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538 lines
20 KiB
C++
538 lines
20 KiB
C++
/*
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Copyright 2013 SINTEF ICT, Applied Mathematics.
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Copyright 2013 Statoil ASA.
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This file is part of the Open Porous Media Project (OPM).
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OPM is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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OPM is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with OPM. If not, see <http://www.gnu.org/licenses/>.
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*/
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#ifndef OPM_IMPESTPFAAD_HEADER_INCLUDED
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#define OPM_IMPESTPFAAD_HEADER_INCLUDED
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#include <opm/autodiff/AutoDiffBlock.hpp>
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#include <opm/autodiff/AutoDiffHelpers.hpp>
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#include <opm/core/simulator/BlackoilState.hpp>
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#include <opm/core/simulator/WellState.hpp>
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#include <opm/core/utility/ErrorMacros.hpp>
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#include <opm/core/linalg/LinearSolverInterface.hpp>
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#include <opm/core/wells.h>
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#include <algorithm>
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#include <cassert>
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#include <vector>
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#include <iterator>
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#include <boost/shared_ptr.hpp>
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struct UnstructuredGrid;
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namespace {
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std::vector<int>
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buildAllCells(const int nc)
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{
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std::vector<int> all_cells(nc);
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for (int c = 0; c < nc; ++c) { all_cells[c] = c; }
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return all_cells;
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}
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template <class GeoProps>
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AutoDiff::ForwardBlock<double>::M
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gravityOperator(const UnstructuredGrid& grid,
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const HelperOps& ops ,
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const GeoProps& geo )
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{
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const int nc = grid.number_of_cells;
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std::vector<int> f2hf(2 * grid.number_of_faces, -1);
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for (int c = 0, i = 0; c < nc; ++c) {
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for (; i < grid.cell_facepos[c + 1]; ++i) {
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const int f = grid.cell_faces[ i ];
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const int p = 0 + (grid.face_cells[2*f + 0] != c);
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f2hf[2*f + p] = i;
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}
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}
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typedef AutoDiff::ForwardBlock<double>::V V;
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typedef AutoDiff::ForwardBlock<double>::M M;
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const V& gpot = geo.gravityPotential();
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const V& trans = geo.transmissibility();
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const HelperOps::IFaces::Index ni = ops.internal_faces.size();
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typedef Eigen::Triplet<double> Tri;
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std::vector<Tri> grav; grav.reserve(2 * ni);
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for (HelperOps::IFaces::Index i = 0; i < ni; ++i) {
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const int f = ops.internal_faces[ i ];
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const int c1 = grid.face_cells[2*f + 0];
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const int c2 = grid.face_cells[2*f + 1];
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assert ((c1 >= 0) && (c2 >= 0));
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const double dG1 = gpot[ f2hf[2*f + 0] ];
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const double dG2 = gpot[ f2hf[2*f + 1] ];
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const double t = trans[ f ];
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grav.push_back(Tri(i, c1, t * dG1));
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grav.push_back(Tri(i, c2, - t * dG2));
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}
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M G(ni, nc); G.setFromTriplets(grav.begin(), grav.end());
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return G;
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}
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}
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namespace Opm {
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template <class BOFluid, class GeoProps>
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class ImpesTPFAAD {
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public:
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ImpesTPFAAD(const UnstructuredGrid& grid ,
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const BOFluid& fluid,
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const GeoProps& geo ,
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const Wells& wells,
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const LinearSolverInterface& linsolver)
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: grid_ (grid)
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, fluid_ (fluid)
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, geo_ (geo)
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, wells_ (wells)
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, linsolver_(linsolver)
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// , pdepfdata_(grid.number_of_cells, fluid)
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, ops_ (grid)
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, grav_ (gravityOperator(grid_, ops_, geo_))
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, cell_residual_ (ADB::null())
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, well_flow_residual_ ()
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, well_residual_ (ADB::null())
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, total_residual_ (ADB::null())
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{
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}
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void
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solve(const double dt,
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BlackoilState& state,
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WellState& well_state)
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{
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const int nc = grid_.number_of_cells;
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const int np = state.numPhases();
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well_flow_residual_.resize(np, ADB::null());
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// Compute relperms once and for all (since saturations are explicit).
