reservoirproblem.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_RESERVOIR_PROBLEM_HH
#define EWOMS_RESERVOIR_PROBLEM_HH
 
#include <dune/common/version.hh>
#include <dune/common/fvector.hh>
#include <dune/common/fmatrix.hh>
 
#include <dune/grid/yaspgrid.hh>
#include <dune/grid/io/file/dgfparser/dgfyasp.hh>
 
#include <opm/material/fluidmatrixinteractions/LinearMaterial.hpp>
#include <opm/material/fluidmatrixinteractions/MaterialTraits.hpp>
#include <opm/material/fluidstates/CompositionalFluidState.hpp>
#include <opm/material/fluidsystems/BlackOilFluidSystem.hpp>
#include <opm/material/constraintsolvers/ComputeFromReferencePhase.hpp>
#include <opm/material/fluidsystems/blackoilpvt/DryGasPvt.hpp>
#include <opm/material/fluidsystems/blackoilpvt/LiveOilPvt.hpp>
#include <opm/material/fluidsystems/blackoilpvt/ConstantCompressibilityWaterPvt.hpp>
 
#include <opm/models/blackoil/blackoilproperties.hh>
 
#include <opm/models/common/multiphasebaseparameters.hh>
 
#include <opm/models/discretization/common/fvbaseparameters.hh>
#include <opm/models/discretization/common/fvbaseproperties.hh>
 
#include <opm/models/nonlinear/newtonmethodparams.hpp>
 
#include <opm/models/utils/basicproperties.hh>
 
#include <string>
#include <vector>
 
namespace Opm {
template <class TypeTag>
class ReservoirProblem;
 
} // namespace Opm
 
namespace Opm::Properties {
 
 
namespace TTag {
 
struct ReservoirBaseProblem {};
 
} // namespace TTag
 
// Set the grid type
template<class TypeTag>
struct Grid<TypeTag, TTag::ReservoirBaseProblem> { using type = Dune::YaspGrid<2>; };
 
// Set the problem property
template<class TypeTag>
struct Problem<TypeTag, TTag::ReservoirBaseProblem> { using type = Opm::ReservoirProblem<TypeTag>; };
 
// Set the material Law
template<class TypeTag>
struct MaterialLaw<TypeTag, TTag::ReservoirBaseProblem>
{
private:
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using FluidSystem = GetPropType<TypeTag, Properties::FluidSystem>;
 
    using Traits = Opm::
        ThreePhaseMaterialTraits<Scalar,
                                 /*wettingPhaseIdx=*/FluidSystem::waterPhaseIdx,
                                 /*nonWettingPhaseIdx=*/FluidSystem::oilPhaseIdx,
                                 /*gasPhaseIdx=*/FluidSystem::gasPhaseIdx,
                                 /* hysteresis */ false,
                                 /* endpointscaling */ false>;
 
public:
    using type = Opm::LinearMaterial<Traits>;
};
 
// Enable constraint DOFs?
template<class TypeTag>
struct EnableConstraints<TypeTag, TTag::ReservoirBaseProblem> { static constexpr bool value = true; };
 
template<class TypeTag>
struct FluidSystem<TypeTag, TTag::ReservoirBaseProblem>
{
private:
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
 
public:
    using type = Opm::BlackOilFluidSystem<Scalar>;
};
 
} // namespace Opm::Properties
 
namespace Opm::Parameters {
 
// Maximum depth of the reservoir
template<class Scalar>
struct MaxDepth { static constexpr Scalar value = 2500.0; };
 
// The temperature inside the reservoir
template<class Scalar>
struct Temperature { static constexpr Scalar value = 293.15; };
 
// The width of producer/injector wells as a fraction of the width of the spatial domain
template<class Scalar>
struct WellWidth { static constexpr Scalar value = 0.01; };
 
} // namespace Opm::Parameters
 
namespace Opm {
 
template <class TypeTag>
class ReservoirProblem : public GetPropType<TypeTag, Properties::BaseProblem>
{
    using ParentType = GetPropType<TypeTag, Properties::BaseProblem>;
 
    using GridView = GetPropType<TypeTag, Properties::GridView>;
    using Scalar = GetPropType<TypeTag, Properties::Scalar>;
    using Evaluation = GetPropType<TypeTag, Properties::Evaluation>;
    using FluidSystem = GetPropType<TypeTag, Properties::FluidSystem>;
 
