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cantera/src/thermo/HMWSoln.cpp

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/**
* @file HMWSoln.cpp
* Definitions for the HMWSoln ThermoPhase object, which
* models concentrated electrolyte solutions
* (see \ref thermoprops and \link Cantera::HMWSoln HMWSoln \endlink) .
*
* Class HMWSoln represents a concentrated liquid electrolyte phase which obeys
* the Pitzer formulation for nonideality using molality-based standard states.
*
* This version of the code was modified to have the binary Beta2 Pitzer
* parameter consistent with the temperature expansions used for Beta0,
* Beta1, and Cphi.(CFJC, SNL)
*/
/*
* Copyright (2006) Sandia Corporation. Under the terms of
* Contract DE-AC04-94AL85000 with Sandia Corporation, the
* U.S. Government retains certain rights in this software.
*/
#include "cantera/thermo/HMWSoln.h"
#include "cantera/thermo/ThermoFactory.h"
#include "cantera/thermo/PDSS_Water.h"
#include "cantera/thermo/electrolytes.h"
#include "cantera/base/stringUtils.h"
namespace Cantera
{
HMWSoln::HMWSoln() :
m_formPitzer(PITZERFORM_BASE),
m_formPitzerTemp(PITZER_TEMP_CONSTANT),
m_formGC(2),
m_IionicMolality(0.0),
m_maxIionicStrength(100.0),
m_TempPitzerRef(298.15),
m_IionicMolalityStoich(0.0),
m_form_A_Debye(A_DEBYE_WATER),
m_A_Debye(1.172576), // units = sqrt(kg/gmol)
m_waterSS(0),
m_densWaterSS(1000.),
m_molalitiesAreCropped(false),
IMS_typeCutoff_(0),
IMS_X_o_cutoff_(0.2),
IMS_gamma_o_min_(1.0E-5),
IMS_gamma_k_min_(10.0),
IMS_cCut_(0.05),
IMS_slopefCut_(0.6),
IMS_slopegCut_(0.0),
IMS_dfCut_(0.0),
IMS_efCut_(0.0),
IMS_afCut_(0.0),
IMS_bfCut_(0.0),
IMS_dgCut_(0.0),
IMS_egCut_(0.0),
IMS_agCut_(0.0),
IMS_bgCut_(0.0),
MC_X_o_cutoff_(0.0),
MC_X_o_min_(0.0),
MC_slopepCut_(0.0),
MC_dpCut_(0.0),
MC_epCut_(0.0),
MC_apCut_(0.0),
MC_bpCut_(0.0),
MC_cpCut_(0.0),
CROP_ln_gamma_o_min(-6.0),
CROP_ln_gamma_o_max(3.0),
CROP_ln_gamma_k_min(-5.0),
CROP_ln_gamma_k_max(15.0),
m_last_is(-1.0),
m_debugCalc(0)
{
}
HMWSoln::HMWSoln(const std::string& inputFile, const std::string& id_) :
m_formPitzer(PITZERFORM_BASE),
m_formPitzerTemp(PITZER_TEMP_CONSTANT),
m_formGC(2),
m_IionicMolality(0.0),
m_maxIionicStrength(100.0),
m_TempPitzerRef(298.15),
m_IionicMolalityStoich(0.0),
m_form_A_Debye(A_DEBYE_WATER),
m_A_Debye(1.172576), // units = sqrt(kg/gmol)
m_waterSS(0),
m_densWaterSS(1000.),
m_molalitiesAreCropped(false),
IMS_typeCutoff_(0),
IMS_X_o_cutoff_(0.2),
IMS_gamma_o_min_(1.0E-5),
IMS_gamma_k_min_(10.0),
IMS_cCut_(0.05),
IMS_slopefCut_(0.6),
IMS_slopegCut_(0.0),
IMS_dfCut_(0.0),
IMS_efCut_(0.0),
IMS_afCut_(0.0),
IMS_bfCut_(0.0),
IMS_dgCut_(0.0),
IMS_egCut_(0.0),
IMS_agCut_(0.0),
IMS_bgCut_(0.0),
MC_X_o_cutoff_(0.0),
MC_X_o_min_(0.0),
MC_slopepCut_(0.0),
MC_dpCut_(0.0),
MC_epCut_(0.0),
MC_apCut_(0.0),
MC_bpCut_(0.0),
MC_cpCut_(0.0),
CROP_ln_gamma_o_min(-6.0),
CROP_ln_gamma_o_max(3.0),
CROP_ln_gamma_k_min(-5.0),
CROP_ln_gamma_k_max(15.0),
m_last_is(-1.0),
m_debugCalc(0)
{
initThermoFile(inputFile, id_);
}
HMWSoln::HMWSoln(XML_Node& phaseRoot, const std::string& id_) :
m_formPitzer(PITZERFORM_BASE),
m_formPitzerTemp(PITZER_TEMP_CONSTANT),
m_formGC(2),
m_IionicMolality(0.0),
m_maxIionicStrength(100.0),
m_TempPitzerRef(298.15),
m_IionicMolalityStoich(0.0),
m_form_A_Debye(A_DEBYE_WATER),
m_A_Debye(1.172576), // units = sqrt(kg/gmol)
m_waterSS(0),
m_densWaterSS(1000.),
m_molalitiesAreCropped(false),
IMS_typeCutoff_(0),
IMS_X_o_cutoff_(0.2),
IMS_gamma_o_min_(1.0E-5),
IMS_gamma_k_min_(10.0),
IMS_cCut_(0.05),
IMS_slopefCut_(0.6),
IMS_slopegCut_(0.0),
IMS_dfCut_(0.0),
IMS_efCut_(0.0),
IMS_afCut_(0.0),
IMS_bfCut_(0.0),
IMS_dgCut_(0.0),
IMS_egCut_(0.0),
IMS_agCut_(0.0),
IMS_bgCut_(0.0),
MC_X_o_cutoff_(0.0),
MC_X_o_min_(0.0),
MC_slopepCut_(0.0),
MC_dpCut_(0.0),
MC_epCut_(0.0),
MC_apCut_(0.0),
MC_bpCut_(0.0),
MC_cpCut_(0.0),
CROP_ln_gamma_o_min(-6.0),
CROP_ln_gamma_o_max(3.0),
CROP_ln_gamma_k_min(-5.0),
CROP_ln_gamma_k_max(15.0),
m_last_is(-1.0),
m_debugCalc(0)
{
importPhase(phaseRoot, this);
}
HMWSoln::HMWSoln(const HMWSoln& b) :
m_formPitzer(PITZERFORM_BASE),
m_formPitzerTemp(PITZER_TEMP_CONSTANT),
m_formGC(2),
m_IionicMolality(0.0),
m_maxIionicStrength(100.0),
m_TempPitzerRef(298.15),
m_IionicMolalityStoich(0.0),
m_form_A_Debye(A_DEBYE_WATER),
m_A_Debye(1.172576), // units = sqrt(kg/gmol)
m_waterSS(0),
m_densWaterSS(1000.),
m_molalitiesAreCropped(false),
IMS_typeCutoff_(0),
IMS_X_o_cutoff_(0.2),
IMS_gamma_o_min_(1.0E-5),
IMS_gamma_k_min_(10.0),
IMS_cCut_(0.05),
IMS_slopefCut_(0.6),
IMS_slopegCut_(0.0),
IMS_dfCut_(0.0),
IMS_efCut_(0.0),
IMS_afCut_(0.0),
IMS_bfCut_(0.0),
IMS_dgCut_(0.0),
IMS_egCut_(0.0),
IMS_agCut_(0.0),
IMS_bgCut_(0.0),
MC_X_o_cutoff_(0.0),
MC_X_o_min_(0.0),
MC_slopepCut_(0.0),
MC_dpCut_(0.0),
MC_epCut_(0.0),
MC_apCut_(0.0),
MC_bpCut_(0.0),
MC_cpCut_(0.0),
CROP_ln_gamma_o_min(-6.0),
CROP_ln_gamma_o_max(3.0),
CROP_ln_gamma_k_min(-5.0),
CROP_ln_gamma_k_max(15.0),
m_last_is(-1.0),
m_debugCalc(0)
{
// Use the assignment operator to do the brunt of the work for the copy
// constructor.
