/* Copyright 2012 SINTEF ICT, Applied Mathematics. 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 3 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 . */ #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include namespace Opm { /// Construct solver. /// \param[in] grid A 2d or 3d grid. /// \param[in] props Rock and fluid properties. /// \param[in] linsolver Linear solver to use. /// \param[in] residual_tol Solution accepted if inf-norm of residual is smaller. /// \param[in] change_tol Solution accepted if inf-norm of change in pressure is smaller. /// \param[in] maxiter Maximum acceptable number of iterations. /// \param[in] gravity Gravity vector. If non-null, the array should /// have D elements. /// \param[in] wells The wells argument. Will be used in solution, /// is ignored if NULL. /// Note: this class observes the well object, and /// makes the assumption that the well topology /// and completions does not change during the /// run. However, controls (only) are allowed /// to change. CompressibleTpfa::CompressibleTpfa(const UnstructuredGrid& grid, const BlackoilPropertiesInterface& props, const RockCompressibility* rock_comp_props, const LinearSolverInterface& linsolver, const double residual_tol, const double change_tol, const int maxiter, const double* gravity, const struct Wells* wells) : grid_(grid), props_(props), rock_comp_props_(rock_comp_props), linsolver_(linsolver), residual_tol_(residual_tol), change_tol_(change_tol), maxiter_(maxiter), gravity_(gravity), wells_(wells), htrans_(grid.cell_facepos[ grid.number_of_cells ]), trans_ (grid.number_of_faces), allcells_(grid.number_of_cells), singular_(false) { if (wells_ && (wells_->number_of_phases != props.numPhases())) { THROW("Inconsistent number of phases specified (wells vs. props): " << wells_->number_of_phases << " != " << props.numPhases()); } const int num_dofs = grid.number_of_cells + (wells ? wells->number_of_wells : 0); pressure_increment_.resize(num_dofs); UnstructuredGrid* gg = const_cast(&grid_); tpfa_htrans_compute(gg, props.permeability(), &htrans_[0]); tpfa_trans_compute(gg, &htrans_[0], &trans_[0]); // If we have rock compressibility, pore volumes are updated // in the compute*() methods, otherwise they are constant and // hence may be computed here. if (rock_comp_props_ == NULL || !rock_comp_props_->isActive()) { computePorevolume(grid_, props.porosity(), porevol_); } for (int c = 0; c < grid.number_of_cells; ++c) { allcells_[c] = c; } cfs_tpfa_res_wells w; w.W = const_cast(wells_); w.data = NULL; h_ = cfs_tpfa_res_construct(gg, &w, props.numPhases()); } /// Destructor. CompressibleTpfa::~CompressibleTpfa() { cfs_tpfa_res_destroy(h_); } /// Solve pressure equation, by Newton iterations. void CompressibleTpfa::solve(const double dt, BlackoilState& state, WellState& well_state) { const int nc = grid_.number_of_cells; const int nw = (wells_ != 0) ? wells_->number_of_wells : 0; // Set up dynamic data. computePerSolveDynamicData(dt, state, well_state); computePerIterationDynamicData(dt, state, well_state); // Assemble J and F. assemble(dt, state, well_state); double inc_norm = 0.0; int iter = 0; double res_norm = residualNorm(); std::cout << "\nIteration Residual Change in p\n" << std::setw(9) << iter << std::setw(18) << res_norm << std::setw(18) << '*' << std::endl; while ((iter < maxiter_) && (res_norm > residual_tol_)) { // Solve for increment in Newton method: // incr = x_{n+1} - x_{n} = -J^{-1}F // (J is Jacobian matrix, F is residual) solveIncrement(); ++iter; // Update pressure vars with increment. for (int c = 0; c < nc; ++c) { state.pressure()[c] += pressure_increment_[c]; } for (int w = 0; w < nw; ++w) { well_state.bhp()[w] += pressure_increment_[nc + w]; } // Stop iterating if increment is small. inc_norm = incrementNorm(); if (inc_norm <= change_tol_) { std::cout << std::setw(9) << iter << std::setw(18) << '*' << std::setw(18) << inc_norm << std::endl; break; } // Set up dynamic data. computePerIterationDynamicData(dt, state, well_state); // Assemble J and F. assemble(dt, state, well_state); // Update residual norm. res_norm = residualNorm(); std::cout << std::setw(9) << iter << std::setw(18) << res_norm << std::setw(18) << inc_norm << std::endl; } if ((iter == maxiter_) && (res_norm > residual_tol_) && (inc_norm > change_tol_)) { THROW("CompressibleTpfa::solve() failed to converge in " << maxiter_ << " iterations."); } std::cout << "Solved pressure in " << iter << " iterations." << std::endl; // Compute fluxes and face pressures. computeResults(state, well_state); } /// @brief After solve(), was the resulting pressure singular. /// Returns true if the pressure is singular in the following /// sense: if everything is incompressible and there are no /// pressure conditions, the absolute values of the pressure /// solution are arbitrary. (But the differences in pressure /// are significant.) bool CompressibleTpfa::singularPressure() const { return singular_; } /// Compute well potentials. void CompressibleTpfa::computeWellPotentials(const BlackoilState& state) { if (wells_ == NULL) return; const int nw = wells_->number_of_wells; const int np = props_.numPhases(); const int nperf = wells_->well_connpos[nw]; const int dim = grid_.dimensions; const double grav = gravity_ ? gravity_[dim - 1] : 0.0; wellperf_gpot_.clear(); wellperf_gpot_.resize(np*nperf, 0.0); if (grav == 0.0) { return; } // Temporary storage for perforation A matrices and densities. std::vector A(np*np, 0.0); std::vector rho(np, 0.0); // Main loop, iterate over all perforations, // using the following formula (by phase): // gpot(perf) = g*(perf_z - well_ref_z)*rho(perf) // where the phase densities rho(perf) are taken to be // the densities in the perforation cell. for (int w = 0; w < nw; ++w) { const double ref_depth = wells_->depth_ref[w]; for (int j = wells_->well_connpos[w]; j < wells_->well_connpos[w + 1]; ++j) { const int cell = wells_->well_cells[j]; const double cell_depth = grid_.cell_centroids[dim * cell + dim - 1]; props_.matrix(1, &state.pressure()[cell], &state.surfacevol()[np*cell], &cell, &A[0], 0); props_.density(1, &A[0], &rho[0]); for (int phase = 0; phase < np; ++phase) { wellperf_gpot_[np*j + phase] = rho[phase]*grav*(cell_depth - ref_depth); } } } } /// Compute per-solve dynamic properties. void CompressibleTpfa::computePerSolveDynamicData(const double /*dt*/, const BlackoilState& state, const WellState& /*well_state*/) { computeWellPotentials(state); if (rock_comp_props_ && rock_comp_props_->isActive()) { computePorevolume(grid_, props_.porosity(), *rock_comp_props_, state.pressure(), initial_porevol_); } } /// Compute per-iteration dynamic properties. void CompressibleTpfa::computePerIterationDynamicData(const double dt, const BlackoilState& state, const WellState& well_state) { // These are the variables that get computed by this function: // // std::vector cell_A_; // std::vector cell_dA_; // std::vector cell_viscosity_; // std::vector cell_phasemob_; // std::vector cell_voldisc_; // std::vector face_A_; // std::vector face_phasemob_; // std::vector face_gravcap_; // std::vector wellperf_A_; // std::vector wellperf_phasemob_; // std::vector porevol_; // Only modified if rock_comp_props_ is non-null. // std::vector rock_comp_; // Empty unless rock_comp_props_ is non-null. computeCellDynamicData(dt, state, well_state); computeFaceDynamicData(dt, state, well_state); computeWellDynamicData(dt, state, well_state); } /// Compute