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adimensional_system.cpp
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/*-------------------------------------------------------
- Module : specmicp
- File : adim_system.cpp
- Author : Fabien Georget
Copyright (c) 2014, Fabien Georget <fabieng@princeton.edu>, Princeton University
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
* Neither the name of the Princeton University nor the
names of its contributors may be used to endorse or promote products
derived from this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
---------------------------------------------------------*/
//#include <iostream>
#include <cmath>
#include "adimensional_system.hpp"
#include "utils/log.hpp"
#include "../equilibrium_data.hpp"
#include "physics/constants.hpp"
#include "physics/laws.hpp"
#include "adimensional_system_solution.hpp"
namespace specmicp {
constexpr scalar_t log10 = std::log(10.0);
AdimensionalSystem::AdimensionalSystem(RawDatabasePtr ptrdata,
const Vector &totconc,
bool conservation_water,
index_t charge_keeper):
m_data(ptrdata),
m_tot_conc(totconc),
m_secondary_conc(ptrdata->nb_aqueous),
m_loggamma(ptrdata->nb_component+ptrdata->nb_aqueous),
m_charge_keeper(charge_keeper)
{
number_eq(conservation_water);
m_secondary_conc.setZero();
m_loggamma.setZero();
}
AdimensionalSystem::AdimensionalSystem(
RawDatabasePtr ptrdata,
const Vector& totconc,
const AdimensionalSystemSolution& previous_solution,
bool conservation_water,
index_t charge_keeper
):
m_data(ptrdata),
m_tot_conc(totconc),
m_secondary_conc(previous_solution.secondary_molalities),
m_loggamma(previous_solution.log_gamma),
m_ionic_strength(previous_solution.ionic_strength),
m_charge_keeper(charge_keeper)
{
number_eq(conservation_water);
}
void AdimensionalSystem::number_eq(bool water_equation)
{
index_t neq = 0;
m_ideq.reserve(m_data->nb_component+m_data->nb_mineral);
if (water_equation)
{
m_ideq.push_back(neq);
++neq;
} else {
m_ideq.push_back(no_equation);
}
for (index_t i: m_data->range_aqueous_component())
{
// Remove components that does not exist
if (m_tot_conc(i) == 0 and i!= 1)
{
INFO << "Component " << m_data->labels_basis[i]
<< "has total concentration equal to zero, we desactivate it" << std::endl;
m_nonactive_component.push_back(i);
m_ideq.push_back(no_equation);
continue;
}
else
{
m_ideq.push_back(neq);
++neq;
}
}
m_nb_free_vars = neq;
for (index_t m: m_data->range_mineral())
{
bool can_precipitate = true;
// Remove minerals that cannot precipitate
for (auto it=m_nonactive_component.begin(); it!=m_nonactive_component.end(); ++it)
{
if (m_data->nu_mineral(m, *it) != 0)
{
can_precipitate = false;
break; // this is not a mineral that can precipitate
}
}
if (can_precipitate)
{
m_ideq.push_back(neq);
++neq;
}
else
{
m_ideq.push_back(no_equation);
}
}
m_nb_tot_vars = neq;
m_nb_compl_vars = m_nb_tot_vars - m_nb_free_vars;
// aqueous species
m_active_aqueous.reserve(m_data->nb_aqueous);
for (index_t j: m_data->range_aqueous())
{
bool can_exist = true;
for (auto it=m_nonactive_component.begin(); it!=m_nonactive_component.end(); ++it)
{
if (m_data->nu_aqueous(j,*it) != 0)
{
can_exist = false;
}
}
m_active_aqueous.push_back(can_exist);
}
}
scalar_t AdimensionalSystem::saturation_water(const Vector& x) const
{
if (ideq_w() != no_equation)
return x(ideq_w());
else
return 1.0 - sum_saturation_minerals(x);
}
scalar_t AdimensionalSystem::saturation_mineral(const Vector& x, index_t mineral) const
{
specmicp_assert(mineral >= 0 and mineral < m_data->nb_mineral);
if (ideq_min(mineral) == no_equation) return 0.0;
else return x(ideq_min(mineral));
}
scalar_t AdimensionalSystem::sum_saturation_minerals(const Vector& x) const
{
scalar_t sum_saturations = 0.0;
for (index_t mineral: m_data->range_mineral())
{
sum_saturations += saturation_mineral(x, mineral);
}
return sum_saturations;