*this = b;
}
HMWSoln& HMWSoln::operator=(const HMWSoln& b)
{
if (&b != this) {
MolalityVPSSTP::operator=(b);
m_formPitzer = b.m_formPitzer;
m_formPitzerTemp = b.m_formPitzerTemp;
m_formGC = b.m_formGC;
m_Aionic = b.m_Aionic;
m_IionicMolality = b.m_IionicMolality;
m_maxIionicStrength = b.m_maxIionicStrength;
m_TempPitzerRef = b.m_TempPitzerRef;
m_IionicMolalityStoich= b.m_IionicMolalityStoich;
m_form_A_Debye = b.m_form_A_Debye;
m_A_Debye = b.m_A_Debye;
// This is an internal shallow copy of the PDSS_Water pointer
m_waterSS = providePDSS(0);
if (!m_waterSS) {
throw CanteraError("HMWSoln::operator=()", "Dynamic cast to PDSS_Water failed");
}
m_densWaterSS = b.m_densWaterSS;
m_waterProps = 0;
if (b.m_waterProps) {
m_waterProps.reset(new WaterProps(dynamic_cast<PDSS_Water*>(m_waterSS)));
}
m_tmpV = b.m_tmpV;
m_speciesCharge_Stoich= b.m_speciesCharge_Stoich;
m_Beta0MX_ij = b.m_Beta0MX_ij;
m_Beta0MX_ij_L = b.m_Beta0MX_ij_L;
m_Beta0MX_ij_LL = b.m_Beta0MX_ij_LL;
m_Beta0MX_ij_P = b.m_Beta0MX_ij_P;
m_Beta0MX_ij_coeff = b.m_Beta0MX_ij_coeff;
m_Beta1MX_ij = b.m_Beta1MX_ij;
m_Beta1MX_ij_L = b.m_Beta1MX_ij_L;
m_Beta1MX_ij_LL = b.m_Beta1MX_ij_LL;
m_Beta1MX_ij_P = b.m_Beta1MX_ij_P;
m_Beta1MX_ij_coeff = b.m_Beta1MX_ij_coeff;
m_Beta2MX_ij = b.m_Beta2MX_ij;
m_Beta2MX_ij_L = b.m_Beta2MX_ij_L;
m_Beta2MX_ij_LL = b.m_Beta2MX_ij_LL;
m_Beta2MX_ij_P = b.m_Beta2MX_ij_P;
m_Beta2MX_ij_coeff = b.m_Beta2MX_ij_coeff;
m_Alpha1MX_ij = b.m_Alpha1MX_ij;
m_Alpha2MX_ij = b.m_Alpha2MX_ij;
m_CphiMX_ij = b.m_CphiMX_ij;
m_CphiMX_ij_L = b.m_CphiMX_ij_L;
m_CphiMX_ij_LL = b.m_CphiMX_ij_LL;
m_CphiMX_ij_P = b.m_CphiMX_ij_P;
m_CphiMX_ij_coeff = b.m_CphiMX_ij_coeff;
m_Theta_ij = b.m_Theta_ij;
m_Theta_ij_L = b.m_Theta_ij_L;
m_Theta_ij_LL = b.m_Theta_ij_LL;
m_Theta_ij_P = b.m_Theta_ij_P;
m_Theta_ij_coeff = b.m_Theta_ij_coeff;
m_Psi_ijk = b.m_Psi_ijk;
m_Psi_ijk_L = b.m_Psi_ijk_L;
m_Psi_ijk_LL = b.m_Psi_ijk_LL;
m_Psi_ijk_P = b.m_Psi_ijk_P;
m_Psi_ijk_coeff = b.m_Psi_ijk_coeff;
m_Lambda_nj = b.m_Lambda_nj;
m_Lambda_nj_L = b.m_Lambda_nj_L;
m_Lambda_nj_LL = b.m_Lambda_nj_LL;
m_Lambda_nj_P = b.m_Lambda_nj_P;
m_Lambda_nj_coeff = b.m_Lambda_nj_coeff;
m_Mu_nnn = b.m_Mu_nnn;
m_Mu_nnn_L = b.m_Mu_nnn_L;
m_Mu_nnn_LL = b.m_Mu_nnn_LL;
m_Mu_nnn_P = b.m_Mu_nnn_P;
m_Mu_nnn_coeff = b.m_Mu_nnn_coeff;
m_lnActCoeffMolal_Scaled = b.m_lnActCoeffMolal_Scaled;
m_lnActCoeffMolal_Unscaled = b.m_lnActCoeffMolal_Unscaled;
m_dlnActCoeffMolaldT_Scaled = b.m_dlnActCoeffMolaldT_Scaled;
m_dlnActCoeffMolaldT_Unscaled = b.m_dlnActCoeffMolaldT_Unscaled;
m_d2lnActCoeffMolaldT2_Scaled = b.m_d2lnActCoeffMolaldT2_Scaled;
m_d2lnActCoeffMolaldT2_Unscaled = b.m_d2lnActCoeffMolaldT2_Unscaled;
m_dlnActCoeffMolaldP_Scaled = b.m_dlnActCoeffMolaldP_Scaled;
m_dlnActCoeffMolaldP_Unscaled = b.m_dlnActCoeffMolaldP_Unscaled;
m_molalitiesCropped = b.m_molalitiesCropped;
m_molalitiesAreCropped = b.m_molalitiesAreCropped;
m_CounterIJ = b.m_CounterIJ;
m_gfunc_IJ = b.m_gfunc_IJ;
m_g2func_IJ = b.m_g2func_IJ;
m_hfunc_IJ = b.m_hfunc_IJ;
m_h2func_IJ = b.m_h2func_IJ;
m_BMX_IJ = b.m_BMX_IJ;
m_BMX_IJ_L = b.m_BMX_IJ_L;
m_BMX_IJ_LL = b.m_BMX_IJ_LL;
m_BMX_IJ_P = b.m_BMX_IJ_P;
m_BprimeMX_IJ = b.m_BprimeMX_IJ;
m_BprimeMX_IJ_L = b.m_BprimeMX_IJ_L;
m_BprimeMX_IJ_LL = b.m_BprimeMX_IJ_LL;
m_BprimeMX_IJ_P = b.m_BprimeMX_IJ_P;
m_BphiMX_IJ = b.m_BphiMX_IJ;
m_BphiMX_IJ_L = b.m_BphiMX_IJ_L;
m_BphiMX_IJ_LL = b.m_BphiMX_IJ_LL;
m_BphiMX_IJ_P = b.m_BphiMX_IJ_P;
m_Phi_IJ = b.m_Phi_IJ;
m_Phi_IJ_L = b.m_Phi_IJ_L;
m_Phi_IJ_LL = b.m_Phi_IJ_LL;
m_Phi_IJ_P = b.m_Phi_IJ_P;
m_Phiprime_IJ = b.m_Phiprime_IJ;
m_PhiPhi_IJ = b.m_PhiPhi_IJ;
m_PhiPhi_IJ_L = b.m_PhiPhi_IJ_L;
m_PhiPhi_IJ_LL = b.m_PhiPhi_IJ_LL;
m_PhiPhi_IJ_P = b.m_PhiPhi_IJ_P;
m_CMX_IJ = b.m_CMX_IJ;
m_CMX_IJ_L = b.m_CMX_IJ_L;
m_CMX_IJ_LL = b.m_CMX_IJ_LL;
m_CMX_IJ_P = b.m_CMX_IJ_P;
m_gamma_tmp = b.m_gamma_tmp;
IMS_lnActCoeffMolal_ = b.IMS_lnActCoeffMolal_;
IMS_typeCutoff_ = b.IMS_typeCutoff_;
IMS_X_o_cutoff_ = b.IMS_X_o_cutoff_;
IMS_gamma_o_min_ = b.IMS_gamma_o_min_;
IMS_gamma_k_min_ = b.IMS_gamma_k_min_;
IMS_cCut_ = b.IMS_cCut_;
IMS_slopefCut_ = b.IMS_slopefCut_;
IMS_dfCut_ = b.IMS_dfCut_;
IMS_efCut_ = b.IMS_efCut_;
IMS_afCut_ = b.IMS_afCut_;
IMS_bfCut_ = b.IMS_bfCut_;
IMS_slopegCut_ = b.IMS_slopegCut_;
IMS_dgCut_ = b.IMS_dgCut_;
IMS_egCut_ = b.IMS_egCut_;
IMS_agCut_ = b.IMS_agCut_;
IMS_bgCut_ = b.IMS_bgCut_;
MC_X_o_cutoff_ = b.MC_X_o_cutoff_;
MC_X_o_min_ = b.MC_X_o_min_;
MC_slopepCut_ = b.MC_slopepCut_;
MC_dpCut_ = b.MC_dpCut_;
MC_epCut_ = b.MC_epCut_;
MC_apCut_ = b.MC_apCut_;
MC_bpCut_ = b.MC_bpCut_;
MC_cpCut_ = b.MC_cpCut_;
CROP_ln_gamma_o_min = b.CROP_ln_gamma_o_min;
CROP_ln_gamma_o_max = b.CROP_ln_gamma_o_max;
CROP_ln_gamma_k_min = b.CROP_ln_gamma_k_min;
CROP_ln_gamma_k_max = b.CROP_ln_gamma_k_max;
CROP_speciesCropped_ = b.CROP_speciesCropped_;
m_debugCalc = b.m_debugCalc;
}
return *this;
}
HMWSoln::~HMWSoln()
{
}
ThermoPhase* HMWSoln::duplMyselfAsThermoPhase() const
{
return new HMWSoln(*this);
}
int HMWSoln::eosType() const
{
int res;
switch (m_formGC) {
case 0:
res = cHMWSoln0;
break;
case 1:
res = cHMWSoln1;
break;
case 2:
res = cHMWSoln2;
break;
default:
