cantera/src/equil/MultiPhaseEquil.cpp

784 lines
26 KiB
C++

/**
* @file MultiPhaseEquil.cpp
*/
// This file is part of Cantera. See License.txt in the top-level directory or
// at http://www.cantera.org/license.txt for license and copyright information.
#include "cantera/equil/MultiPhaseEquil.h"
#include "cantera/thermo/MolalityVPSSTP.h"
#include "cantera/base/stringUtils.h"
#include <cstdio>
using namespace std;
namespace Cantera
{
MultiPhaseEquil::MultiPhaseEquil(MultiPhase* mix, bool start, int loglevel) : m_mix(mix)
{
// store some mixture parameters locally
m_nel_mix = mix->nElements();
m_nsp_mix = mix->nSpecies();
m_press = mix->pressure();
m_temp = mix->temperature();
m_force = true;
m_nel = 0;
m_nsp = 0;
m_eloc = 1000;
m_incl_species.resize(m_nsp_mix,1);
m_incl_element.resize(m_nel_mix,1);
for (size_t m = 0; m < m_nel_mix; m++) {
string enm = mix->elementName(m);
// element 'E' or 'e' represents an electron; this requires special
// handling, so save its index for later use
if (enm == "E" || enm == "e") {
m_eloc = m;
}
// if an element other than electrons is not present in the mixture,
// then exclude it and all species containing it from the calculation.
// Electrons are a special case, since a species can have a negative
// number of 'atoms' of electrons (positive ions).
if (m_mix->elementMoles(m) <= 0.0 && m != m_eloc) {
m_incl_element[m] = 0;
for (size_t k = 0; k < m_nsp_mix; k++) {
if (m_mix->nAtoms(k,m) != 0.0) {
m_incl_species[k] = 0;
}
}
}
}
// Now build the list of elements to be included, starting with
// electrons, if they are present.
if (m_eloc < m_nel_mix) {
m_element.push_back(m_eloc);
m_nel++;
}
// add the included elements other than electrons
for (size_t m = 0; m < m_nel_mix; m++) {
if (m_incl_element[m] == 1 && m != m_eloc) {
m_nel++;
m_element.push_back(m);
}
}
// include pure single-constituent phases only if their thermo data are
// valid for this temperature. This is necessary, since some thermo
// polynomial fits are done only for a limited temperature range. For
// example, using the NASA polynomial fits for solid ice and liquid water,
// if this were not done the calculation would predict solid ice to be
// present far above its melting point, since the thermo polynomial fits
// only extend to 273.15 K, and give unphysical results above this
// temperature, leading (incorrectly) to Gibbs free energies at high
// temperature lower than for liquid water.
for (size_t k = 0; k < m_nsp_mix; k++) {
size_t ip = m_mix->speciesPhaseIndex(k);
if (!m_mix->solutionSpecies(k) &&
!m_mix->tempOK(ip)) {
m_incl_species[k] = 0;
if (m_mix->speciesMoles(k) > 0.0) {
throw CanteraError("MultiPhaseEquil",
"condensed-phase species"+ m_mix->speciesName(k)
+ " is excluded since its thermo properties are \n"
"not valid at this temperature, but it has "
"non-zero moles in the initial state.");
}
}
}
// Now build the list of all species to be included in the calculation.
for (size_t k = 0; k < m_nsp_mix; k++) {
if (m_incl_species[k] ==1) {
m_nsp++;
m_species.push_back(k);
}
}
// some work arrays for internal use
m_work.resize(m_nsp);
m_work2.resize(m_nsp);
m_work3.resize(m_nsp_mix);
m_mu.resize(m_nsp_mix);
// number of moles of each species
m_moles.resize(m_nsp);
m_lastmoles.resize(m_nsp);
m_dxi.resize(nFree());
// initialize the mole numbers to the mixture composition
for (size_t ik = 0; ik < m_nsp; ik++) {
m_moles[ik] = m_mix->speciesMoles(m_species[ik]);
}
// Delta G / RT for each reaction
m_deltaG_RT.resize(nFree(), 0.0);
m_majorsp.resize(m_nsp);
m_sortindex.resize(m_nsp,0);
m_lastsort.resize(m_nel);
m_solnrxn.resize(nFree());
m_A.resize(m_nel, m_nsp, 0.0);
m_N.resize(m_nsp, nFree());
m_order.resize(std::max(m_nsp, m_nel), 0);
iota(m_order.begin(), m_order.begin() + m_nsp, 0);
// if the 'start' flag is set, estimate the initial mole numbers by doing a
// linear Gibbs minimization. In this case, only the elemental composition
// of the initial mixture state matters.