    // Grid and world dimension
    enum { dim = GridView::dimension };
    enum { dimWorld = GridView::dimensionworld };
 
    // copy some indices for convenience
    enum { numPhases = FluidSystem::numPhases };
    enum { numComponents = FluidSystem::numComponents };
    enum { gasPhaseIdx = FluidSystem::gasPhaseIdx };
    enum { oilPhaseIdx = FluidSystem::oilPhaseIdx };
    enum { waterPhaseIdx = FluidSystem::waterPhaseIdx };
    enum { gasCompIdx = FluidSystem::gasCompIdx };
    enum { oilCompIdx = FluidSystem::oilCompIdx };
    enum { waterCompIdx = FluidSystem::waterCompIdx };
 
    using Model = GetPropType<TypeTag, Properties::Model>;
    using ElementContext = GetPropType<TypeTag, Properties::ElementContext>;
    using PrimaryVariables = GetPropType<TypeTag, Properties::PrimaryVariables>;
    using EqVector = GetPropType<TypeTag, Properties::EqVector>;
    using RateVector = GetPropType<TypeTag, Properties::RateVector>;
    using BoundaryRateVector = GetPropType<TypeTag, Properties::BoundaryRateVector>;
    using Constraints = GetPropType<TypeTag, Properties::Constraints>;
    using MaterialLaw = GetPropType<TypeTag, Properties::MaterialLaw>;
    using Simulator = GetPropType<TypeTag, Properties::Simulator>;
    using MaterialLawParams = GetPropType<TypeTag, Properties::MaterialLawParams>;
 
    using CoordScalar = typename GridView::ctype;
    using GlobalPosition = Dune::FieldVector<CoordScalar, dimWorld>;
    using DimMatrix = Dune::FieldMatrix<Scalar, dimWorld, dimWorld>;
    using PhaseVector = Dune::FieldVector<Scalar, numPhases>;
 
    using InitialFluidState = Opm::CompositionalFluidState<Scalar,
                                                           FluidSystem,
                                                           /*enableEnthalpy=*/true>;
 
public:
    explicit ReservoirProblem(Simulator& simulator)
        : ParentType(simulator)
    { }
 
    void finishInit()
    {
        ParentType::finishInit();
 
        temperature_ = Parameters::Get<Parameters::Temperature<Scalar>>();
        maxDepth_ = Parameters::Get<Parameters::MaxDepth<Scalar>>();
        wellWidth_ = Parameters::Get<Parameters::WellWidth<Scalar>>();
 
        std::vector<std::pair<Scalar, Scalar> > Bo = {
            { 101353, 1.062 },
            { 1.82504e+06, 1.15 },
            { 3.54873e+06, 1.207 },
            { 6.99611e+06, 1.295 },
            { 1.38909e+07, 1.435 },
            { 1.73382e+07, 1.5 },
            { 2.07856e+07, 1.565 },
            { 2.76804e+07, 1.695 },
            { 3.45751e+07, 1.827 }
        };
        std::vector<std::pair<Scalar, Scalar> > muo = {
            { 101353, 0.00104 },
            { 1.82504e+06, 0.000975 },
            { 3.54873e+06, 0.00091 },
            { 6.99611e+06, 0.00083 },
            { 1.38909e+07, 0.000695 },
            { 1.73382e+07, 0.000641 },
            { 2.07856e+07, 0.000594 },
            { 2.76804e+07, 0.00051 },
            { 3.45751e+07, 0.000449 }
        };
        std::vector<std::pair<Scalar, Scalar> > Rs = {
            { 101353, 0.178108 },
            { 1.82504e+06, 16.1187 },
            { 3.54873e+06, 32.0594 },
            { 6.99611e+06, 66.0779 },
            { 1.38909e+07, 113.276 },
            { 1.73382e+07, 138.033 },
            { 2.07856e+07, 165.64 },
            { 2.76804e+07, 226.197 },
            { 3.45751e+07, 288.178 }
        };
        std::vector<std::pair<Scalar, Scalar> > Bg = {
            { 101353, 0.93576 },
            { 1.82504e+06, 0.0678972 },
            { 3.54873e+06, 0.0352259 },
            { 6.99611e+06, 0.0179498 },
            { 1.38909e+07, 0.00906194 },
            { 1.73382e+07, 0.00726527 },
            { 2.07856e+07, 0.00606375 },
            { 2.76804e+07, 0.00455343 },
            { 3.45751e+07, 0.00364386 },
            { 6.21542e+07, 0.00216723 }
        };
        std::vector<std::pair<Scalar, Scalar> > mug = {
            { 101353, 8e-06 },
            { 1.82504e+06, 9.6e-06 },
            { 3.54873e+06, 1.12e-05 },
            { 6.99611e+06, 1.4e-05 },
            { 1.38909e+07, 1.89e-05 },
            { 1.73382e+07, 2.08e-05 },
            { 2.07856e+07, 2.28e-05 },
            { 2.76804e+07, 2.68e-05 },
            { 3.45751e+07, 3.09e-05 },
            { 6.21542e+07, 4.7e-05 }
        };
 
