FluidSystemPressureHigh<Scalar>>();
        nPressure_ = Parameters::Get<Parameters::FluidSystemNumPressure>();
 
        maxDepth_ = Parameters::Get<Parameters::MaxDepth<Scalar>>();
        temperature_ = Parameters::Get<Parameters::Temperature<Scalar>>();
 
        // initialize the tables of the fluid system
        // FluidSystem::init();
        FluidSystem::init(/*Tmin=*/temperatureLow_,
                          /*Tmax=*/temperatureHigh_,
                          /*nT=*/nTemperature_,
                          /*pmin=*/pressureLow_,
                          /*pmax=*/pressureHigh_,
                          /*np=*/nPressure_);
 
        fineLayerBottom_ = 22.0;
 
        // intrinsic permeabilities
        fineK_ = this->toDimMatrix_(1e-13);
        coarseK_ = this->toDimMatrix_(1e-12);
 
        // porosities
        finePorosity_ = 0.3;
        coarsePorosity_ = 0.3;
 
        // residual saturations
        fineMaterialParams_.setResidualSaturation(liquidPhaseIdx, 0.2);
        fineMaterialParams_.setResidualSaturation(gasPhaseIdx, 0.0);
        coarseMaterialParams_.setResidualSaturation(liquidPhaseIdx, 0.2);
        coarseMaterialParams_.setResidualSaturation(gasPhaseIdx, 0.0);
 
        // parameters for the Brooks-Corey law
        fineMaterialParams_.setEntryPressure(1e4);
        coarseMaterialParams_.setEntryPressure(5e3);
        fineMaterialParams_.setLambda(2.0);
        coarseMaterialParams_.setLambda(2.0);
 
        fineMaterialParams_.finalize();
        coarseMaterialParams_.finalize();
 
        // parameters for the somerton law thermal conduction
        computeThermalCondParams_(fineThermalCondParams_, finePorosity_);
        computeThermalCondParams_(coarseThermalCondParams_, coarsePorosity_);
 
        // assume constant heat capacity and granite
        solidEnergyLawParams_.setSolidHeatCapacity(790.0 // specific heat capacity of granite [J / (kg K)]
                                                   * 2700.0); // density of granite [kg/m^3]
        solidEnergyLawParams_.finalize();
    }
 
    static void registerParameters()
    {
        ParentType::registerParameters();
 
        Parameters::Register<Parameters::FluidSystemTemperatureLow<Scalar>>
            ("The lower temperature [K] for tabulation of the fluid system");
        Parameters::Register<Parameters::FluidSystemTemperatureHigh<Scalar>>
            ("The upper temperature [K] for tabulation of the fluid system");
        Parameters::Register<Parameters::FluidSystemNumTemperature>
            ("The number of intervals between the lower and upper temperature");
        Parameters::Register<Parameters::FluidSystemPressureLow<Scalar>>
            ("The lower pressure [Pa] for tabulation of the fluid system");
        Parameters::Register<Parameters::FluidSystemPressureHigh<Scalar>>
            ("The upper pressure [Pa] for tabulation of the fluid system");
        Parameters::Register<Parameters::FluidSystemNumPressure>
            ("The number of intervals between the lower and upper pressure");
        Parameters::Register<Parameters::Temperature<Scalar>>
            ("The temperature [K] in the reservoir");
        Parameters::Register<Parameters::MaxDepth<Scalar>>
            ("The maximum depth [m] of the reservoir");
        Parameters::Register<Parameters::SimulationName>
            ("The name of the simulation used for the output files");
 
        Parameters::SetDefault<Parameters::GridFile>("data/co2injection.dgf");
        Parameters::SetDefault<Parameters::EndTime<Scalar>>(1e4);
        Parameters::SetDefault<Parameters::InitialTimeStepSize<Scalar>>(250);
        Parameters::SetDefault<Parameters::NewtonTolerance<Scalar>>(Scalar{Co2InjectionTolerance});
        Parameters::SetDefault<Parameters::EnableGravity>(true);
    }
 
 
    std::string name() const
    {
        std::ostringstream oss;
        oss << Parameters::Get<Parameters::SimulationName>()
            << "_" << Model::name();
        if (getPropValue<TypeTag, Properties::EnableEnergy>())
            oss << "_ni";
        oss << "_" << Model::discretizationName();
        return oss.str();
    }
 
    void endTimeStep()
    {
#ifndef NDEBUG
        Scalar tol = this->model().newtonMethod().tolerance()*1e5;
        this->model().checkConservativeness(tol);
 