throw CanteraError("eosType", "Unknown type");
}
return res;
}
// -------- Molar Thermodynamic Properties of the Solution ---------------
doublereal HMWSoln::enthalpy_mole() const
{
getPartialMolarEnthalpies(m_tmpV.data());
return mean_X(m_tmpV);
}
doublereal HMWSoln::relative_enthalpy() const
{
getPartialMolarEnthalpies(m_tmpV.data());
double hbar = mean_X(m_tmpV);
getEnthalpy_RT(m_gamma_tmp.data());
for (size_t k = 0; k < m_kk; k++) {
m_gamma_tmp[k] *= RT();
}
double h0bar = mean_X(m_gamma_tmp);
return hbar - h0bar;
}
doublereal HMWSoln::relative_molal_enthalpy() const
{
double L = relative_enthalpy();
getMoleFractions(m_tmpV.data());
double xanion = 0.0;
size_t kcation = npos;
double xcation = 0.0;
size_t kanion = npos;
for (size_t k = 0; k < m_kk; k++) {
if (charge(k) > 0.0) {
if (m_tmpV[k] > xanion) {
xanion = m_tmpV[k];
kanion = k;
}
} else if (charge(k) < 0.0) {
if (m_tmpV[k] > xcation) {
xcation = m_tmpV[k];
kcation = k;
}
}
}
if (kcation == npos || kanion == npos) {
return L;
}
double xuse = xcation;
double factor = 1;
if (xanion < xcation) {
xuse = xanion;
if (charge(kcation) != 1.0) {
factor = charge(kcation);
}
} else {
if (charge(kanion) != 1.0) {
factor = charge(kanion);
}
}
xuse = xuse / factor;
return L / xuse;
}
doublereal HMWSoln::entropy_mole() const
{
getPartialMolarEntropies(m_tmpV.data());
return mean_X(m_tmpV);
}
doublereal HMWSoln::gibbs_mole() const
{
getChemPotentials(m_tmpV.data());
return mean_X(m_tmpV);
}
doublereal HMWSoln::cp_mole() const
{
getPartialMolarCp(m_tmpV.data());
return mean_X(m_tmpV);
}
doublereal HMWSoln::cv_mole() const
{
double kappa_t = isothermalCompressibility();
double beta = thermalExpansionCoeff();
double cp = cp_mole();
double tt = temperature();
double molarV = molarVolume();
return cp - beta * beta * tt * molarV / kappa_t;
}
// ------- Mechanical Equation of State Properties ------------------------
void HMWSoln::calcDensity()
{
static const int cacheId = m_cache.getId();
CachedScalar cached = m_cache.getScalar(cacheId);
if(cached.validate(temperature(), pressure(), stateMFNumber())) {
return;
}
// Store the internal density of the water SS. Note, we would have to do
// this for all other species if they had pressure dependent properties.
m_densWaterSS = m_waterSS->density();
// Calculate all of the other standard volumes. Note these are constant for
// now
getPartialMolarVolumes(m_tmpV.data());
double dd = meanMolecularWeight() / mean_X(m_tmpV);
Phase::setDensity(dd);
}
void HMWSoln::setDensity(const doublereal rho)
{
double dens_old = density();
if (rho != dens_old) {
throw CanteraError("HMWSoln::setDensity",
"Density is not an independent variable");
}
}
void HMWSoln::setMolarDensity(const doublereal rho)
{
throw CanteraError("HMWSoln::setMolarDensity",
"Density is not an independent variable");
}
// ------- Activities and Activity Concentrations
void HMWSoln::getActivityConcentrations(doublereal* c) const
{
double cs_solvent = standardConcentration();
getActivities(c);
c[0] *= cs_solvent;
if (m_kk > 1) {
double cs_solute = standardConcentration(1);
for (size_t k = 1; k < m_kk; k++) {
c[k] *= cs_solute;
}
}
}
doublereal HMWSoln::standardConcentration(size_t k) const
{
getStandardVolumes(m_tmpV.data());
double mvSolvent = m_tmpV[m_indexSolvent];
if (k > 0) {
return m_Mnaught / mvSolvent;
}
return 1.0 / mvSolvent;
}
void HMWSoln::getActivities(doublereal* ac) const
{
updateStandardStateThermo();
// Update the molality array, m_molalities(). This requires an update due to
// mole fractions
s_update_lnMolalityActCoeff();
// Now calculate the array of activities.
for (size_t k = 0; k < m_kk; k++) {
if (k != m_indexSolvent) {
ac[k] = m_molalities[k] * exp(m_lnActCoeffMolal_Scaled[k]);
}
}
double xmolSolvent = moleFraction(m_indexSolvent);
ac[m_indexSolvent] =
exp(m_lnActCoeffMolal_Scaled[m_indexSolvent]) * xmolSolvent;
}
void HMWSoln::getUnscaledMolalityActivityCoefficients(doublereal* acMolality) const
{
updateStandardStateThermo();
A_Debye_TP(-1.0, -1.0);
s_update_lnMolalityActCoeff();
std::copy(m_lnActCoeffMolal_Unscaled.begin(), m_lnActCoeffMolal_Unscaled.end(), acMolality);
for (size_t k = 0; k < m_kk; k++) {
acMolality[k] = exp(acMolality[k]);
}
}
// ------ Partial Molar Properties of the Solution -----------------
void HMWSoln::getChemPotentials(doublereal* mu) const
{
double xx;
// First get the standard chemical potentials in molar form. This requires
// updates of standard state as a function of T and P
getStandardChemPotentials(mu);
// Update the activity coefficients. This also updates the internal molality
// array.
s_update_lnMolalityActCoeff();
double xmolSolvent = moleFraction(m_indexSolvent);
for (size_t k = 0; k < m_kk; k++) {
if (m_indexSolvent != k) {
xx = std::max(m_molalities[k], SmallNumber);
mu[k] += RT() * (log(xx) + m_lnActCoeffMolal_Scaled[k]);
}
}
xx = std::max(xmolSolvent, SmallNumber);
mu[m_indexSolvent] +=
RT() * (log(xx) + m_lnActCoeffMolal_Scaled[m_indexSolvent]);
}
void HMWSoln::getPartialMolarEnthalpies(doublereal* hbar) const
{
// Get the nondimensional standard state enthalpies
getEnthalpy_RT(hbar);
// dimensionalize it.