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DataBlock s = Eigen::Map<const DataBlock>(state.saturation().data(), nc, np);
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ASSERT(np == 2);
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kr_ = fluid_.relperm(s.col(0), s.col(1), V::Zero(nc,1), buildAllCells(nc));
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// Compute relperms for wells. This must be revisited for crossflow.
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const int nw = wells_.number_of_wells;
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const int nperf = wells_.well_connpos[nw];
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DataBlock well_s(nperf, np);
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for (int w = 0; w < nw; ++w) {
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const double* comp_frac = &wells_.comp_frac[np*w];
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for (int j = wells_.well_connpos[w]; j < wells_.well_connpos[w+1]; ++j) {
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well_s.row(j) = Eigen::Map<const DataBlock>(comp_frac, 1, np);
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}
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}
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const std::vector<int> well_cells(wells_.well_cells,
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wells_.well_cells + nperf);
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well_kr_ = fluid_.relperm(well_s.col(0), well_s.col(1), V::Zero(nperf,1), well_cells);
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const double atol = 1.0e-15;
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const double rtol = 5.0e-10;
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const int maxit = 15;
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assemble(dt, state, well_state);
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const double r0 = residualNorm();
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int it = 0;
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bool resTooLarge = r0 > atol;
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while (resTooLarge && (it < maxit)) {
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solveJacobianSystem(state, well_state);
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assemble(dt, state, well_state);
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const double r = residualNorm();
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resTooLarge = (r > atol) && (r > rtol*r0);
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it += 1;
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}
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if (resTooLarge) {
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THROW("Failed to compute converged pressure solution");
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}
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else {
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computeFluxes(state);
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}
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}
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private:
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// Disallow copying and assignment
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ImpesTPFAAD(const ImpesTPFAAD& rhs);
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ImpesTPFAAD& operator=(const ImpesTPFAAD& rhs);
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// typedef PressureDependentFluidData<double, BOFluid> PDepFData;
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// typedef typename PDepFData::ADB ADB;
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typedef AutoDiff::ForwardBlock<double> ADB;
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typedef ADB::V V;
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typedef ADB::M M;
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typedef Eigen::Array<double,
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Eigen::Dynamic,
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Eigen::Dynamic,
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Eigen::RowMajor> DataBlock;
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const UnstructuredGrid& grid_;
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const BOFluid& fluid_;
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const GeoProps& geo_ ;
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const Wells& wells_;
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const LinearSolverInterface& linsolver_;
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HelperOps ops_;
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const M grav_;
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ADB cell_residual_;
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std::vector<ADB> well_flow_residual_;
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ADB well_residual_;
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ADB total_residual_;
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std::vector<V> kr_;
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std::vector<V> well_kr_;
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enum { Water = BOFluid::Water,
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Oil = BOFluid::Oil,
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Gas = BOFluid::Gas };
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void
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assemble(const double dt,
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const BlackoilState& state,
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const WellState& well_state)
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{
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const V& pv = geo_.poreVolume();
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const int nc = grid_.number_of_cells;
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const int np = state.numPhases();
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const int nw = wells_.number_of_wells;
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const int nperf = wells_.well_connpos[nw];
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const std::vector<int> cells = buildAllCells(nc);
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const Eigen::Map<const DataBlock> z0all(&state.surfacevol()[0], nc, np);
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const DataBlock qall = DataBlock::Zero(nc, np);
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const V delta_t = dt * V::Ones(nc, 1);
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const V transi = subset(geo_.transmissibility(),
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ops_.internal_faces);
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const std::vector<int> well_cells(wells_.well_cells,
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wells_.well_cells + nperf);
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const V transw = Eigen::Map<const V>(wells_.WI, nperf, 1);
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// Initialize AD variables: p (cell pressures), qs (well rates) and bhp (well bhp).