        // Calculate storage terms
        PrimaryVariables storageL, storageG;
        this->model().globalPhaseStorage(storageL, /*phaseIdx=*/0);
        this->model().globalPhaseStorage(storageG, /*phaseIdx=*/1);
 
        // Write mass balance information for rank 0
        if (this->gridView().comm().rank() == 0) {
            std::cout << "Storage: liquid=[" << storageL << "]"
                      << " gas=[" << storageG << "]\n" << std::flush;
        }
#endif // NDEBUG
    }
 
    template <class Context>
    Scalar temperature(const Context& context, unsigned spaceIdx, unsigned timeIdx) const
    {
        const auto& pos = context.pos(spaceIdx, timeIdx);
        if (inHighTemperatureRegion_(pos))
            return temperature_ + 100;
        return temperature_;
    }
 
    template <class Context>
    const DimMatrix& intrinsicPermeability(const Context& context, unsigned spaceIdx,
                                           unsigned timeIdx) const
    {
        const GlobalPosition& pos = context.pos(spaceIdx, timeIdx);
        if (isFineMaterial_(pos))
            return fineK_;
        return coarseK_;
    }
 
    template <class Context>
    Scalar porosity(const Context& context, unsigned spaceIdx, unsigned timeIdx) const
    {
        const GlobalPosition& pos = context.pos(spaceIdx, timeIdx);
        if (isFineMaterial_(pos))
            return finePorosity_;
        return coarsePorosity_;
    }
 
    template <class Context>
    const MaterialLawParams& materialLawParams(const Context& context,
                                               unsigned spaceIdx, unsigned timeIdx) const
    {
        const GlobalPosition& pos = context.pos(spaceIdx, timeIdx);
        if (isFineMaterial_(pos))
            return fineMaterialParams_;
        return coarseMaterialParams_;
    }
 
    template <class Context>
    const SolidEnergyLawParams&
    solidEnergyLawParams(const Context& /*context*/,
                         unsigned /*spaceIdx*/,
                         unsigned /*timeIdx*/) const
    { return solidEnergyLawParams_; }
 
    template <class Context>
    const ThermalConductionLawParams &
    thermalConductionLawParams(const Context& context,
                            unsigned spaceIdx,
                            unsigned timeIdx) const
    {
        const GlobalPosition& pos = context.pos(spaceIdx, timeIdx);
        if (isFineMaterial_(pos))
            return fineThermalCondParams_;
        return coarseThermalCondParams_;
    }
 
 
 
    template <class Context>
    void boundary(BoundaryRateVector& values, const Context& context,
                  unsigned spaceIdx, unsigned timeIdx) const
    {
        const auto& pos = context.pos(spaceIdx, timeIdx);
        if (onLeftBoundary_(pos)) {
            Opm::CompositionalFluidState<Scalar, FluidSystem> fs;
            initialFluidState_(fs, context, spaceIdx, timeIdx);
            fs.checkDefined();
 
            // impose an freeflow boundary condition
            values.setFreeFlow(context, spaceIdx, timeIdx, fs);
        }
        else if (onInlet_(pos)) {
            RateVector massRate(0.0);
            massRate[contiCO2EqIdx] = -1e-3; // [kg/(m^3 s)]
 
            using FluidState = Opm::ImmiscibleFluidState<Scalar, FluidSystem>;
            FluidState fs;
            fs.setSaturation(gasPhaseIdx, 1.0);
            const auto& pg =
                context.intensiveQuantities(spaceIdx, timeIdx).fluidState().pressure(gasPhaseIdx);
            fs.setPressure(gasPhaseIdx, Toolbox::value(pg));
            fs.setTemperature(temperature(context, spaceIdx, timeIdx));
 
            typename FluidSystem::template ParameterCache<Scalar> paramCache;
            paramCache.updatePhase(fs, gasPhaseIdx);
            Scalar h = FluidSystem::template enthalpy<FluidState, Scalar>(fs, paramCache, gasPhaseIdx);
 
            // impose an forced inflow boundary condition for pure CO2
            values.setMassRate(massRate);
            values.setEnthalpyRate(massRate[contiCO2EqIdx] * h);
        }
        else
            // no flow on top and bottom
            values.setNoFlow();
    }
 
    // \}
 
 
    template <class Context>
    void initial(PrimaryVariables& values, const Context& context, unsigned spaceIdx,
                 unsigned timeIdx) const
    {
        Opm::CompositionalFluidState<Scalar, FluidSystem> fs;
        initialFluidState_(fs, context, spaceIdx, timeIdx);
 