for (size_t k = 0; k < m_kk; k++) {
hbar[k] *= RT();
}
// Update the activity coefficients, This also update the internally stored
// molalities.
s_update_lnMolalityActCoeff();
s_update_dlnMolalityActCoeff_dT();
for (size_t k = 0; k < m_kk; k++) {
hbar[k] -= RT() * temperature() * m_dlnActCoeffMolaldT_Scaled[k];
}
}
void HMWSoln::getPartialMolarEntropies(doublereal* sbar) const
{
// Get the standard state entropies at the temperature and pressure of the
// solution.
getEntropy_R(sbar);
// Dimensionalize the entropies
for (size_t k = 0; k < m_kk; k++) {
sbar[k] *= GasConstant;
}
// Update the activity coefficients, This also update the internally stored
// molalities.
s_update_lnMolalityActCoeff();
// First we will add in the obvious dependence on the T term out front of
// the log activity term
doublereal mm;
for (size_t k = 0; k < m_kk; k++) {
if (k != m_indexSolvent) {
mm = std::max(SmallNumber, m_molalities[k]);
sbar[k] -= GasConstant * (log(mm) + m_lnActCoeffMolal_Scaled[k]);
}
}
double xmolSolvent = moleFraction(m_indexSolvent);
mm = std::max(SmallNumber, xmolSolvent);
sbar[m_indexSolvent] -= GasConstant *(log(mm) + m_lnActCoeffMolal_Scaled[m_indexSolvent]);
// Check to see whether activity coefficients are temperature dependent. If
// they are, then calculate the their temperature derivatives and add them
// into the result.
s_update_dlnMolalityActCoeff_dT();
for (size_t k = 0; k < m_kk; k++) {
sbar[k] -= RT() * m_dlnActCoeffMolaldT_Scaled[k];
}
}
void HMWSoln::getPartialMolarVolumes(doublereal* vbar) const
{
// Get the standard state values in m^3 kmol-1
getStandardVolumes(vbar);
// Update the derivatives wrt the activity coefficients.
s_update_lnMolalityActCoeff();
s_update_dlnMolalityActCoeff_dP();
for (size_t k = 0; k < m_kk; k++) {
vbar[k] += RT() * m_dlnActCoeffMolaldP_Scaled[k];
}
}
void HMWSoln::getPartialMolarCp(doublereal* cpbar) const
{
getCp_R(cpbar);
for (size_t k = 0; k < m_kk; k++) {
cpbar[k] *= GasConstant;
}
// Update the activity coefficients, This also update the internally stored
// molalities.
s_update_lnMolalityActCoeff();
s_update_dlnMolalityActCoeff_dT();
s_update_d2lnMolalityActCoeff_dT2();
for (size_t k = 0; k < m_kk; k++) {
cpbar[k] -= (2.0 * RT() * m_dlnActCoeffMolaldT_Scaled[k] +
RT() * temperature() * m_d2lnActCoeffMolaldT2_Scaled[k]);
}
}
// -------------- Utilities -------------------------------
doublereal HMWSoln::satPressure(doublereal t) {
double p_old = pressure();
double t_old = temperature();
double pres = m_waterSS->satPressure(t);
// Set the underlying object back to its original state.
m_waterSS->setState_TP(t_old, p_old);
return pres;
}
double HMWSoln::A_Debye_TP(double tempArg, double presArg) const
{
double T = temperature();
double A;
if (tempArg != -1.0) {
T = tempArg;
}
double P = pressure();
if (presArg != -1.0) {
P = presArg;
}
static const int cacheId = m_cache.getId();
CachedScalar cached = m_cache.getScalar(cacheId);
if(cached.validate(T, P)) {
return m_A_Debye;
}
switch (m_form_A_Debye) {
case A_DEBYE_CONST:
A = m_A_Debye;
break;
case A_DEBYE_WATER:
A = m_waterProps->ADebye(T, P, 0);
m_A_Debye = A;
break;
default:
throw CanteraError("HMWSoln::A_Debye_TP", "shouldn't be here");
}
return A;
}
double HMWSoln::dA_DebyedT_TP(double tempArg, double presArg) const
{
doublereal T = temperature();
if (tempArg != -1.0) {
T = tempArg;
}
doublereal P = pressure();
if (presArg != -1.0) {
P = presArg;
}
doublereal dAdT;
switch (m_form_A_Debye) {
case A_DEBYE_CONST:
dAdT = 0.0;
break;
case A_DEBYE_WATER:
dAdT = m_waterProps->ADebye(T, P, 1);
break;
default:
throw CanteraError("HMWSoln::dA_DebyedT_TP", "shouldn't be here");
}
return dAdT;
}
double HMWSoln::dA_DebyedP_TP(double tempArg, double presArg) const
{
double T = temperature();
if (tempArg != -1.0) {
T = tempArg;
}
double P = pressure();
if (presArg != -1.0) {
P = presArg;
}
double dAdP;
static const int cacheId = m_cache.getId();
CachedScalar cached = m_cache.getScalar(cacheId);
switch (m_form_A_Debye) {
case A_DEBYE_CONST:
dAdP = 0.0;
break;
case A_DEBYE_WATER:
if(cached.validate(T, P)) {
dAdP = cached.value;
} else {
dAdP = m_waterProps->ADebye(T, P, 3);
cached.value = dAdP;
}
break;
default:
throw CanteraError("HMWSoln::dA_DebyedP_TP", "shouldn't be here");
}
return dAdP;
}
double HMWSoln::ADebye_L(double tempArg, double presArg) const
{
double dAdT = dA_DebyedT_TP();
double dAphidT = dAdT /3.0;
double T = temperature();
if (tempArg != -1.0) {
T = tempArg;
}
return dAphidT * (4.0 * GasConstant * T * T);
}
double HMWSoln::ADebye_V(double tempArg, double presArg) const
{
double dAdP = dA_DebyedP_TP();
double dAphidP = dAdP /3.0;
double T = temperature();
if (tempArg != -1.0) {
T = tempArg;
}
return - dAphidP * (4.0 * GasConstant * T);
}
double HMWSoln::ADebye_J(double tempArg, double presArg) const
{
double T = temperature();
if (tempArg != -1.0) {
T = tempArg;
}
double A_L = ADebye_L(T, presArg);
double d2 = d2A_DebyedT2_TP(T, presArg);
double d2Aphi = d2 / 3.0;
return 2.0 * A_L / T + 4.0 * GasConstant * T * T *d2Aphi;
}
double HMWSoln::d2A_DebyedT2_TP(double tempArg, double presArg) const
{
double T = temperature();
if (tempArg != -1.0) {
T = tempArg;
}
double P = pressure();
if (presArg != -1.0) {
P = presArg;
}
double d2AdT2;
switch (m_form_A_Debye) {
case A_DEBYE_CONST:
d2AdT2 = 0.0;
break;
case A_DEBYE_WATER:
d2AdT2 = m_waterProps->ADebye(T, P, 2);
break;
default:
throw CanteraError("HMWSoln::d2A_DebyedT2_TP", "shouldn't be here");
}
return d2AdT2;
}
// ---------- Other Property Functions
double HMWSoln::AionicRadius(int k) const
{
return m_Aionic[k];
}
// ------------ Private and Restricted Functions ------------------
void HMWSoln::initLengths()
{
// Resize lengths equal to the number of species in the phase.