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const V p0 = Eigen::Map<const V>(&state.pressure()[0], nc, 1);
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const V qs0 = Eigen::Map<const V>(&well_state.wellRates()[0], nw*np, 1);
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const V bhp0 = Eigen::Map<const V>(&well_state.bhp()[0], nw, 1);
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std::vector<V> vars0 = { p0, qs0, bhp0 };
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std::vector<ADB> vars = ADB::variables(vars0);
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const ADB& p = vars[0];
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const ADB& qs = vars[1];
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const ADB& bhp = vars[2];
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std::vector<int> bpat = p.blockPattern();
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// Compute T_ij * (p_i - p_j) and use for upwinding.
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const ADB nkgradp = transi * (ops_.ngrad * p);
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const UpwindSelector<double> upwind(grid_, ops_, nkgradp.value());
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// Extract variables for perforation cell pressures
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// and corresponding perforation well pressures.
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const ADB p_perfcell = subset(p, well_cells);
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// Construct matrix to map wells->perforations.
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M well_to_perf(well_cells.size(), nw);
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typedef Eigen::Triplet<double> Tri;
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std::vector<Tri> w2p;
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for (int w = 0; w < nw; ++w) {
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for (int perf = wells_.well_connpos[w]; perf < wells_.well_connpos[w+1]; ++perf) {
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w2p.emplace_back(perf, w, 1.0);
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}
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}
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well_to_perf.setFromTriplets(w2p.begin(), w2p.end());
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const M perf_to_well = well_to_perf.transpose();
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// Construct pressure difference vector for wells.
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const V well_perf_dp = V::Zero(well_cells.size()); // No gravity yet!
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// Finally construct well perforation pressures and well flows.
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const ADB p_perfwell = well_to_perf*bhp + well_perf_dp;
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const ADB nkgradp_well = transw * (p_perfcell - p_perfwell);
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const Selector<double> cell_to_well_selector(nkgradp_well.value());
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cell_residual_ = ADB::constant(pv, bpat);
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well_residual_ = ADB::constant(V::Zero(nw,1), bpat);
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ADB divcontrib_sum = ADB::constant(V::Zero(nc,1), bpat);
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for (int phase = 0; phase < np; ++phase) {
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const ADB cell_b = fluidFvf(phase, p, cells);
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const ADB cell_rho = fluidRho(phase, p, cells);
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const ADB well_b = fluidFvf(phase, p_perfwell, well_cells);
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const V kr = fluidKr(phase);
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// Explicitly not asking for derivatives of viscosity,
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// since they are not available yet.
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const V mu = fluidMu(phase, p.value(), cells);
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const V cell_mob = kr / mu;
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const V face_mob = upwind.select(cell_mob);
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const V well_kr = fluidKrWell(phase);
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const V well_mu = fluidMu(phase, p_perfwell.value(), well_cells);
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const V well_mob = well_kr / well_mu;
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const V perf_mob = cell_to_well_selector.select(subset(cell_mob, well_cells), well_mob);
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const ADB flux = face_mob * (nkgradp + (grav_ * cell_rho));
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const ADB perf_flux = perf_mob * (nkgradp_well); // No gravity term for perforations.
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const ADB face_b = upwind.select(cell_b);
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const ADB perf_b = cell_to_well_selector.select(subset(cell_b, well_cells), well_b);
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const V z0 = z0all.block(0, phase, nc, 1);
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const V q = qall .block(0, phase, nc, 1);
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const ADB well_contrib = superset(perf_flux*perf_b, well_cells, nc);
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const ADB divcontrib = delta_t * (ops_.div * (flux * face_b)
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+ well_contrib);
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const V qcontrib = delta_t * q;
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const ADB pvcontrib = ADB::constant(pv*z0, bpat);
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const ADB component_contrib = pvcontrib + qcontrib;
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divcontrib_sum = divcontrib_sum - divcontrib/cell_b;
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cell_residual_ = cell_residual_ - (component_contrib/cell_b);
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const ADB well_rates = perf_to_well * (perf_flux*perf_b);
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std::vector<int> well_flow_res_phase_idx(nw);
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for (int w = 0; w < nw; ++w) {
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well_flow_res_phase_idx[w] = w + phase*nw;
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}
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well_flow_residual_[phase] = well_rates - subset(qs, well_flow_res_phase_idx);
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}
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cell_residual_ = cell_residual_ + divcontrib_sum;
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// Handling BHP and SURFACE_RATE wells.