}
scalar_t AdimensionalSystem::density_water() const
{
scalar_t scaling = 1.0;
if (mass_unit() == units::MassUnit::gram) scaling *= 1e-3;
if (length_unit() == units::LengthUnit::centimeter) scaling *= 1e-6;
else if (length_unit() == units::LengthUnit::decimeter) scaling = 1e-3;
return scaling*1e3;
}
scalar_t AdimensionalSystem::molar_volume_mineral(index_t mineral) const
{
return m_data->molar_volume_mineral(mineral, length_unit());
}
scalar_t AdimensionalSystem::residual_water(const Vector& x) const
{
const scalar_t conc_w = density_water()*saturation_water(x);
scalar_t res = m_tot_conc(0) - conc_w/m_data->molar_mass_basis_si(0);
for (index_t j: m_data->range_aqueous())
{
if (not is_aqueous_active(j)) continue;
res -= conc_w*m_data->nu_aqueous(j, 0)*m_secondary_conc(j);
}
for (index_t m: m_data->range_mineral())
{
if (ideq_min(m) == no_equation or m_data->nu_mineral(m, 0) == 0.0) continue;
res -= m_data->nu_mineral(m, 0)*saturation_mineral(x, m)/molar_volume_mineral(m);
}
return res;
}
double AdimensionalSystem::residual_component(const Vector &x, index_t component) const
{
const scalar_t conc_w = density_water()*saturation_water(x);
scalar_t res = m_tot_conc(component) - conc_w*component_molality(x, component);
for (index_t j: m_data->range_aqueous())
{
if (not is_aqueous_active(j)) continue;
res -= conc_w*m_data->nu_aqueous(j, component)*secondary_molality(j);
}
for (index_t m: m_data->range_mineral())
{
if (ideq_min(m) == no_equation) continue;
res -= m_data->nu_mineral(m, component)*saturation_mineral(x, m)/molar_volume_mineral(m);
}
return res;
}
double AdimensionalSystem::residual_mineral(const Vector& x, index_t m) const
{
scalar_t res = m_data->logk_mineral(m);
for (index_t i: m_data->range_aqueous_component())
{
if (m_data->nu_mineral(m, i) != 0)
res -= m_data->nu_mineral(m, i)*(log_component_molality(x, i) + log_gamma_component(i));
}
return res;
}
double AdimensionalSystem::residual_charge_conservation(const Vector& x) const
{
scalar_t res = 0.0;
for (index_t i: m_data->range_aqueous_component())
{
if (m_data->charge_component(i) != 0 and ideq_paq(i) != no_equation)
res += m_data->charge_component(i)*component_molality(x, i);
}
for (index_t j: m_data->range_aqueous())
{
if (m_data->charge_aqueous(j) == 0 and not is_aqueous_active(j)) continue;
res += m_data->charge_aqueous(j)*secondary_molality(j);
}
return res;
}
void AdimensionalSystem::get_residuals(const Vector& x, Vector& residual)
{
set_secondary_concentration(x);
if (ideq_w() != no_equation) residual(ideq_w()) = residual_water(x);
for (index_t i: m_data->range_aqueous_component())
{
if (ideq_paq(i) == no_equation) continue;
if (is_charge_keeper(i)) residual(ideq_paq(i)) = residual_charge_conservation(x);
else residual(ideq_paq(i)) = residual_component(x, i);
}
for (index_t m: m_data->range_mineral())
{
if (ideq_min(m) != no_equation) residual(ideq_min(m)) = residual_mineral(x, m);
}
}
// //non-optimized Finite difference, for test only
//void AdimensionalSystem::get_jacobian(Eigen::VectorXd& x,
// Eigen::MatrixXd& jacobian)
//{
// const int neq = total_variables();
// Eigen::VectorXd res(total_variables());
// Eigen::VectorXd perturbed_res(total_variables());
// get_residuals(x, res);
// for (int j=0; j<neq; ++j)
// {
// double h = 1e-8*std::abs(x(j));
// //h = std::copysign(h, x(j));
// if (h==0) h = 1e-8;
// double tmp = x(j);
// x(j) += h;
// h = x(j) - tmp;
// get_residuals(x, perturbed_res);
// for (int i=0; i<neq; ++i)
// {
// jacobian(i, j) = (perturbed_res(i) - res(i))/h;
// }
// x(j) = tmp;
// }
// std::cout << jacobian << std::endl;
// return;
//}
void AdimensionalSystem::get_jacobian(Vector& x, Matrix& jacobian)
{
jacobian.resize(total_variables(), total_variables());
jacobian.setZero();
// water
jacobian_water(x, jacobian);
// aqueous component
jacobian_aqueous_components(x, jacobian);
// mineral equilibrium