m_electrolyteSpeciesType.resize(m_kk, cEST_polarNeutral);
m_speciesSize.resize(m_kk);
m_speciesCharge_Stoich.resize(m_kk, 0.0);
m_Aionic.resize(m_kk, 0.0);
m_tmpV.resize(m_kk, 0.0);
m_molalitiesCropped.resize(m_kk, 0.0);
size_t maxCounterIJlen = 1 + (m_kk-1) * (m_kk-2) / 2;
// Figure out the size of the temperature coefficient arrays
int TCoeffLength = 1;
if (m_formPitzerTemp == PITZER_TEMP_LINEAR) {
TCoeffLength = 2;
} else if (m_formPitzerTemp == PITZER_TEMP_COMPLEX1) {
TCoeffLength = 5;
}
m_Beta0MX_ij.resize(maxCounterIJlen, 0.0);
m_Beta0MX_ij_L.resize(maxCounterIJlen, 0.0);
m_Beta0MX_ij_LL.resize(maxCounterIJlen, 0.0);
m_Beta0MX_ij_P.resize(maxCounterIJlen, 0.0);
m_Beta0MX_ij_coeff.resize(TCoeffLength, maxCounterIJlen, 0.0);
m_Beta1MX_ij.resize(maxCounterIJlen, 0.0);
m_Beta1MX_ij_L.resize(maxCounterIJlen, 0.0);
m_Beta1MX_ij_LL.resize(maxCounterIJlen, 0.0);
m_Beta1MX_ij_P.resize(maxCounterIJlen, 0.0);
m_Beta1MX_ij_coeff.resize(TCoeffLength, maxCounterIJlen, 0.0);
m_Beta2MX_ij.resize(maxCounterIJlen, 0.0);
m_Beta2MX_ij_L.resize(maxCounterIJlen, 0.0);
m_Beta2MX_ij_LL.resize(maxCounterIJlen, 0.0);
m_Beta2MX_ij_P.resize(maxCounterIJlen, 0.0);
m_Beta2MX_ij_coeff.resize(TCoeffLength, maxCounterIJlen, 0.0);
m_CphiMX_ij.resize(maxCounterIJlen, 0.0);
m_CphiMX_ij_L.resize(maxCounterIJlen, 0.0);
m_CphiMX_ij_LL.resize(maxCounterIJlen, 0.0);
m_CphiMX_ij_P.resize(maxCounterIJlen, 0.0);
m_CphiMX_ij_coeff.resize(TCoeffLength, maxCounterIJlen, 0.0);
m_Alpha1MX_ij.resize(maxCounterIJlen, 2.0);
m_Alpha2MX_ij.resize(maxCounterIJlen, 12.0);
m_Theta_ij.resize(maxCounterIJlen, 0.0);
m_Theta_ij_L.resize(maxCounterIJlen, 0.0);
m_Theta_ij_LL.resize(maxCounterIJlen, 0.0);
m_Theta_ij_P.resize(maxCounterIJlen, 0.0);
m_Theta_ij_coeff.resize(TCoeffLength, maxCounterIJlen, 0.0);
size_t n = m_kk*m_kk*m_kk;
m_Psi_ijk.resize(n, 0.0);
m_Psi_ijk_L.resize(n, 0.0);
m_Psi_ijk_LL.resize(n, 0.0);
m_Psi_ijk_P.resize(n, 0.0);
m_Psi_ijk_coeff.resize(TCoeffLength, n, 0.0);
m_Lambda_nj.resize(m_kk, m_kk, 0.0);
m_Lambda_nj_L.resize(m_kk, m_kk, 0.0);
m_Lambda_nj_LL.resize(m_kk, m_kk, 0.0);
m_Lambda_nj_P.resize(m_kk, m_kk, 0.0);
m_Lambda_nj_coeff.resize(TCoeffLength, m_kk * m_kk, 0.0);
m_Mu_nnn.resize(m_kk, 0.0);
m_Mu_nnn_L.resize(m_kk, 0.0);
m_Mu_nnn_LL.resize(m_kk, 0.0);
m_Mu_nnn_P.resize(m_kk, 0.0);
m_Mu_nnn_coeff.resize(TCoeffLength, m_kk, 0.0);
m_lnActCoeffMolal_Scaled.resize(m_kk, 0.0);
m_dlnActCoeffMolaldT_Scaled.resize(m_kk, 0.0);
m_d2lnActCoeffMolaldT2_Scaled.resize(m_kk, 0.0);
m_dlnActCoeffMolaldP_Scaled.resize(m_kk, 0.0);
m_lnActCoeffMolal_Unscaled.resize(m_kk, 0.0);
m_dlnActCoeffMolaldT_Unscaled.resize(m_kk, 0.0);
m_d2lnActCoeffMolaldT2_Unscaled.resize(m_kk, 0.0);
m_dlnActCoeffMolaldP_Unscaled.resize(m_kk, 0.0);
m_CounterIJ.resize(m_kk*m_kk, 0);
m_gfunc_IJ.resize(maxCounterIJlen, 0.0);
m_g2func_IJ.resize(maxCounterIJlen, 0.0);
m_hfunc_IJ.resize(maxCounterIJlen, 0.0);
m_h2func_IJ.resize(maxCounterIJlen, 0.0);
m_BMX_IJ.resize(maxCounterIJlen, 0.0);
m_BMX_IJ_L.resize(maxCounterIJlen, 0.0);
m_BMX_IJ_LL.resize(maxCounterIJlen, 0.0);
m_BMX_IJ_P.resize(maxCounterIJlen, 0.0);
m_BprimeMX_IJ.resize(maxCounterIJlen, 0.0);
m_BprimeMX_IJ_L.resize(maxCounterIJlen, 0.0);
m_BprimeMX_IJ_LL.resize(maxCounterIJlen, 0.0);
m_BprimeMX_IJ_P.resize(maxCounterIJlen, 0.0);
m_BphiMX_IJ.resize(maxCounterIJlen, 0.0);
m_BphiMX_IJ_L.resize(maxCounterIJlen, 0.0);
m_BphiMX_IJ_LL.resize(maxCounterIJlen, 0.0);
m_BphiMX_IJ_P.resize(maxCounterIJlen, 0.0);
m_Phi_IJ.resize(maxCounterIJlen, 0.0);
m_Phi_IJ_L.resize(maxCounterIJlen, 0.0);
m_Phi_IJ_LL.resize(maxCounterIJlen, 0.0);
m_Phi_IJ_P.resize(maxCounterIJlen, 0.0);
m_Phiprime_IJ.resize(maxCounterIJlen, 0.0);
m_PhiPhi_IJ.resize(maxCounterIJlen, 0.0);
m_PhiPhi_IJ_L.resize(maxCounterIJlen, 0.0);
m_PhiPhi_IJ_LL.resize(maxCounterIJlen, 0.0);
m_PhiPhi_IJ_P.resize(maxCounterIJlen, 0.0);
m_CMX_IJ.resize(maxCounterIJlen, 0.0);
m_CMX_IJ_L.resize(maxCounterIJlen, 0.0);
m_CMX_IJ_LL.resize(maxCounterIJlen, 0.0);
m_CMX_IJ_P.resize(maxCounterIJlen, 0.0);
m_gamma_tmp.resize(m_kk, 0.0);
IMS_lnActCoeffMolal_.resize(m_kk, 0.0);
CROP_speciesCropped_.resize(m_kk, 0);
counterIJ_setup();
}
void HMWSoln::s_update_lnMolalityActCoeff() const
{
static const int cacheId = m_cache.getId();
CachedScalar cached = m_cache.getScalar(cacheId);
if( cached.validate(temperature(), pressure(), stateMFNumber()) ) {
return;
}
// Calculate the molalities. Currently, the molalities may not be current
// with respect to the contents of the State objects' data.
calcMolalities();
// Calculate a cropped set of molalities that will be used in all activity
// coefficient calculations.
calcMolalitiesCropped();
// Calculate the stoichiometric ionic charge. This isn't used in the Pitzer
// formulation.
m_IionicMolalityStoich = 0.0;
for (size_t k = 0; k < m_kk; k++) {
double z_k = charge(k);
double zs_k1 = m_speciesCharge_Stoich[k];
if (z_k == zs_k1) {
m_IionicMolalityStoich += m_molalities[k] * z_k * z_k;
} else {
double zs_k2 = z_k - zs_k1;
m_IionicMolalityStoich += m_molalities[k] * (zs_k1 * zs_k1 + zs_k2 * zs_k2);
}
}
// Update the temperature dependence of the pitzer coefficients and their
// derivatives
s_updatePitzer_CoeffWRTemp();
// Calculate the IMS cutoff factors
s_updateIMS_lnMolalityActCoeff();
// Now do the main calculation.