if (start) {
setInitialMoles(loglevel-1);
}
computeN();
// Take a very small step in composition space, so that no
// species has precisely zero moles.
vector_fp dxi(nFree(), 1.0e-20);
if (!dxi.empty()) {
multiply(m_N, dxi.data(), m_work.data());
unsort(m_work);
}
for (size_t k = 0; k < m_nsp; k++) {
m_moles[k] += m_work[k];
m_lastmoles[k] = m_moles[k];
if (m_mix->solutionSpecies(m_species[k])) {
m_dsoln.push_back(1);
} else {
m_dsoln.push_back(0);
}
}
m_force = false;
updateMixMoles();
// At this point, the instance has been created, the species to be included
// have been determined, and an initial composition has been selected that
// has all non-zero mole numbers for the included species.
}
doublereal MultiPhaseEquil::equilibrate(int XY, doublereal err,
int maxsteps, int loglevel)
{
int i;
m_iter = 0;
for (i = 0; i < maxsteps; i++) {
stepComposition(loglevel-1);
if (error() < err) {
break;
}
}
if (i >= maxsteps) {
throw CanteraError("MultiPhaseEquil::equilibrate",
"no convergence in {} iterations. Error = {}",
maxsteps, error());
}
finish();
return error();
}
void MultiPhaseEquil::updateMixMoles()
{
fill(m_work3.begin(), m_work3.end(), 0.0);
for (size_t k = 0; k < m_nsp; k++) {
m_work3[m_species[k]] = m_moles[k];
}
m_mix->setMoles(m_work3.data());
}
void MultiPhaseEquil::finish()
{
fill(m_work3.begin(), m_work3.end(), 0.0);
for (size_t k = 0; k < m_nsp; k++) {
m_work3[m_species[k]] = (m_moles[k] > 0.0 ? m_moles[k] : 0.0);
}
m_mix->setMoles(m_work3.data());
}
int MultiPhaseEquil::setInitialMoles(int loglevel)
{
double not_mu = 1.0e12;
m_mix->getValidChemPotentials(not_mu, m_mu.data(), true);
double dxi_min = 1.0e10;
bool redo = true;
int iter = 0;
while (redo) {
// choose a set of components based on the current composition
computeN();
redo = false;
iter++;
if (iter > 4) {
break;
}
// loop over all reactions
for (size_t j = 0; j < nFree(); j++) {
double dg_rt = 0.0;
dxi_min = 1.0e10;
for (size_t ik = 0; ik < m_nsp; ik++) {
dg_rt += mu(ik) * m_N(ik,j);
}
// fwd or rev direction
int idir = (dg_rt < 0.0 ? 1 : -1);
for (size_t ik = 0; ik < m_nsp; ik++) {
double nu = m_N(ik, j);
// set max change in progress variable by
// non-negativity requirement
// -> Note, 0.99 factor is so that difference of 2 numbers
// isn't zero. This causes differences between
// optimized and debug versions of the code
if (nu*idir < 0) {
double delta_xi = fabs(0.99*moles(ik)/nu);
// if a component has nearly zero moles, redo
// with a new set of components
if (!redo && delta_xi < 1.0e-10 && ik < m_nel) {
redo = true;
}
dxi_min = std::min(dxi_min, delta_xi);
}
}
// step the composition by dxi_min
for (size_t ik = 0; ik < m_nsp; ik++) {
moles(ik) += m_N(ik, j) * idir*dxi_min;
}
}
// set the moles of the phase objects to match
updateMixMoles();
}
return 0;
}
void MultiPhaseEquil::getComponents(const std::vector<size_t>& order)
{
// if the input species array has the wrong size, ignore it
// and consider the species for components in declaration order.