        Scalar rhoRefO = 786.0; // [kg]
        Scalar rhoRefG = 0.97; // [kg]
        Scalar rhoRefW = 1037.0; // [kg]
        FluidSystem::initBegin(/*numPvtRegions=*/1);
        FluidSystem::setEnableDissolvedGas(true);
        FluidSystem::setEnableVaporizedOil(false);
        FluidSystem::setReferenceDensities(rhoRefO, rhoRefW, rhoRefG, /*regionIdx=*/0);
 
        Opm::GasPvtMultiplexer<Scalar> *gasPvt = new Opm::GasPvtMultiplexer<Scalar>;
        gasPvt->setApproach(GasPvtApproach::DryGas);
        auto& dryGasPvt = gasPvt->template getRealPvt<GasPvtApproach::DryGas>();
        dryGasPvt.setNumRegions(/*numPvtRegion=*/1);
        dryGasPvt.setReferenceDensities(/*regionIdx=*/0, rhoRefO, rhoRefG, rhoRefW);
        dryGasPvt.setGasFormationVolumeFactor(/*regionIdx=*/0, Bg);
        dryGasPvt.setGasViscosity(/*regionIdx=*/0, Opm::Tabulated1DFunction<Scalar>(mug));
 
        Opm::OilPvtMultiplexer<Scalar> *oilPvt = new Opm::OilPvtMultiplexer<Scalar>;
        oilPvt->setApproach(OilPvtApproach::LiveOil);
        auto& liveOilPvt = oilPvt->template getRealPvt<OilPvtApproach::LiveOil>();
        liveOilPvt.setNumRegions(/*numPvtRegion=*/1);
        liveOilPvt.setReferenceDensities(/*regionIdx=*/0, rhoRefO, rhoRefG, rhoRefW);
        liveOilPvt.setSaturatedOilGasDissolutionFactor(/*regionIdx=*/0, Rs);
        liveOilPvt.setSaturatedOilFormationVolumeFactor(/*regionIdx=*/0, Bo);
        liveOilPvt.setSaturatedOilViscosity(/*regionIdx=*/0, muo);
 
        Opm::WaterPvtMultiplexer<Scalar> *waterPvt = new Opm::WaterPvtMultiplexer<Scalar>;
        waterPvt->setApproach(WaterPvtApproach::ConstantCompressibilityWater);
        auto& ccWaterPvt = waterPvt->template getRealPvt<WaterPvtApproach::ConstantCompressibilityWater>();
        ccWaterPvt.setNumRegions(/*numPvtRegions=*/1);
        ccWaterPvt.setReferenceDensities(/*regionIdx=*/0, rhoRefO, rhoRefG, rhoRefW);
        ccWaterPvt.setViscosity(/*regionIdx=*/0, 9.6e-4);
        ccWaterPvt.setCompressibility(/*regionIdx=*/0, 1.450377e-10);
 
        gasPvt->initEnd();
        oilPvt->initEnd();
        waterPvt->initEnd();
 
        using GasPvtSharedPtr = std::shared_ptr<Opm::GasPvtMultiplexer<Scalar> >;
        FluidSystem::setGasPvt(GasPvtSharedPtr(gasPvt));
 
        using OilPvtSharedPtr = std::shared_ptr<Opm::OilPvtMultiplexer<Scalar> >;
        FluidSystem::setOilPvt(OilPvtSharedPtr(oilPvt));
 
        using WaterPvtSharedPtr = std::shared_ptr<Opm::WaterPvtMultiplexer<Scalar> >;
        FluidSystem::setWaterPvt(WaterPvtSharedPtr(waterPvt));
 