        // const auto& matParams = this->materialLawParams(context, spaceIdx,
        // timeIdx);
        // values.assignMassConservative(fs, matParams, /*inEquilibrium=*/true);
        values.assignNaive(fs);
    }
 
    template <class Context>
    void source(RateVector& rate,
                const Context& /*context*/,
                unsigned /*spaceIdx*/,
                unsigned /*timeIdx*/) const
    { rate = Scalar(0.0); }
 
 
private:
    template <class Context, class FluidState>
    void initialFluidState_(FluidState& fs,
                            const Context& context,
                            unsigned spaceIdx,
                            unsigned timeIdx) const
    {
        const GlobalPosition& pos = context.pos(spaceIdx, timeIdx);
 
        // set temperature
        fs.setTemperature(temperature(context, spaceIdx, timeIdx));
 
        // set saturations
        fs.setSaturation(FluidSystem::liquidPhaseIdx, 1.0);
        fs.setSaturation(FluidSystem::gasPhaseIdx, 0.0);
 
        // set pressures
        Scalar densityL = FluidSystem::Brine::liquidDensity(temperature_, Scalar(1e5));
        Scalar depth = maxDepth_ - pos[dim - 1];
        Scalar pl = 1e5 - densityL * this->gravity()[dim - 1] * depth;
 
        Scalar pC[numPhases];
        const auto& matParams = this->materialLawParams(context, spaceIdx, timeIdx);
        MaterialLaw::capillaryPressures(pC, matParams, fs);
 
        fs.setPressure(liquidPhaseIdx, pl + (pC[liquidPhaseIdx] - pC[liquidPhaseIdx]));
        fs.setPressure(gasPhaseIdx, pl + (pC[gasPhaseIdx] - pC[liquidPhaseIdx]));
 
        // set composition of the liquid phase
        fs.setMoleFraction(liquidPhaseIdx, CO2Idx, 0.005);
        fs.setMoleFraction(liquidPhaseIdx, BrineIdx,
                           1.0 - fs.moleFraction(liquidPhaseIdx, CO2Idx));
 
        typename FluidSystem::template ParameterCache<Scalar> paramCache;
        using CFRP = Opm::ComputeFromReferencePhase<Scalar, FluidSystem>;
        CFRP::solve(fs, paramCache,
                    /*refPhaseIdx=*/liquidPhaseIdx,
                    /*setViscosity=*/true,
                    /*setEnthalpy=*/true);
    }
 
    bool onLeftBoundary_(const GlobalPosition& pos) const
    { return pos[0] < eps_; }
 
    bool onRightBoundary_(const GlobalPosition& pos) const
    { return pos[0] > this->boundingBoxMax()[0] - eps_; }
 
    bool onInlet_(const GlobalPosition& pos) const
    { return onRightBoundary_(pos) && (5 < pos[1]) && (pos[1] < 15); }
 
    bool inHighTemperatureRegion_(const GlobalPosition& pos) const
    { return (pos[0] > 20) && (pos[0] < 30) && (pos[1] > 5) && (pos[1] < 35); }
 
    void computeThermalCondParams_(ThermalConductionLawParams& params, Scalar poro)
    {
        Scalar lambdaWater = 0.6;
        Scalar lambdaGranite = 2.8;
 
        Scalar lambdaWet = std::pow(lambdaGranite, (1 - poro))
                           * std::pow(lambdaWater, poro);
        Scalar lambdaDry = std::pow(lambdaGranite, (1 - poro));
 
        params.setFullySaturatedLambda(gasPhaseIdx, lambdaDry);
        params.setFullySaturatedLambda(liquidPhaseIdx, lambdaWet);
        params.setVacuumLambda(lambdaDry);
    }
 
    bool isFineMaterial_(const GlobalPosition& pos) const
    { return pos[dim - 1] > fineLayerBottom_; }
 
    DimMatrix fineK_;
    DimMatrix coarseK_;
    Scalar fineLayerBottom_;
 
    Scalar finePorosity_;
    Scalar coarsePorosity_;
 
    MaterialLawParams fineMaterialParams_;
    MaterialLawParams coarseMaterialParams_;
 
    ThermalConductionLawParams fineThermalCondParams_;
    ThermalConductionLawParams coarseThermalCondParams_;
    SolidEnergyLawParams solidEnergyLawParams_;
 
    Scalar temperature_;
    Scalar maxDepth_;
    Scalar eps_;
 
    unsigned nTemperature_;
    unsigned nPressure_;
 
    Scalar pressureLow_, pressureHigh_;
    Scalar temperatureLow_, temperatureHigh_;
};
 
} // namespace Opm
 
#endif