per-iteration dynamic properties for cells. void CompressibleTpfa::computeCellDynamicData(const double /*dt*/, const BlackoilState& state, const WellState& /*well_state*/) { // These are the variables that get computed by this function: // // std::vector cell_A_; // std::vector cell_dA_; // std::vector cell_viscosity_; // std::vector cell_phasemob_; // std::vector cell_voldisc_; // std::vector porevol_; // Only modified if rock_comp_props_ is non-null. // std::vector rock_comp_; // Empty unless rock_comp_props_ is non-null. const int nc = grid_.number_of_cells; const int np = props_.numPhases(); const double* cell_p = &state.pressure()[0]; const double* cell_z = &state.surfacevol()[0]; const double* cell_s = &state.saturation()[0]; cell_A_.resize(nc*np*np); cell_dA_.resize(nc*np*np); props_.matrix(nc, cell_p, cell_z, &allcells_[0], &cell_A_[0], &cell_dA_[0]); cell_viscosity_.resize(nc*np); props_.viscosity(nc, cell_p, cell_z, &allcells_[0], &cell_viscosity_[0], 0); cell_phasemob_.resize(nc*np); props_.relperm(nc, cell_s, &allcells_[0], &cell_phasemob_[0], 0); std::transform(cell_phasemob_.begin(), cell_phasemob_.end(), cell_viscosity_.begin(), cell_phasemob_.begin(), std::divides()); // Volume discrepancy: we have that // z = Au, voldiscr = sum(u) - 1, // but I am not sure it is actually needed. // Use zero for now. // TODO: Check this! cell_voldisc_.clear(); cell_voldisc_.resize(nc, 0.0); if (rock_comp_props_ && rock_comp_props_->isActive()) { computePorevolume(grid_, props_.porosity(), *rock_comp_props_, state.pressure(), porevol_); rock_comp_.resize(nc); for (int cell = 0; cell < nc; ++cell) { rock_comp_[cell] = rock_comp_props_->rockComp(state.pressure()[cell]); } } } /// Compute per-iteration dynamic properties for faces. void CompressibleTpfa::computeFaceDynamicData(const double /*dt*/, const BlackoilState& state, const WellState& /*well_state*/) { // These are the variables that get computed by this function: // // std::vector face_A_; // std::vector face_phasemob_; // std::vector face_gravcap_; const int np = props_.numPhases(); const int nf = grid_.number_of_faces; const int dim = grid_.dimensions; const double grav = gravity_ ? gravity_[dim - 1] : 0.0; std::vector gravcontrib[2]; std::vector pot[2]; gravcontrib[0].resize(np); gravcontrib[1].resize(np); pot[0].resize(np); pot[1].resize(np); face_A_.resize(nf*np*np); face_phasemob_.resize(nf*np); face_gravcap_.resize(nf*np); for (int face = 0; face < nf; ++face) { // Obtain properties from both sides of the face. const double face_depth = grid_.face_centroids[face*dim + dim - 1]; const int* c = &grid_.face_cells[2*face]; // Get pressures and compute gravity contributions, // to decide upwind directions. double c_press[2]; for (int j = 0; j < 2; ++j) { if (c[j] >= 0) { // Pressure c_press[j] = state.pressure()[c[j]]; // Gravity contribution, gravcontrib = rho*(face_z - cell_z) [per phase]. if (grav != 0.0) { const double depth_diff = face_depth - grid_.cell_centroids[c[j]*dim + dim - 1]; props_.density(1, &cell_A_[np*np*c[j]], &gravcontrib[j][0]); for (int p = 0; p < np; ++p) { gravcontrib[j][p] *= depth_diff*grav; } } else { std::fill(gravcontrib[j].begin(), gravcontrib[j].end(), 0.0); } } else { // Pressures c_press[j] = state.facepressure()[face]; // Gravity contribution. std::fill(gravcontrib[j].begin(), gravcontrib[j].end(), 0.0); } } // Gravity contribution: // gravcapf = rho_1*g*(z_12 - z_1) - rho_2*g*(z_12 - z_2) // where _1 and _2 refers to two neigbour cells, z is the // z coordinate of the centroid, and z_12 is the face centroid. // Also compute the potentials. for (int phase = 0; phase < np; ++phase) { face_gravcap_[np*face + phase] = gravcontrib[0][phase] - gravcontrib[1][phase]; pot[0][phase] = c_press[0] + face_gravcap_[np*face + phase]; pot[1][phase] = c_press[1]; } // Now we can easily find the upwind direction for every phase, // we can also tell which boundary faces are inflow bdys. // Get upwind mobilities by phase. // Get upwind A matrix rows by phase. // NOTE: // We should be careful to upwind the R factors, // the B factors are not that vital. // z = Au = RB^{-1}u, // where (this example is for gas-oil) // R = [1 RgL; RoV 1], B = [BL 0 ; 0 BV] // (RgL is gas in Liquid phase, RoV is oil in Vapour phase.) // A = [1/BL RgL/BV; RoV/BL 1/BV] // This presents us with a dilemma, as V factors should be // upwinded according to V phase flow, same for L. What then // about the RgL/BV and RoV/BL numbers? // We give priority to R, and therefore upwind the rows of A // by phase (but remember, Fortran matrix ordering). // This prompts the question if we should split the matrix() // property method into formation volume and R-factor methods. for (int phase = 0; phase < np; ++phase) { int upwindc = -1; if (c[0] >=0 && c[1] >= 0) { upwindc = (pot[0] < pot[1]) ? c[1] : c[0]; } else { upwindc = (c[0] >= 0) ? c[0] : c[1]; } face_phasemob_[np*face + phase] = cell_phasemob_[np*upwindc + phase]; for (int p2 = 0; p2 < np; ++p2) { // Recall: column-major ordering. face_A_[np*np*face + phase + np*p2] = cell_A_[np*np*upwindc + phase + np*p2]; } } } } /// Compute per-iteration dynamic properties for wells. void CompressibleTpfa::computeWellDynamicData(const double /*dt*/, const BlackoilState& /*state*/, const WellState& well_state) { // These are the variables that get computed by this function: // // std::vector wellperf_A_; // std::vector wellperf_phasemob_; const int np = props_.numPhases(); const int nw = (wells_ != 0) ? wells_->number_of_wells : 0; const int nperf = (wells_ != 0) ? wells_->well_connpos[nw] : 0; wellperf_A_.resize(nperf*np*np); wellperf_phasemob_.resize(nperf*np); // The A matrix is set equal to the perforation grid cells' // matrix for producers, computed from bhp and injection // component fractions from // The mobilities are set equal to the perforation grid cells' // mobilities for producers. std::vector mu(np); for (int w = 0; w < nw; ++w) { bool producer = (wells_->type[w] == PRODUCER); const double* comp_frac = &wells_->comp_frac[np*w]; for (int j = wells_->well_connpos[w]; j < wells_->well_connpos[w+1]; ++j) { const int c = wells_->well_cells[j]; double* wpA = &wellperf_A_[np*np*j]; double* wpM = &wellperf_phasemob_[np*j]; if (producer) { const double* cA = &cell_A_[np*np*c]; std::copy(cA, cA + np*np, wpA); const double* cM = &cell_phasemob_[np*c]; std::copy(cM, cM + np, wpM); } else { const double bhp = well_state.bhp()[w]; double perf_p = bhp; for (int phase = 0; phase < np; ++phase) { perf_p += wellperf_gpot_[np*j + phase]*comp_frac[phase]; } // Hack warning: comp_frac is used as a component // surface-volume variable in calls to matrix() and // viscosity(), but as a saturation in the call to // relperm(). This is probably ok as long as injectors // only inject pure fluids. props_.matrix(1, &perf_p, comp_frac, &c, wpA, NULL); props_.viscosity(1, &perf_p, comp_frac, &c, &mu[0], NULL); ASSERT(std::fabs(std::accumulate(comp_frac, comp_frac + np, 0.0) - 1.0) < 1e-6); props_.relperm (1, comp_frac, &c, wpM , NULL); for (int phase = 0; phase < np; ++phase) { wpM[phase] /= mu[phase]; } } } } } /// Compute the residual and Jacobian. void CompressibleTpfa::assemble(const double dt, const BlackoilState& state, const WellState& well_state) { const double* cell_press = &state.pressure()[0]; const double* well_bhp = well_state.bhp().empty() ? NULL : &well_state.bhp()[0]; const double* z = &state.surfacevol()[0]; UnstructuredGrid* gg = const_cast(&grid_); CompletionData completion_data; completion_data.gpot = ! wellperf_gpot_.empty() ? &wellperf_gpot_[0] : 0; completion_data.A = ! wellperf_A_.empty() ? &wellperf_A_[0] : 0; completion_data.phasemob = ! wellperf_phasemob_.empty() ? &wellperf_phasemob_[0] : 0; cfs_tpfa_res_wells wells_tmp; wells_tmp.W = const_cast(wells_); wells_tmp.data = &completion_data; cfs_tpfa_res_forces forces; forces.wells = &wells_tmp; forces.src = NULL; // Check if it is legal to leave it as NULL. compr_quantities_gen cq; cq.nphases = props_.numPhases(); cq.Ac = &cell_A_[0]; cq.dAc = &cell_dA_[0]; cq.Af = &face_A_[0]; cq.phasemobf = &face_phasemob_[0]; cq.voldiscr = &cell_voldisc_[0]; int was_adjusted = 0; if (! (rock_comp_props_ && rock_comp_props_->isActive())) { was_adjusted = cfs_tpfa_res_assemble(gg, dt, &forces, z, &cq, &trans_[0], &face_gravcap_[0], cell_press, well_bhp, &porevol_[0], h_); } else { was_adjusted = cfs_tpfa_res_comprock_assemble(gg, dt, &forces, z, &cq, &trans_[0], &face_gravcap_[0], cell_press, well_bhp, &porevol_[0], &initial_porevol_[0], &rock_comp_[0], h_); } singular_ = (was_adjusted == 1); } /// Computes pressure_increment_. void CompressibleTpfa::solveIncrement() { // Increment is equal to -J^{-1}F linsolver_.solve(h_->J, h_->F, &pressure_increment_[0]); std::transform(pressure_increment_.begin(), pressure_increment_.end(), pressure_increment_.begin(), std::negate()); } namespace { template double infnorm(FI beg, FI end) { double norm = 0.0; for (; beg != end; ++beg) { norm = std::max(norm, std::fabs(*beg)); } return norm; } } // anonymous namespace /// Computes the inf-norm of the residual. double CompressibleTpfa::residualNorm() const { const int ndof = pressure_increment_.size(); return infnorm(h_->F, h_->F + ndof); } /// Computes the inf-norm of pressure_increment_. double CompressibleTpfa::incrementNorm() const { return infnorm(pressure_increment_.begin(), pressure_increment_.end()); } /// Compute the output. void CompressibleTpfa::computeResults(BlackoilState& state, WellState& well_state) const { UnstructuredGrid* gg = const_cast(&grid_); CompletionData completion_data; completion_data.gpot = ! wellperf_gpot_.empty() ? const_cast(&wellperf_gpot_[0]) : 0; completion_data.A = ! wellperf_A_.empty() ? const_cast(&wellperf_A_[0]) : 0; completion_data.phasemob = ! wellperf_phasemob_.empty() ? const_cast(&wellperf_phasemob_[0]) : 0; cfs_tpfa_res_wells wells_tmp; wells_tmp.W = const_cast(wells_); wells_tmp.data = &completion_data; cfs_tpfa_res_forces forces; forces.wells = &wells_tmp; forces.src = NULL; double* wpress = ! well_state.bhp ().empty() ? & well_state.bhp ()[0] : 0; double* wflux = ! well_state.perfRates().empty() ? & well_state.perfRates()[0] : 0; cfs_tpfa_res_flux(gg, &forces, props_.numPhases(), &trans_[0], &cell_phasemob_[0], &face_phasemob_[0], &face_gravcap_[0], &state.pressure()[0], wpress, &state.faceflux()[0], wflux); cfs_tpfa_res_fpress(gg, props_.numPhases(), &htrans_[0], &face_phasemob_[0], &face_gravcap_[0], h_, &state.pressure()[0], &state.faceflux()[0], &state.facepressure()[0]); // Compute well perforation pressures (not done by the C code). if (wells_ != 0) { const int nw = wells_->number_of_wells; const int np = props_.numPhases(); for (int w = 0; w < nw; ++w) { const double* comp_frac = &wells_->comp_frac[np*w]; for (int j = wells_->well_connpos[w]; j < wells_->well_connpos[w+1]; ++j) { const double bhp = well_state.bhp()[w]; double perf_p = bhp; for (int phase = 0; phase < np; ++phase) { perf_p += wellperf_gpot_[np*j + phase]*comp_frac[phase]; } well_state.perfPress()[j] = perf_p; } } } } } // namespace Opm