        FluidSystem::initEnd();
 
        pReservoir_ = 330e5;
        layerBottom_ = 22.0;
 
        // intrinsic permeabilities
        fineK_ = this->toDimMatrix_(1e-12);
        coarseK_ = this->toDimMatrix_(1e-11);
 
        // porosities
        finePorosity_ = 0.2;
        coarsePorosity_ = 0.3;
 
        for (unsigned phaseIdx = 0; phaseIdx < numPhases; ++phaseIdx) {
            fineMaterialParams_.setPcMinSat(phaseIdx, 0.0);
            fineMaterialParams_.setPcMaxSat(phaseIdx, 0.0);
 
            coarseMaterialParams_.setPcMinSat(phaseIdx, 0.0);
            coarseMaterialParams_.setPcMaxSat(phaseIdx, 0.0);
        }
 
        // wrap up the initialization of the material law's parameters
        fineMaterialParams_.finalize();
        coarseMaterialParams_.finalize();
 
        materialParams_.resize(this->model().numGridDof());
        ElementContext elemCtx(this->simulator());
        auto eIt = this->simulator().gridView().template begin<0>();
        const auto& eEndIt = this->simulator().gridView().template end<0>();
        for (; eIt != eEndIt; ++eIt) {
            elemCtx.updateStencil(*eIt);
            size_t nDof = elemCtx.numPrimaryDof(/*timeIdx=*/0);
            for (unsigned dofIdx = 0; dofIdx < nDof; ++ dofIdx) {
                unsigned globalDofIdx = elemCtx.globalSpaceIndex(dofIdx, /*timeIdx=*/0);
                const GlobalPosition& pos = elemCtx.pos(dofIdx, /*timeIdx=*/0);
 
                if (isFineMaterial_(pos))
                    materialParams_[globalDofIdx] = &fineMaterialParams_;
                else
                    materialParams_[globalDofIdx] = &coarseMaterialParams_;
            }
        }
 
        initFluidState_();
 
        // start the first ("settle down") episode for 100 days
        this->simulator().startNextEpisode(100.0*24*60*60);
    }
 
    static void registerParameters()
    {
        ParentType::registerParameters();
 
        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::WellWidth<Scalar>>
            ("The width of producer/injector wells as a fraction of the width"
             " of the spatial domain");
 
        Parameters::SetDefault<Parameters::GridFile>("data/reservoir.dgf");
 
        Parameters::SetDefault<Parameters::EndTime<Scalar>>(1000.0*24*60*60);
 
        Parameters::SetDefault<Parameters::EnableStorageCache>(true);
        Parameters::SetDefault<Parameters::GridFile>("data/reservoir.dgf");
        Parameters::SetDefault<Parameters::InitialTimeStepSize<Scalar>>(100e3);
        // increase the tolerance for this problem to get larger time steps
        Parameters::SetDefault<Parameters::NewtonTolerance<Scalar>>(1e-6);
 
        Parameters::SetDefault<Parameters::EnableGravity>(true);
    }
 
    std::string name() const
    { return std::string("reservoir_") + Model::name() + "_" + Model::discretizationName(); }
 
    void endEpisode()
    {
        // in the second episode, the actual work is done (the first is "settle down"
        // episode). we need to use a pretty short initial time step here as the change
        // in conditions is quite abrupt.
        this->simulator().startNextEpisode(1e100);
        this->simulator().setTimeStepSize(5.0);
    }
 
    void endTimeStep()
    {
#ifndef NDEBUG
        // checkConservativeness() does not include the effect of constraints, so we
        // disable it for this problem...
        //this->model().checkConservativeness();
 
        // Calculate storage terms
        EqVector storage;
        this->model().globalStorage(storage);
 
        // Write mass balance information for rank 0
        if (this->gridView().comm().rank() == 0) {
            std::cout << "Storage: " << storage << std::endl << std::flush;
        }
#endif // NDEBUG
    }
 
    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
    {
        unsigned globalIdx = context.globalSpaceIndex(spaceIdx, timeIdx);
        return *materialParams_[globalIdx];
    }
 
    const MaterialLawParams& materialLawParams(unsigned globalIdx) const
    { return *materialParams_[globalIdx]; }
 
 
 
    template <class Context>
    Scalar temperature(const Context& /*context*/,
                       unsigned /*spaceIdx*/,
                       unsigned /*timeIdx*/) const
    { return temperature_; }
 