s_updatePitzer_lnMolalityActCoeff();
double xmolSolvent = moleFraction(m_indexSolvent);
double xx = std::max(m_xmolSolventMIN, xmolSolvent);
double lnActCoeffMolal0 = - log(xx) + (xx - 1.0)/xx;
double lnxs = log(xx);
for (size_t k = 1; k < m_kk; k++) {
CROP_speciesCropped_[k] = 0;
m_lnActCoeffMolal_Unscaled[k] += IMS_lnActCoeffMolal_[k];
if (m_lnActCoeffMolal_Unscaled[k] > (CROP_ln_gamma_k_max- 2.5 *lnxs)) {
CROP_speciesCropped_[k] = 2;
m_lnActCoeffMolal_Unscaled[k] = CROP_ln_gamma_k_max - 2.5 * lnxs;
}
if (m_lnActCoeffMolal_Unscaled[k] < (CROP_ln_gamma_k_min - 2.5 *lnxs)) {
// -1.0 and -1.5 caused multiple solutions
CROP_speciesCropped_[k] = 2;
m_lnActCoeffMolal_Unscaled[k] = CROP_ln_gamma_k_min - 2.5 * lnxs;
}
}
CROP_speciesCropped_[0] = 0;
m_lnActCoeffMolal_Unscaled[0] += (IMS_lnActCoeffMolal_[0] - lnActCoeffMolal0);
if (m_lnActCoeffMolal_Unscaled[0] < CROP_ln_gamma_o_min) {
CROP_speciesCropped_[0] = 2;
m_lnActCoeffMolal_Unscaled[0] = CROP_ln_gamma_o_min;
}
if (m_lnActCoeffMolal_Unscaled[0] > CROP_ln_gamma_o_max) {
CROP_speciesCropped_[0] = 2;
// -0.5 caused multiple solutions
m_lnActCoeffMolal_Unscaled[0] = CROP_ln_gamma_o_max;
}
if (m_lnActCoeffMolal_Unscaled[0] > CROP_ln_gamma_o_max - 0.5 * lnxs) {
CROP_speciesCropped_[0] = 2;
m_lnActCoeffMolal_Unscaled[0] = CROP_ln_gamma_o_max - 0.5 * lnxs;
}
// Now do the pH Scaling
s_updateScaling_pHScaling();
}
void HMWSoln::calcMolalitiesCropped() const
{
doublereal Imax = 0.0;
m_molalitiesAreCropped = false;
for (size_t k = 0; k < m_kk; k++) {
m_molalitiesCropped[k] = m_molalities[k];
Imax = std::max(m_molalities[k] * charge(k) * charge(k), Imax);
}
int cropMethod = 1;
if (cropMethod == 0) {
// Quick return
if (Imax < m_maxIionicStrength) {
return;
}
m_molalitiesAreCropped = true;
for (size_t i = 1; i < (m_kk - 1); i++) {
double charge_i = charge(i);
double abs_charge_i = fabs(charge_i);
if (charge_i == 0.0) {
continue;
}
for (size_t j = (i+1); j < m_kk; j++) {
double charge_j = charge(j);
double abs_charge_j = fabs(charge_j);
// Only loop over oppositely charge species
if (charge_i * charge_j < 0) {
double Iac_max = m_maxIionicStrength;
if (m_molalitiesCropped[i] > m_molalitiesCropped[j]) {
Imax = m_molalitiesCropped[i] * abs_charge_i * abs_charge_i;
if (Imax > Iac_max) {
m_molalitiesCropped[i] = Iac_max / (abs_charge_i * abs_charge_i);
}
Imax = m_molalitiesCropped[j] * fabs(abs_charge_j * abs_charge_i);
if (Imax > Iac_max) {
m_molalitiesCropped[j] = Iac_max / (abs_charge_j * abs_charge_i);
}
} else {
Imax = m_molalitiesCropped[j] * abs_charge_j * abs_charge_j;
if (Imax > Iac_max) {
m_molalitiesCropped[j] = Iac_max / (abs_charge_j * abs_charge_j);
}
Imax = m_molalitiesCropped[i] * abs_charge_j * abs_charge_i;
if (Imax > Iac_max) {
m_molalitiesCropped[i] = Iac_max / (abs_charge_j * abs_charge_i);
}
}
}
}
}
// Do this loop 10 times until we have achieved charge neutrality in the
// cropped molalities
for (int times = 0; times< 10; times++) {
double anion_charge = 0.0;
double cation_charge = 0.0;
size_t anion_contrib_max_i = npos;
double anion_contrib_max = -1.0;
size_t cation_contrib_max_i = npos;
double cation_contrib_max = -1.0;
for (size_t i = 0; i < m_kk; i++) {
double charge_i = charge(i);
if (charge_i < 0.0) {
double anion_contrib = - m_molalitiesCropped[i] * charge_i;
anion_charge += anion_contrib;
if (anion_contrib > anion_contrib_max) {
anion_contrib_max = anion_contrib;
anion_contrib_max_i = i;
}
} else if (charge_i > 0.0) {
double cation_contrib = m_molalitiesCropped[i] * charge_i;
cation_charge += cation_contrib;
if (cation_contrib > cation_contrib_max) {
cation_contrib_max = cation_contrib;
cation_contrib_max_i = i;
}
}
}
double total_charge = cation_charge - anion_charge;
if (total_charge > 1.0E-8) {
double desiredCrop = total_charge/charge(cation_contrib_max_i);
double maxCrop = 0.66 * m_molalitiesCropped[cation_contrib_max_i];
if (desiredCrop < maxCrop) {
m_molalitiesCropped[cation_contrib_max_i] -= desiredCrop;
break;
} else {
m_molalitiesCropped[cation_contrib_max_i] -= maxCrop;
}
} else if (total_charge < -1.0E-8) {
double desiredCrop = total_charge/charge(anion_contrib_max_i);
double maxCrop = 0.66 * m_molalitiesCropped[anion_contrib_max_i];
if (desiredCrop < maxCrop) {
m_molalitiesCropped[anion_contrib_max_i] -= desiredCrop;
break;
} else {
m_molalitiesCropped[anion_contrib_max_i] -= maxCrop;
}
} else {
break;
}
}
}
if (cropMethod == 1) {
double* molF = m_gamma_tmp.data();
getMoleFractions(molF);
double xmolSolvent = molF[m_indexSolvent];
if (xmolSolvent >= MC_X_o_cutoff_) {
return;
}
m_molalitiesAreCropped = true;
double poly = MC_apCut_ + MC_bpCut_ * xmolSolvent + MC_dpCut_* xmolSolvent * xmolSolvent;
double p = xmolSolvent + MC_epCut_ + exp(- xmolSolvent/ MC_cpCut_) * poly;
double denomInv = 1.0/ (m_Mnaught * p);
for (size_t k = 0; k < m_kk; k++) {
m_molalitiesCropped[k] = molF[k] * denomInv;
}
// Do a further check to see if the Ionic strength is below a max value
// Reduce the molalities to enforce this. Note, this algorithm preserves
// the charge neutrality of the solution after cropping.