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V bhp_targets(nw,1);
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V rate_targets(nw,1);
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M rate_distr(nw, np*nw);
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for (int w = 0; w < nw; ++w) {
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const WellControls* wc = wells_.ctrls[w];
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if (wc->type[wc->current] == BHP) {
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bhp_targets[w] = wc->target[wc->current];
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rate_targets[w] = -1e100;
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} else if (wc->type[wc->current] == SURFACE_RATE) {
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bhp_targets[w] = -1e100;
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rate_targets[w] = wc->target[wc->current];
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for (int phase = 0; phase < np; ++phase) {
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rate_distr.insert(w, phase*nw + w) = wc->distr[phase];
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}
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} else {
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THROW("Can only handle BHP and SURFACE_RATE type controls.");
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}
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}
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const ADB bhp_residual = bhp - bhp_targets;
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const ADB rate_residual = rate_distr * qs - rate_targets;
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// Choose bhp residual for positive bhp targets.
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Selector<double> bhp_selector(bhp_targets);
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well_residual_ = bhp_selector.select(bhp_residual, rate_residual);
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ASSERT(np == 2);
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const ADB well_flow_res = vertcat(well_flow_residual_[0], well_flow_residual_[1]);
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const ADB well_res = vertcat(well_flow_res, well_residual_);
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total_residual_ = collapseJacs(vertcat(cell_residual_, well_res));
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}
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void
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solveJacobianSystem(BlackoilState& state,
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WellState& well_state) const
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{
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const int nc = grid_.number_of_cells;
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const int nw = wells_.number_of_wells;
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const int np = state.numPhases();
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Eigen::SparseMatrix<double, Eigen::RowMajor> matr = total_residual_.derivative()[0];
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#if HACK_INCOMPRESSIBLE_GRAVITY
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matr.coeffRef(0, 0) *= 2;
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#endif
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V dx(total_residual_.size());
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Opm::LinearSolverInterface::LinearSolverReport rep
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= linsolver_.solve(matr.rows(), matr.nonZeros(),
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matr.outerIndexPtr(), matr.innerIndexPtr(), matr.valuePtr(),
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total_residual_.value().data(), dx.data());
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if (!rep.converged) {
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THROW("ImpesTPFAAD::solve(): Linear solver convergence failure.");
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}
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const V p0 = Eigen::Map<const V>(&state.pressure()[0], nc, 1);
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const V dp = subset(dx, buildAllCells(nc));
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const V p = p0 - dp;
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std::copy(&p[0], &p[0] + nc, state.pressure().begin());
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const V qs0 = Eigen::Map<const V>(&well_state.wellRates()[0], nw*np, 1);
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std::vector<int> qs_dofs(np*nw);
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for (int w = 0; w < nw; ++w) {
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for (int phase = 0; phase < np; ++phase) {
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qs_dofs[w*np + phase] = nc + w*np + phase;
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}
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}
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const V dqs = subset(dx, qs_dofs);
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const V qs = qs0 - dqs;
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std::copy(&qs[0], &qs[0] + np*nw, well_state.wellRates().begin());
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const V bhp0 = Eigen::Map<const V>(&well_state.bhp()[0], nw, 1);