if (order.size() != m_nsp) {
for (size_t k = 0; k < m_nsp; k++) {
m_order[k] = k;
}
} else {
for (size_t k = 0; k < m_nsp; k++) {
m_order[k] = order[k];
}
}
size_t nRows = m_nel;
size_t nColumns = m_nsp;
// set up the atomic composition matrix
for (size_t m = 0; m < nRows; m++) {
for (size_t k = 0; k < nColumns; k++) {
m_A(m, k) = m_mix->nAtoms(m_species[m_order[k]], m_element[m]);
}
}
// Do Gaussian elimination
for (size_t m = 0; m < nRows; m++) {
// Check for rows that are zero
bool isZeroRow = true;
for (size_t k = m; k < nColumns; k++) {
if (fabs(m_A(m,k)) > sqrt(Tiny)) {
isZeroRow = false;
break;
}
}
if (isZeroRow) {
// Find the last non-zero row
size_t n = nRows - 1;
bool foundSwapCandidate = false;
for (; n > m; n--) {
for (size_t k = m; k < nColumns; k++) {
if (fabs(m_A(n,k)) > sqrt(Tiny)) {
foundSwapCandidate = true;
break;
}
}
if (foundSwapCandidate) {
break;
}
}
if (m != n) {
// Swap this row with the last non-zero row
for (size_t k = 0; k < nColumns; k++) {
std::swap(m_A(n,k), m_A(m,k));
}
} else {
// All remaining rows are zero. Elimination is complete.
break;
}
}
// If a pivot is zero, exchange columns. This occurs when a species has
// an elemental composition that is not linearly independent of the
// component species that have already been assigned
if (m < nColumns && m_A(m,m) == 0.0) {
// First, we need to find a good candidate for a component species
// to swap in for the one that has zero pivot. It must contain
// element m, be linearly independent of the components processed so
// far (m_A(m,k) != 0), and should be a major species if possible.
// We'll choose the species with greatest mole fraction that
// satisfies these criteria.
doublereal maxmoles = -999.0;
size_t kmax = 0;
for (size_t k = m+1; k < nColumns; k++) {
if (m_A(m,k) != 0.0 && fabs(m_moles[m_order[k]]) > maxmoles) {
kmax = k;
maxmoles = fabs(m_moles[m_order[k]]);
}
}
// Now exchange the column with zero pivot with the
// column for this major species
for (size_t n = 0; n < nRows; n++) {
std::swap(m_A(n, m), m_A(n, kmax));
}
// exchange the species labels on the columns
std::swap(m_order[m], m_order[kmax]);
}
// scale row m so that the diagonal element is unity
double fctr = 1.0/m_A(m,m);
for (size_t k = 0; k < nColumns; k++) {
m_A(m,k) *= fctr;
}
// For all rows below the diagonal, subtract A(n,m)/A(m,m)
// * (row m) from row n, so that A(n,m) = 0.
for (size_t n = m+1; n < m_nel; n++) {
fctr = m_A(n,m)/m_A(m,m);
for (size_t k = 0; k < m_nsp; k++) {
m_A(n,k) -= m_A(m,k)*fctr;
}
}
}
// The left m_nel columns of A are now upper-diagonal. Now
// reduce the m_nel columns to diagonal form by back-solving
for (size_t m = std::min(nRows,nColumns)-1; m > 0; m--) {
for (size_t n = m-1; n != npos; n--) {
if (m_A(n,m) != 0.0) {
double fctr = m_A(n,m);
for (size_t k = m; k < m_nsp; k++) {
m_A(n,k) -= fctr*m_A(m,k);
}
}
}
}
// create stoichiometric coefficient matrix.
for (size_t n = 0; n < m_nsp; n++) {
if (n < m_nel) {
for (size_t k = 0; k < nFree(); k++) {
m_N(n, k) = -m_A(n, k + m_nel);
}
} else {
for (size_t k = 0; k < nFree(); k++) {
m_N(n, k) = 0.0;
}
m_N(n, n - m_nel) = 1.0;
}
}
// find reactions involving solution phase species
for (size_t j = 0; j < nFree(); j++) {
m_solnrxn[j] = false;
for (size_t k = 0; k < m_nsp; k++) {
if (m_N(k, j) != 0 && m_mix->solutionSpecies(m_species[m_order[k]])) {
m_solnrxn[j] = true;
}
}
}
}
void MultiPhaseEquil::unsort(vector_fp& x)
{
m_work2 = x;
for (size_t k = 0; k < m_nsp; k++) {
x[m_order[k]] = m_work2[k];
}
}
void MultiPhaseEquil::step(doublereal omega, vector_fp& deltaN,
int loglevel)
{
if (omega < 0.0) {
throw CanteraError("MultiPhaseEquil::step","negative omega");
}
for (size_t ik = 0; ik < m_nel; ik++) {
size_t k = m_order[ik];
m_lastmoles[k] = m_moles[k];
m_moles[k] += omega * deltaN[k];
}
for (size_t ik = m_nel; ik < m_nsp; ik++) {
size_t k = m_order[ik];
m_lastmoles[k] = m_moles[k];
if (m_majorsp[k]) {
m_moles[k] += omega * deltaN[k];
} else {
m_moles[k] = fabs(m_moles[k])*std::min(10.0,
exp(-m_deltaG_RT[ik - m_nel]));
}
}
updateMixMoles();
}
doublereal MultiPhaseEquil::stepComposition(int loglevel)
{
m_iter++;
doublereal grad0 = computeReactionSteps(m_dxi);
// compute the mole fraction changes.