    Scalar temperature(unsigned /*globalDofIdx*/,
                       unsigned /*timeIdx*/) const
    { return temperature_; }
 
    // \}
 
 
    template <class Context>
    void boundary(BoundaryRateVector& values,
                  const Context& /*context*/,
                  unsigned /*spaceIdx*/,
                  unsigned /*timeIdx*/) const
    {
        // no flow on top and bottom
        values.setNoFlow();
    }
 
 
 
    template <class Context>
    void initial(PrimaryVariables& values,
                 const Context& /*context*/,
                 unsigned /*spaceIdx*/,
                 unsigned /*timeIdx*/) const
    {
        values.assignNaive(initialFluidState_);
 
#ifndef NDEBUG
        for (unsigned pvIdx = 0; pvIdx < values.size(); ++ pvIdx)
            assert(std::isfinite(values[pvIdx]));
#endif
    }
 
    template <class Context>
    void constraints(Constraints& constraintValues,
                     const Context& context,
                     unsigned spaceIdx,
                     unsigned timeIdx) const
    {
        if (this->simulator().episodeIndex() == 1)
            return; // no constraints during the "settle down" episode
 
        const auto& pos = context.pos(spaceIdx, timeIdx);
        if (isInjector_(pos)) {
            constraintValues.setActive(true);
            constraintValues.assignNaive(injectorFluidState_);
        }
        else if (isProducer_(pos)) {
            constraintValues.setActive(true);
            constraintValues.assignNaive(producerFluidState_);
        }
    }
 
    template <class Context>
    void source(RateVector& rate,
                const Context& /*context*/,
                unsigned /*spaceIdx*/,
                unsigned /*timeIdx*/) const
    { rate = Scalar(0.0); }
 
 
private:
    void initFluidState_()
    {
        auto& fs = initialFluidState_;
 
        // set temperatures
        fs.setTemperature(temperature_);
 
        // set saturations
        fs.setSaturation(FluidSystem::oilPhaseIdx, 1.0);
        fs.setSaturation(FluidSystem::waterPhaseIdx, 0.0);
        fs.setSaturation(FluidSystem::gasPhaseIdx, 0.0);
 
        // set pressures
        Scalar pw = pReservoir_;
 
        PhaseVector pC;
        const auto& matParams = fineMaterialParams_;
        MaterialLaw::capillaryPressures(pC, matParams, fs);
 
        fs.setPressure(oilPhaseIdx, pw + (pC[oilPhaseIdx] - pC[waterPhaseIdx]));
        fs.setPressure(waterPhaseIdx, pw + (pC[waterPhaseIdx] - pC[waterPhaseIdx]));
        fs.setPressure(gasPhaseIdx, pw + (pC[gasPhaseIdx] - pC[waterPhaseIdx]));
 
        // reset all mole fractions to 0
        for (unsigned phaseIdx = 0; phaseIdx < numPhases; ++phaseIdx)
            for (unsigned compIdx = 0; compIdx < numComponents; ++compIdx)
                fs.setMoleFraction(phaseIdx, compIdx, 0.0);
 
        // set composition of the gas and water phases
        fs.setMoleFraction(waterPhaseIdx, waterCompIdx, 1.0);
        fs.setMoleFraction(gasPhaseIdx, gasCompIdx, 1.0);
 
        // set composition of the oil phase
        Scalar RsSat =
            FluidSystem::saturatedDissolutionFactor(fs, oilPhaseIdx, /*pvtRegionIdx=*/0);
        Scalar XoGSat = FluidSystem::convertRsToXoG(RsSat, /*pvtRegionIdx=*/0);
        Scalar xoGSat = FluidSystem::convertXoGToxoG(XoGSat, /*pvtRegionIdx=*/0);
        Scalar xoG = 0.95*xoGSat;
        Scalar xoO = 1.0 - xoG;
 
        // finally set the oil-phase composition
        fs.setMoleFraction(oilPhaseIdx, gasCompIdx, xoG);
        fs.setMoleFraction(oilPhaseIdx, oilCompIdx, xoO);
 
        using CFRP = Opm::ComputeFromReferencePhase<Scalar, FluidSystem>;
        typename FluidSystem::template ParameterCache<Scalar> paramCache;
        CFRP::solve(fs,
                    paramCache,
                    /*refPhaseIdx=*/oilPhaseIdx,
                    /*setViscosities=*/false,
                    /*setEnthalpies=*/false);
 