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std::vector<int> bhp_dofs(nw);
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for (int w = 0; w < nw; ++w) {
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bhp_dofs[w] = nc + np*nw + w;
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}
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ASSERT(bhp_dofs.back() + 1 == total_residual_.size());
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const V dbhp = subset(dx, bhp_dofs);
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const V bhp = bhp0 - dbhp;
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std::copy(&bhp[0], &bhp[0] + nw, well_state.bhp().begin());
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}
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double
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residualNorm() const
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{
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return total_residual_.value().matrix().norm();
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}
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void
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computeFluxes(BlackoilState& state) const
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{
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const int nc = grid_.number_of_cells;
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const int np = state.numPhases();
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const std::vector<int> cells = buildAllCells(nc);
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const V p0 = Eigen::Map<const V>(&state.pressure()[0], nc, 1);
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const ADB p = ADB::constant(p0, cell_residual_.blockPattern());
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const V transi = subset(geo_.transmissibility(),
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ops_.internal_faces);
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const V nkgradp = transi * (ops_.ngrad * p0.matrix()).array();
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V flux = V::Zero(ops_.internal_faces.size(), 1);
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for (int phase = 0; phase < np; ++phase) {
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const ADB cell_rho = fluidRho(phase, p, cells);
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const V head = nkgradp + (grav_ * cell_rho.value().matrix()).array();
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const UpwindSelector<double> upwind(grid_, ops_, head);
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const V kr = fluidKr(phase);
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const V mu = fluidMu(phase, p.value(), cells);
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const V mf = upwind.select(kr / mu);
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flux += mf * head;
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}
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V all_flux = superset(flux, ops_.internal_faces, grid_.number_of_faces);
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std::copy(all_flux.data(), all_flux.data() + grid_.number_of_faces, state.faceflux().data());
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}
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V fluidMu(const int phase, const V& p, const std::vector<int>& cells) const
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{
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switch (phase) {
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case Water:
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return fluid_.muWat(p, cells);
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case Oil: {
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V dummy_rs = V::Zero(p.size(), 1) * p;
|
|
return fluid_.muOil(p, dummy_rs, cells);
|
|
}
|
|
case Gas:
|
|
return fluid_.muGas(p, cells);
|
|
default:
|
|
THROW("Unknown phase index " << phase);
|
|
}
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
ADB fluidMu(const int phase, const ADB& p, const std::vector<int>& cells) const
|
|
{
|
|
switch (phase) {
|
|
case Water:
|
|
return fluid_.muWat(p, cells);
|
|
case Oil: {
|
|
ADB dummy_rs = V::Zero(p.size(), 1) * p;
|
|
return fluid_.muOil(p, dummy_rs, cells);
|
|
}
|
|
case Gas:
|
|
return fluid_.muGas(p, cells);
|
|
default:
|
|
THROW("Unknown phase index " << phase);
|
|
}
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
ADB fluidFvf(const int phase, const ADB& p, const std::vector<int>& cells) const
|
|
{
|
|
switch (phase) {
|
|
case Water:
|
|
return fluid_.bWat(p, cells);
|
|
case Oil: {
|
|
ADB dummy_rs = V::Zero(p.size(), 1) * p;
|
|
return fluid_.bOil(p, dummy_rs, cells);
|
|
}
|
|
case Gas:
|
|
return fluid_.bGas(p, cells);
|
|
default:
|
|
THROW("Unknown phase index " << phase);
|
|
}
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
ADB fluidRho(const int phase, const ADB& p, const std::vector<int>& cells) const
|
|
{
|
|
const double* rhos = fluid_.surfaceDensity();
|
|
ADB b = fluidFvf(phase, p, cells);
|
|
ADB rho = V::Constant(p.size(), 1, rhos[phase]) * b;
|
|
return rho;
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
V fluidKr(const int phase) const
|
|
{
|
|
return kr_[phase];
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
V fluidKrWell(const int phase) const
|
|
{
|
|
return well_kr_[phase];
|
|
}
|
|
|
|
};
|
|
} // namespace Opm
|
|
|
|
#endif /* OPM_IMPESTPFAAD_HEADER_INCLUDED */
|