if (nFree()) {
multiply(m_N, m_dxi.data(), m_work.data());
}
// change to sequential form
unsort(m_work);
// scale omega to keep the major species non-negative
doublereal FCTR = 0.99;
const doublereal MAJOR_THRESHOLD = 1.0e-12;
double omegamax = 1.0;
for (size_t ik = 0; ik < m_nsp; ik++) {
size_t k = m_order[ik];
if (ik < m_nel) {
FCTR = 0.99;
if (m_moles[k] < MAJOR_THRESHOLD) {
m_force = true;
}
} else {
FCTR = 0.9;
}
// if species k is in a multi-species solution phase, then its mole
// number must remain positive, unless the entire phase goes away. First
// we'll determine an upper bound on omega, such that all
if (m_dsoln[k] == 1) {
if ((m_moles[k] > MAJOR_THRESHOLD) || (ik < m_nel)) {
if (m_moles[k] < MAJOR_THRESHOLD) {
m_force = true;
}
double omax = m_moles[k]*FCTR/(fabs(m_work[k]) + Tiny);
if (m_work[k] < 0.0 && omax < omegamax) {
omegamax = omax;
if (omegamax < 1.0e-5) {
m_force = true;
}
}
m_majorsp[k] = true;
} else {
m_majorsp[k] = false;
}
} else {
if (m_work[k] < 0.0 && m_moles[k] > 0.0) {
double omax = -m_moles[k]/m_work[k];
if (omax < omegamax) {
omegamax = omax;
if (omegamax < 1.0e-5) {
m_force = true;
}
}
}
m_majorsp[k] = true;
}
}
// now take a step with this scaled omega
step(omegamax, m_work);
// compute the gradient of G at this new position in the current direction.
// If it is positive, then we have overshot the minimum. In this case,
// interpolate back.
doublereal not_mu = 1.0e12;
m_mix->getValidChemPotentials(not_mu, m_mu.data());
doublereal grad1 = 0.0;
for (size_t k = 0; k < m_nsp; k++) {
grad1 += m_work[k] * m_mu[m_species[k]];
}
double omega = omegamax;
if (grad1 > 0.0) {
omega *= fabs(grad0) / (grad1 + fabs(grad0));
for (size_t k = 0; k < m_nsp; k++) {
m_moles[k] = m_lastmoles[k];
}
step(omega, m_work);
}
return omega;
}
doublereal MultiPhaseEquil::computeReactionSteps(vector_fp& dxi)
{
vector_fp nu;
doublereal grad = 0.0;
dxi.resize(nFree());
computeN();
doublereal not_mu = 1.0e12;
m_mix->getValidChemPotentials(not_mu, m_mu.data());
for (size_t j = 0; j < nFree(); j++) {
// get stoichiometric vector
getStoichVector(j, nu);
// compute Delta G
doublereal dg_rt = 0.0;
for (size_t k = 0; k < m_nsp; k++) {
dg_rt += m_mu[m_species[k]] * nu[k];
}
dg_rt /= (m_temp * GasConstant);
m_deltaG_RT[j] = dg_rt;
double fctr = 1.0;
// if this is a formation reaction for a single-component phase,
// check whether reaction should be included
size_t k = m_order[j + m_nel];
if (!m_dsoln[k]) {
if (m_moles[k] <= 0.0 && dg_rt > 0.0) {
fctr = 0.0;
} else {
fctr = 0.5;
}
} else if (!m_solnrxn[j]) {
fctr = 1.0;
} else {
// component sum
double csum = 0.0;
for (k = 0; k < m_nel; k++) {
size_t kc = m_order[k];
double nmoles = fabs(m_mix->speciesMoles(m_species[kc])) + Tiny;
csum += pow(nu[kc], 2)*m_dsoln[kc]/nmoles;
}
// noncomponent term
size_t kc = m_order[j + m_nel];
double nmoles = fabs(m_mix->speciesMoles(m_species[kc])) + Tiny;