double Itmp = 0.0;
for (size_t k = 0; k < m_kk; k++) {
Itmp += m_molalitiesCropped[k] * charge(k) * charge(k);
}
if (Itmp > m_maxIionicStrength) {
double ratio = Itmp / m_maxIionicStrength;
for (size_t k = 0; k < m_kk; k++) {
if (charge(k) != 0.0) {
m_molalitiesCropped[k] *= ratio;
}
}
}
}
}
void HMWSoln::counterIJ_setup() const
{
m_CounterIJ.resize(m_kk * m_kk);
int counter = 0;
for (size_t i = 0; i < m_kk; i++) {
size_t n = i;
size_t nc = m_kk * i;
m_CounterIJ[n] = 0;
m_CounterIJ[nc] = 0;
}
for (size_t i = 1; i < (m_kk - 1); i++) {
size_t n = m_kk * i + i;
m_CounterIJ[n] = 0;
for (size_t j = (i+1); j < m_kk; j++) {
n = m_kk * j + i;
size_t nc = m_kk * i + j;
counter++;
m_CounterIJ[n] = counter;
m_CounterIJ[nc] = counter;
}
}
}
void HMWSoln::s_updatePitzer_CoeffWRTemp(int doDerivs) const
{
double T = temperature();
const double twoT = 2.0 * T;
const double invT = 1.0 / T;
const double invT2 = invT * invT;
const double twoinvT3 = 2.0 * invT * invT2;
double tinv = 0.0, tln = 0.0, tlin = 0.0, tquad = 0.0;
if (m_formPitzerTemp == PITZER_TEMP_LINEAR) {
tlin = T - m_TempPitzerRef;
} else if (m_formPitzerTemp == PITZER_TEMP_COMPLEX1) {
tlin = T - m_TempPitzerRef;
tquad = T * T - m_TempPitzerRef * m_TempPitzerRef;
tln = log(T/ m_TempPitzerRef);
tinv = 1.0/T - 1.0/m_TempPitzerRef;
}
for (size_t i = 1; i < (m_kk - 1); i++) {
for (size_t j = (i+1); j < m_kk; j++) {
// Find the counterIJ for the symmetric binary interaction
size_t n = m_kk*i + j;
size_t counterIJ = m_CounterIJ[n];
const double* beta0MX_coeff = m_Beta0MX_ij_coeff.ptrColumn(counterIJ);
const double* beta1MX_coeff = m_Beta1MX_ij_coeff.ptrColumn(counterIJ);
const double* beta2MX_coeff = m_Beta2MX_ij_coeff.ptrColumn(counterIJ);
const double* CphiMX_coeff = m_CphiMX_ij_coeff.ptrColumn(counterIJ);
const double* Theta_coeff = m_Theta_ij_coeff.ptrColumn(counterIJ);
switch (m_formPitzerTemp) {
case PITZER_TEMP_CONSTANT:
break;
case PITZER_TEMP_LINEAR:
m_Beta0MX_ij[counterIJ] = beta0MX_coeff[0]
+ beta0MX_coeff[1]*tlin;
m_Beta0MX_ij_L[counterIJ] = beta0MX_coeff[1];
m_Beta0MX_ij_LL[counterIJ] = 0.0;
m_Beta1MX_ij[counterIJ] = beta1MX_coeff[0]
+ beta1MX_coeff[1]*tlin;
m_Beta1MX_ij_L[counterIJ] = beta1MX_coeff[1];
m_Beta1MX_ij_LL[counterIJ] = 0.0;
m_Beta2MX_ij[counterIJ] = beta2MX_coeff[0]
+ beta2MX_coeff[1]*tlin;
m_Beta2MX_ij_L[counterIJ] = beta2MX_coeff[1];
m_Beta2MX_ij_LL[counterIJ] = 0.0;
m_CphiMX_ij[counterIJ] = CphiMX_coeff[0]
+ CphiMX_coeff[1]*tlin;
m_CphiMX_ij_L[counterIJ] = CphiMX_coeff[1];
m_CphiMX_ij_LL[counterIJ] = 0.0;
m_Theta_ij[counterIJ] = Theta_coeff[0] + Theta_coeff[1]*tlin;
m_Theta_ij_L[counterIJ] = Theta_coeff[1];
m_Theta_ij_LL[counterIJ] = 0.0;
break;
case PITZER_TEMP_COMPLEX1:
m_Beta0MX_ij[counterIJ] = beta0MX_coeff[0]
+ beta0MX_coeff[1]*tlin
+ beta0MX_coeff[2]*tquad
+ beta0MX_coeff[3]*tinv
+ beta0MX_coeff[4]*tln;
m_Beta1MX_ij[counterIJ] = beta1MX_coeff[0]
+ beta1MX_coeff[1]*tlin
+ beta1MX_coeff[2]*tquad
+ beta1MX_coeff[3]*tinv
+ beta1MX_coeff[4]*tln;
m_Beta2MX_ij[counterIJ] = beta2MX_coeff[0]
+ beta2MX_coeff[1]*tlin
+ beta2MX_coeff[2]*tquad
+ beta2MX_coeff[3]*tinv
+ beta2MX_coeff[4]*tln;
m_CphiMX_ij[counterIJ] = CphiMX_coeff[0]
+ CphiMX_coeff[1]*tlin
+ CphiMX_coeff[2]*tquad
+ CphiMX_coeff[3]*tinv
+ CphiMX_coeff[4]*tln;
m_Theta_ij[counterIJ] = Theta_coeff[0]
+ Theta_coeff[1]*tlin
+ Theta_coeff[2]*tquad
+ Theta_coeff[3]*tinv
+ Theta_coeff[4]*tln;
m_Beta0MX_ij_L[counterIJ] = beta0MX_coeff[1]
+ beta0MX_coeff[2]*twoT
- beta0MX_coeff[3]*invT2
+ beta0MX_coeff[4]*invT;
m_Beta1MX_ij_L[counterIJ] = beta1MX_coeff[1]
+ beta1MX_coeff[2]*twoT
- beta1MX_coeff[3]*invT2
+ beta1MX_coeff[4]*invT;
m_Beta2MX_ij_L[counterIJ] = beta2MX_coeff[1]
+ beta2MX_coeff[2]*twoT
- beta2MX_coeff[3]*invT2
+ beta2MX_coeff[4]*invT;
m_CphiMX_ij_L[counterIJ] = CphiMX_coeff[1]
+ CphiMX_coeff[2]*twoT
- CphiMX_coeff[3]*invT2
+ CphiMX_coeff[4]*invT;
m_Theta_ij_L[counterIJ] = Theta_coeff[1]
+ Theta_coeff[2]*twoT
- Theta_coeff[3]*invT2
+ Theta_coeff[4]*invT;
doDerivs = 2;
if (doDerivs > 1) {
m_Beta0MX_ij_LL[counterIJ] =
+ beta0MX_coeff[2]*2.0
+ beta0MX_coeff[3]*twoinvT3
- beta0MX_coeff[4]*invT2;
m_Beta1MX_ij_LL[counterIJ] =
+ beta1MX_coeff[2]*2.0
+ beta1MX_coeff[3]*twoinvT3
- beta1MX_coeff[4]*invT2;
m_Beta2MX_ij_LL[counterIJ] =
+ beta2MX_coeff[2]*2.0
+ beta2MX_coeff[3]*twoinvT3
- beta2MX_coeff[4]*invT2;
m_CphiMX_ij_LL[counterIJ] =
+ CphiMX_coeff[2]*2.0
+ CphiMX_coeff[3]*twoinvT3
- CphiMX_coeff[4]*invT2;
m_Theta_ij_LL[counterIJ] =
+ Theta_coeff[2]*2.0
+ Theta_coeff[3]*twoinvT3
- Theta_coeff[4]*invT2;
}
break;
}
}
}
// Lambda interactions and Mu_nnn
// i must be neutral for this term to be nonzero. We take advantage of this
// here to lower the operation count.