        // set up the fluid state used for the injectors
        auto& injFs = injectorFluidState_;
        injFs = initialFluidState_;
 
        Scalar pInj = pReservoir_ * 1.5;
        injFs.setPressure(waterPhaseIdx, pInj);
        injFs.setPressure(oilPhaseIdx, pInj);
        injFs.setPressure(gasPhaseIdx, pInj);
        injFs.setSaturation(waterPhaseIdx, 1.0);
        injFs.setSaturation(oilPhaseIdx, 0.0);
        injFs.setSaturation(gasPhaseIdx, 0.0);
 
        // set the composition of the phases to immiscible
        for (unsigned phaseIdx = 0; phaseIdx < numPhases; ++phaseIdx)
            for (unsigned compIdx = 0; compIdx < numComponents; ++compIdx)
                injFs.setMoleFraction(phaseIdx, compIdx, 0.0);
 
        injFs.setMoleFraction(gasPhaseIdx, gasCompIdx, 1.0);
        injFs.setMoleFraction(oilPhaseIdx, oilCompIdx, 1.0);
        injFs.setMoleFraction(waterPhaseIdx, waterCompIdx, 1.0);
 
        CFRP::solve(injFs,
                    paramCache,
                    /*refPhaseIdx=*/waterPhaseIdx,
                    /*setViscosities=*/true,
                    /*setEnthalpies=*/false);
 
        // set up the fluid state used for the producer
        auto& prodFs = producerFluidState_;
        prodFs = initialFluidState_;
 
        Scalar pProd = pReservoir_ / 1.5;
        prodFs.setPressure(waterPhaseIdx, pProd);
        prodFs.setPressure(oilPhaseIdx, pProd);
        prodFs.setPressure(gasPhaseIdx, pProd);
        prodFs.setSaturation(waterPhaseIdx, 0.0);
        prodFs.setSaturation(oilPhaseIdx, 1.0);
        prodFs.setSaturation(gasPhaseIdx, 0.0);
 
        CFRP::solve(prodFs,
                    paramCache,
                    /*refPhaseIdx=*/oilPhaseIdx,
                    /*setViscosities=*/true,
                    /*setEnthalpies=*/false);
    }
 
    bool isProducer_(const GlobalPosition& pos) const
    {
        Scalar x = pos[0] - this->boundingBoxMin()[0];
        Scalar y = pos[dim - 1] - this->boundingBoxMin()[dim - 1];
        Scalar width = this->boundingBoxMax()[0] - this->boundingBoxMin()[0];
        Scalar height = this->boundingBoxMax()[dim - 1] - this->boundingBoxMin()[dim - 1];
 
        // only the upper half of the center section of the spatial domain is assumed to
        // be the producer
        if (y <= height/2.0)
            return false;
 
        return width/2.0 - width*1e-5 < x && x < width/2.0 + width*(wellWidth_ + 1e-5);
    }
 
    bool isInjector_(const GlobalPosition& pos) const
    {
        Scalar x = pos[0] - this->boundingBoxMin()[0];
        Scalar y = pos[dim - 1] - this->boundingBoxMin()[dim - 1];
        Scalar width = this->boundingBoxMax()[0] - this->boundingBoxMin()[0];
        Scalar height = this->boundingBoxMax()[dim - 1] - this->boundingBoxMin()[dim - 1];
 
        // only the lower half of the leftmost and rightmost part of the spatial domain
        // are assumed to be the water injectors
        if (y > height/2.0)
            return false;
 
        return x < width*wellWidth_ - width*1e-5 || x > width*(1.0 - wellWidth_) + width*1e-5;
    }
 
    bool isFineMaterial_(const GlobalPosition& pos) const
    { return pos[dim - 1] > layerBottom_; }
 
    DimMatrix fineK_;
    DimMatrix coarseK_;
    Scalar layerBottom_;
    Scalar pReservoir_;
 
    Scalar finePorosity_;
    Scalar coarsePorosity_;
 
    MaterialLawParams fineMaterialParams_;
    MaterialLawParams coarseMaterialParams_;
    std::vector<const MaterialLawParams*> materialParams_;
 
    InitialFluidState initialFluidState_;
    InitialFluidState injectorFluidState_;
    InitialFluidState producerFluidState_;
 
    Scalar temperature_;
    Scalar maxDepth_;
    Scalar wellWidth_;
};
} // namespace Opm
 
#endif