double term1 = m_dsoln[kc]/nmoles;
// sum over solution phases
doublereal sum = 0.0;
for (size_t ip = 0; ip < m_mix->nPhases(); ip++) {
ThermoPhase& p = m_mix->phase(ip);
if (p.nSpecies() > 1) {
double psum = 0.0;
for (k = 0; k < m_nsp; k++) {
kc = m_species[k];
if (m_mix->speciesPhaseIndex(kc) == ip) {
psum += pow(nu[k], 2);
}
}
sum -= psum / (fabs(m_mix->phaseMoles(ip)) + Tiny);
}
}
double rfctr = term1 + csum + sum;
if (fabs(rfctr) < Tiny) {
fctr = 1.0;
} else {
fctr = 1.0/(term1 + csum + sum);
}
}
dxi[j] = -fctr*dg_rt;
for (size_t m = 0; m < m_nel; m++) {
if (m_moles[m_order[m]] <= 0.0 && (m_N(m, j)*dxi[j] < 0.0)) {
dxi[j] = 0.0;
}
}
grad += dxi[j]*dg_rt;
}
return grad*GasConstant*m_temp;
}
void MultiPhaseEquil::computeN()
{
// Sort the list of species by mole fraction (decreasing order)
std::vector<std::pair<double, size_t> > moleFractions(m_nsp);
for (size_t k = 0; k < m_nsp; k++) {
// use -Xk to generate reversed sort order
moleFractions[k].first = - m_mix->speciesMoles(m_species[k]);
moleFractions[k].second = k;
}
std::sort(moleFractions.begin(), moleFractions.end());
for (size_t k = 0; k < m_nsp; k++) {
m_sortindex[k] = moleFractions[k].second;
}
for (size_t m = 0; m < m_nel; m++) {
size_t k = 0;
for (size_t ik = 0; ik < m_nsp; ik++) {
k = m_sortindex[ik];
if (m_mix->nAtoms(m_species[k],m_element[m]) != 0) {
break;
}
}
bool ok = false;
for (size_t ij = 0; ij < m_nel; ij++) {
if (k == m_order[ij]) {
ok = true;
}
}
if (!ok || m_force) {
getComponents(m_sortindex);
m_force = true;
break;
}
}
}
doublereal MultiPhaseEquil::error()
{
doublereal err, maxerr = 0.0;
// examine every reaction
for (size_t j = 0; j < nFree(); j++) {
size_t ik = j + m_nel;
// don't require formation reactions for solution species
// present in trace amounts to be equilibrated
if (!isStoichPhase(ik) && fabs(moles(ik)) <= SmallNumber) {
err = 0.0;
}
// for stoichiometric phase species, no error if not present and
// delta G for the formation reaction is positive
if (isStoichPhase(ik) && moles(ik) <= 0.0 &&
m_deltaG_RT[j] >= 0.0) {
err = 0.0;
} else {
err = fabs(m_deltaG_RT[j]);
}
maxerr = std::max(maxerr, err);
}
return maxerr;
}
double MultiPhaseEquil::phaseMoles(size_t iph) const
{
return m_mix->phaseMoles(iph);
}
void MultiPhaseEquil::reportCSV(const std::string& reportFile)
{
FILE* FP = fopen(reportFile.c_str(), "w");
if (!FP) {
throw CanteraError("MultiPhaseEquil::reportCSV", "Failure to open file");
}
vector_fp mf(m_nsp_mix, 1.0);
vector_fp fe(m_nsp_mix, 0.0);
vector_fp VolPM;
vector_fp activity;
vector_fp ac;
vector_fp mu;
vector_fp mu0;
vector_fp molalities;
double vol = 0.0;
for (size_t iphase = 0; iphase < m_mix->nPhases(); iphase++) {
size_t istart = m_mix->speciesIndex(0, iphase);
ThermoPhase& tref = m_mix->phase(iphase);
size_t nSpecies = tref.nSpecies();
VolPM.resize(nSpecies, 0.0);
tref.getMoleFractions(&mf[istart]);
tref.getPartialMolarVolumes(VolPM.data());