jacobian_minerals(x, jacobian);
}
void AdimensionalSystem::jacobian_water(Vector& x, Matrix& jacobian)
{
if (ideq_w() != no_equation)
{
scalar_t tmp = -density_water()/m_data->molar_mass_basis_si(0);
for (index_t j: m_data->range_aqueous())
{
if ( m_data->nu_aqueous(j, 0) == 0 and not is_aqueous_active(j)) continue;
tmp -= m_data->nu_aqueous(j, 0)*secondary_molality(j);
}
jacobian(0, 0) = tmp;
const scalar_t conc_w = density_water()*saturation_water(x);
for (index_t k: m_data->range_aqueous_component())
{
if (ideq_paq(k) == no_equation) continue;
scalar_t tmp = 0;
for (index_t j: m_data->range_aqueous())
{
tmp -= m_data->nu_aqueous(j,0)*m_data->nu_aqueous(j,k)*secondary_molality(j);
}
jacobian(0, ideq_paq(k)) = conc_w*log10 * tmp;
}
for (index_t m: m_data->range_mineral())
{
if (ideq_min(m) == no_equation) continue;
jacobian(0, ideq_min(m)) = -m_data->nu_mineral(m, 0)/molar_volume_mineral(m);
}
}
}
void AdimensionalSystem::jacobian_aqueous_components(Vector& x, Matrix& jacobian)
{
for (index_t i: m_data->range_aqueous_component())
{
const index_t idp = ideq_paq(i);
if (idp == no_equation) continue;
// Charge balance equation
// ----------------------
if (is_charge_keeper(i))
{
// Aqueous components
for (index_t k: m_data->range_aqueous_component())
{
const index_t idc = ideq_paq(k);
if (idc == no_equation) continue;
scalar_t tmp_drdb = 0.0;
if (m_data->charge_component(k) != 0.0)
tmp_drdb = m_data->charge_component(k);
// Secondary species
for (index_t j: m_data->range_aqueous())
{
if ( not is_aqueous_active(j)
or m_data->nu_aqueous(j, k) == 0.0
or m_data->charge_aqueous(j) == 0.0
)
continue;
scalar_t tmp_value = m_data->nu_aqueous(j, k)*m_data->charge_aqueous(j);
tmp_value *= secondary_molality(j)/component_molality(x, k);
tmp_drdb += tmp_value;
}
jacobian(idp, idc) += component_molality(x,k)*log10*tmp_drdb;
}
}
// Mass balance equation
// ---------------------
else
{
const scalar_t conc_w = density_water()*saturation_water(x);
// Aqueous components
for (index_t k: m_data->range_aqueous_component())
{
if (ideq_paq(k) == no_equation) continue;
scalar_t tmp_iip = 0;
if (k == i) tmp_iip -= component_molality(x, i)*log10;
for (index_t j: m_data->range_aqueous())
{
tmp_iip -= log10*m_data->nu_aqueous(j, i)*m_data->nu_aqueous(j, k)*secondary_molality(j);
}
jacobian(idp, ideq_paq(k)) = conc_w*tmp_iip;
}
// Minerals
for (index_t m: m_data->range_mineral())
{
if (ideq_min(m) == no_equation) continue;
jacobian(idp, ideq_min(m)) = - m_data->nu_mineral(m, i)/molar_volume_mineral(m);
}
// Water
if (ideq_w() != no_equation)
{
scalar_t tmp_iw = -component_molality(x, i);
for (index_t j: m_data->range_aqueous())
{
if ( m_data->nu_aqueous(j, i) == 0 ) continue;
tmp_iw -= m_data->nu_aqueous(j, i)*secondary_molality(j);
}
jacobian(idp, ideq_w()) = density_water()*tmp_iw;
}
}
}
}
void AdimensionalSystem::jacobian_minerals(Vector& x, Matrix& jacobian)
{
for (index_t m: m_data->range_mineral())
{
const index_t idm = ideq_min(m);
if (idm == no_equation) continue;
for (index_t i: m_data->range_aqueous_component())
{
if (ideq_paq(i) == no_equation) continue;
jacobian(idm, ideq_paq(i)) = -m_data->nu_mineral(m, i);
}
}
}
void AdimensionalSystem::set_secondary_concentration(const Vector& x)
{
for (index_t j: m_data->range_aqueous())
{
if (not is_aqueous_active(j))
{
m_secondary_conc(j) = 0;
continue;
}
scalar_t logconc = -m_data->logk_aqueous(j) - m_loggamma(j+m_data->nb_component);
for (index_t k: m_data->range_aqueous_component())
{
if (m_data->nu_aqueous(j, k) == 0) continue;
logconc += m_data->nu_aqueous(j, k)*(log_component_molality(x, k) + m_loggamma(k));
}
m_secondary_conc(j) = pow10(logconc);
}
}
void AdimensionalSystem::set_ionic_strength(const Vector& x)
{
scalar_t ionic = 0;
for (index_t i: m_data->range_aqueous_component())
{
if (ideq_paq(i) == no_equation or m_data->charge_component(i) == 0) continue;