double TMolesPhase = phaseMoles(iphase);
double VolPhaseVolumes = 0.0;
for (size_t k = 0; k < nSpecies; k++) {
VolPhaseVolumes += VolPM[k] * mf[istart + k];
}
VolPhaseVolumes *= TMolesPhase;
vol += VolPhaseVolumes;
}
fprintf(FP,"--------------------- VCS_MULTIPHASE_EQUIL FINAL REPORT"
" -----------------------------\n");
fprintf(FP,"Temperature = %11.5g kelvin\n", m_mix->temperature());
fprintf(FP,"Pressure = %11.5g Pascal\n", m_mix->pressure());
fprintf(FP,"Total Volume = %11.5g m**3\n", vol);
for (size_t iphase = 0; iphase < m_mix->nPhases(); iphase++) {
size_t istart = m_mix->speciesIndex(0, iphase);
ThermoPhase& tref = m_mix->phase(iphase);
ThermoPhase* tp = &tref;
tp->getMoleFractions(&mf[istart]);
string phaseName = tref.name();
double TMolesPhase = phaseMoles(iphase);
size_t nSpecies = tref.nSpecies();
activity.resize(nSpecies, 0.0);
ac.resize(nSpecies, 0.0);
mu0.resize(nSpecies, 0.0);
mu.resize(nSpecies, 0.0);
VolPM.resize(nSpecies, 0.0);
molalities.resize(nSpecies, 0.0);
int actConvention = tp->activityConvention();
tp->getActivities(activity.data());
tp->getActivityCoefficients(ac.data());
tp->getStandardChemPotentials(mu0.data());
tp->getPartialMolarVolumes(VolPM.data());
tp->getChemPotentials(mu.data());
double VolPhaseVolumes = 0.0;
for (size_t k = 0; k < nSpecies; k++) {
VolPhaseVolumes += VolPM[k] * mf[istart + k];
}
VolPhaseVolumes *= TMolesPhase;
vol += VolPhaseVolumes;
if (actConvention == 1) {
MolalityVPSSTP* mTP = static_cast<MolalityVPSSTP*>(tp);
mTP->getMolalities(molalities.data());
tp->getChemPotentials(mu.data());
if (iphase == 0) {
fprintf(FP," Name, Phase, PhaseMoles, Mole_Fract, "
"Molalities, ActCoeff, Activity,"
"ChemPot_SS0, ChemPot, mole_num, PMVol, Phase_Volume\n");
fprintf(FP," , , (kmol), , "
", , ,"
" (kJ/gmol), (kJ/gmol), (kmol), (m**3/kmol), (m**3)\n");
}
for (size_t k = 0; k < nSpecies; k++) {
string sName = tp->speciesName(k);
fprintf(FP,"%12s, %11s, %11.3e, %11.3e, %11.3e, %11.3e, %11.3e,"
"%11.3e, %11.3e, %11.3e, %11.3e, %11.3e\n",
sName.c_str(),
phaseName.c_str(), TMolesPhase,
mf[istart + k], molalities[k], ac[k], activity[k],
mu0[k]*1.0E-6, mu[k]*1.0E-6,
mf[istart + k] * TMolesPhase,
VolPM[k], VolPhaseVolumes);
}
} else {
if (iphase == 0) {
fprintf(FP," Name, Phase, PhaseMoles, Mole_Fract, "
"Molalities, ActCoeff, Activity,"
" ChemPotSS0, ChemPot, mole_num, PMVol, Phase_Volume\n");
fprintf(FP," , , (kmol), , "
", , ,"
" (kJ/gmol), (kJ/gmol), (kmol), (m**3/kmol), (m**3)\n");
}
for (size_t k = 0; k < nSpecies; k++) {
molalities[k] = 0.0;
}
for (size_t k = 0; k < nSpecies; k++) {
string sName = tp->speciesName(k);
fprintf(FP,"%12s, %11s, %11.3e, %11.3e, %11.3e, %11.3e, %11.3e, "
"%11.3e, %11.3e,% 11.3e, %11.3e, %11.3e\n",
sName.c_str(),
phaseName.c_str(), TMolesPhase,
mf[istart + k], molalities[k], ac[k],
activity[k], mu0[k]*1.0E-6, mu[k]*1.0E-6,
mf[istart + k] * TMolesPhase,
VolPM[k], VolPhaseVolumes);
}
}
}
fclose(FP);
}
}