ionic += component_molality(x, i)*std::pow(m_data->charge_component(i),2);
}
for (index_t j: m_data->range_aqueous())
{
if (not is_aqueous_active(j) or m_data->charge_aqueous(j) == 0) continue;
ionic += secondary_molality(j)*std::pow(m_data->charge_aqueous(j),2);
}
ionic_strength() = ionic/2;
}
void AdimensionalSystem::compute_log_gamma(const Vector& x)
{
set_ionic_strength(x);
const scalar_t sqrti = std::sqrt(ionic_strength());
for (index_t i: m_data->range_aqueous_component())
{
if (ideq_paq(i) == no_equation)
{
log_gamma_component(i) = 0.0;
continue;
}
log_gamma_component(i) = laws::extended_debye_huckel(
ionic_strength(), sqrti,
m_data->charge_component(i),
m_data->a_debye_component(i),
m_data->b_debye_component(i)
);
}
for (index_t j: m_data->range_aqueous())
{
if (not is_aqueous_active(j))
{
log_gamma_secondary(j) = 0.0;
continue;
}
log_gamma_secondary(j) = laws::extended_debye_huckel(
ionic_strength(), sqrti,
m_data->charge_aqueous(j),
m_data->a_debye_aqueous(j),
m_data->b_debye_aqueous(j)
);
}
}
bool AdimensionalSystem::hook_start_iteration(const Vector& x, scalar_t norm_residual)
{
not_in_linesearch = true;
scalar_t previous_norm = m_loggamma.norm();
bool may_have_converged = false;
if (norm_residual < nb_free_variables())
{
// Use fixed point iterations for non-ideality
for (int i=0; i<10; ++i)
{
set_secondary_concentration(x);
compute_log_gamma(x);
if (std::abs(previous_norm - m_loggamma.norm())/previous_norm < 1e-10) {may_have_converged = true; break;}
previous_norm = m_loggamma.norm();
}
}
return may_have_converged;
}
double AdimensionalSystem::max_lambda(const Vector& x, const Vector& update)
{
if (ideq_w() != no_equation)
{
return 1.0/std::max(1.0, -update(0)/(0.9*x(0)));
}
else
{
return 1.0;
}
}
void AdimensionalSystem::reasonable_starting_guess(Vector &x)
{
x.resize(m_data->nb_component+ m_data->nb_mineral);
x(0) = 1.0;
for (index_t i: m_data->range_aqueous_component())
{
x(i) = -4.0;
}
x.block(m_data->nb_component, 0, m_data->nb_mineral, 1).setZero();
m_loggamma.setZero();
m_secondary_conc.setZero();
}
void AdimensionalSystem::reasonable_restarting_guess(Vector& x)
{
x(0) = 0.5;
for (index_t i: m_data->range_aqueous_component())
{
if (x(i) > 0 or x(i) < -9)
x(i) = -3;
}
x.segment(m_data->nb_component, m_data->nb_mineral).setZero();
m_loggamma.setZero();
m_secondary_conc.setZero();
}
AdimensionalSystemSolution AdimensionalSystem::get_solution(const Vector& xtot, const Vector& x)
{
double previous_norm = m_loggamma.norm();
set_secondary_concentration(x);
compute_log_gamma(x);
if (std::abs(previous_norm - m_loggamma.norm()) > 1e-6)
{
WARNING << "Activity coefficient have not converged !" << std::endl
<< "output can not be trusted\n Difference : "
+std::to_string(std::abs(previous_norm - m_loggamma.norm()));
}
return AdimensionalSystemSolution(xtot, m_secondary_conc, m_loggamma, m_ionic_strength);
}
void AdimensionalSystem::reduce_mineral_problem(Vector& true_var)
{
for (index_t mineral: m_data->range_mineral())
{
if (ideq_min(mineral) == no_equation) continue;
if (m_data->stability_mineral(mineral) == database::MineralStabilityClass::cannot_dissolve)
{
if (true_var(ideq_min(mineral)) == 0.0) continue;
for (index_t component: m_data->range_component())
{
if (m_data->nu_mineral(mineral, component) == 0.0) continue;
m_tot_conc(component) -= m_data->nu_mineral(mineral, component)*true_var(ideq_min(mineral));
}
true_var(ideq_min(mineral)) = 0.0;
}
}
}
void AdimensionalSystem::reset_mineral_system(Vector& true_var, Vector& output_var)
{
for (index_t mineral: m_data->range_mineral())
{
if (ideq_min(mineral) == no_equation) continue;
if (m_data->stability_mineral(mineral) == database::MineralStabilityClass::cannot_dissolve)
{
output_var(mineral) += true_var(ideq_min(mineral));
}
}
}
} // end namespace specmicp

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