for (size_t i = 1; i < m_kk; i++) {
if (charge(i) == 0.0) {
for (size_t j = 1; j < m_kk; j++) {
size_t n = i * m_kk + j;
const double* Lambda_coeff = m_Lambda_nj_coeff.ptrColumn(n);
switch (m_formPitzerTemp) {
case PITZER_TEMP_CONSTANT:
m_Lambda_nj(i,j) = Lambda_coeff[0];
break;
case PITZER_TEMP_LINEAR:
m_Lambda_nj(i,j) = Lambda_coeff[0] + Lambda_coeff[1]*tlin;
m_Lambda_nj_L(i,j) = Lambda_coeff[1];
m_Lambda_nj_LL(i,j) = 0.0;
break;
case PITZER_TEMP_COMPLEX1:
m_Lambda_nj(i,j) = Lambda_coeff[0]
+ Lambda_coeff[1]*tlin
+ Lambda_coeff[2]*tquad
+ Lambda_coeff[3]*tinv
+ Lambda_coeff[4]*tln;
m_Lambda_nj_L(i,j) = Lambda_coeff[1]
+ Lambda_coeff[2]*twoT
- Lambda_coeff[3]*invT2
+ Lambda_coeff[4]*invT;
m_Lambda_nj_LL(i,j) =
Lambda_coeff[2]*2.0
+ Lambda_coeff[3]*twoinvT3
- Lambda_coeff[4]*invT2;
}
if (j == i) {
const double* Mu_coeff = m_Mu_nnn_coeff.ptrColumn(i);
switch (m_formPitzerTemp) {
case PITZER_TEMP_CONSTANT:
m_Mu_nnn[i] = Mu_coeff[0];
break;
case PITZER_TEMP_LINEAR:
m_Mu_nnn[i] = Mu_coeff[0] + Mu_coeff[1]*tlin;
m_Mu_nnn_L[i] = Mu_coeff[1];
m_Mu_nnn_LL[i] = 0.0;
break;
case PITZER_TEMP_COMPLEX1:
m_Mu_nnn[i] = Mu_coeff[0]
+ Mu_coeff[1]*tlin
+ Mu_coeff[2]*tquad
+ Mu_coeff[3]*tinv
+ Mu_coeff[4]*tln;
m_Mu_nnn_L[i] = Mu_coeff[1]
+ Mu_coeff[2]*twoT
- Mu_coeff[3]*invT2
+ Mu_coeff[4]*invT;
m_Mu_nnn_LL[i] =
Mu_coeff[2]*2.0
+ Mu_coeff[3]*twoinvT3
- Mu_coeff[4]*invT2;
}
}
}
}
}
switch(m_formPitzerTemp) {
case PITZER_TEMP_CONSTANT:
for (size_t i = 1; i < m_kk; i++) {
for (size_t j = 1; j < m_kk; j++) {
for (size_t k = 1; k < m_kk; k++) {
size_t n = i * m_kk *m_kk + j * m_kk + k;
const double* Psi_coeff = m_Psi_ijk_coeff.ptrColumn(n);
m_Psi_ijk[n] = Psi_coeff[0];
}
}
}
break;
case PITZER_TEMP_LINEAR:
for (size_t i = 1; i < m_kk; i++) {
for (size_t j = 1; j < m_kk; j++) {
for (size_t k = 1; k < m_kk; k++) {
size_t n = i * m_kk *m_kk + j * m_kk + k;
const double* Psi_coeff = m_Psi_ijk_coeff.ptrColumn(n);
m_Psi_ijk[n] = Psi_coeff[0] + Psi_coeff[1]*tlin;
m_Psi_ijk_L[n] = Psi_coeff[1];
m_Psi_ijk_LL[n] = 0.0;
}
}
}
break;
case PITZER_TEMP_COMPLEX1:
for (size_t i = 1; i < m_kk; i++) {
for (size_t j = 1; j < m_kk; j++) {
for (size_t k = 1; k < m_kk; k++) {
size_t n = i * m_kk *m_kk + j * m_kk + k;
const double* Psi_coeff = m_Psi_ijk_coeff.ptrColumn(n);
m_Psi_ijk[n] = Psi_coeff[0]
+ Psi_coeff[1]*tlin
+ Psi_coeff[2]*tquad
+ Psi_coeff[3]*tinv
+ Psi_coeff[4]*tln;
m_Psi_ijk_L[n] = Psi_coeff[1]
+ Psi_coeff[2]*twoT
- Psi_coeff[3]*invT2
+ Psi_coeff[4]*invT;
m_Psi_ijk_LL[n] =
Psi_coeff[2]*2.0
+ Psi_coeff[3]*twoinvT3
- Psi_coeff[4]*invT2;
}
}
}
break;
}
}
void HMWSoln::s_updatePitzer_lnMolalityActCoeff() const
{
// HKM -> Assumption is made that the solvent is species 0.
if (m_indexSolvent != 0) {
throw CanteraError("HMWSoln::s_updatePitzer_lnMolalityActCoeff",
"Wrong index solvent value!");
}
// Use the CROPPED molality of the species in solution.
const vector_fp& molality = m_molalitiesCropped;
// These are data inputs about the Pitzer correlation. They come from the
// input file for the Pitzer model.
vector_fp& gamma_Unscaled = m_gamma_tmp;
// Local variables defined by Coltrin
double etheta[5][5], etheta_prime[5][5], sqrtIs;
// Molality based ionic strength of the solution
double Is = 0.0;
// Molarcharge of the solution: In Pitzer's notation, this is his variable
// called "Z".
double molarcharge = 0.0;
// molalitysum is the sum of the molalities over all solutes, even those
// with zero charge.
double molalitysumUncropped = 0.0;
debuglog("\n Debugging information from hmw_act \n", m_debugCalc);
// Make sure the counter variables are setup
counterIJ_setup();
// ---------- Calculate common sums over solutes ---------------------
for (size_t n = 1; n < m_kk; n++) {
// ionic strength
Is += charge(n) * charge(n) * molality[n];
// total molar charge
molarcharge += fabs(charge(n)) * molality[n];
molalitysumUncropped += m_molalities[n];
}
Is *= 0.5;
// Store the ionic molality in the object for reference.
m_IionicMolality = Is;
sqrtIs = sqrt(Is);
if (m_debugCalc) {
writelog(" Step 1: \n");
writelogf(" ionic strenth = %14.7le \n total molar "
"charge = %14.7le \n", Is, molarcharge);
}
// The following call to calc_lambdas() calculates all 16 elements of the
// elambda and elambda1 arrays, given the value of the ionic strength (Is)
calc_lambdas(Is);
// Step 2: Find the coefficients E-theta and E-thetaprime for all
// combinations of positive unlike charges up to 4
debuglog(" Step 2: \n", m_debugCalc);
for (int z1 = 1; z1 <=4; z1++) {
for (int z2 =1; z2 <=4; z2++) {
calc_thetas(z1, z2, &etheta[z1][z2], &etheta_prime[z1][z2]);
if (m_debugCalc) {
writelogf(" z1=%3d z2=%3d E-theta(I) = %f, E-thetaprime(I) = %f\n",
z1, z2, etheta[z1][z2], etheta_prime[z1][z2]);
}
}
}
debuglog(" Step 3: \n"
" Species Species g(x) hfunc(x)\n",
m_debugCalc);
// calculate g(x) and hfunc(x) for each cation-anion pair MX. In the
// original literature, hfunc, was called gprime. However, it's not the
// derivative of g(x), so I renamed it.
for (size_t i = 1; i < (m_kk - 1); i++) {
for (size_t j = (i+1); j < m_kk; j++) {
// Find the counterIJ for the symmetric binary interaction
size_t n = m_kk*i + j;
size_t counterIJ = m_CounterIJ[n];
// Only loop over oppositely charge species
if (charge(i)*charge(j) < 0) {
// x is a reduced function variable
double x1 = sqrtIs * m_Alpha1MX_ij[counterIJ];
if (x1 > 1.0E-100) {
m_gfunc_IJ[counterIJ] = 2.0*(1.0-(1.0 + x1) * exp(-x1)) / (x1 * x1);
m_hfunc_IJ[counterIJ] = -2.0 *
(1.0-(1.0 + x1 + 0.5 * x1 * x1) * exp(-x1)) / (x1 * x1);
} else {
m_gfunc_IJ[counterIJ] = 0.0;
m_hfunc_IJ[counterIJ] = 0.0;
}
if (m_Beta2MX_ij[counterIJ] != 0.0) {
double x2 = sqrtIs * m_Alpha2MX_ij[counterIJ];
if (x2 > 1.0E-100) {
m_g2func_IJ[counterIJ] = 2.0*(1.0-(1.0 + x2) * exp(-x2)) / (x2 * x2);
m_h2func_IJ[counterIJ] = -2.0 *
(1.0-(1.0 + x2 + 0.5 * x2 * x2) * exp(-x2)) / (x2 * x2);
} else {
m_g2func_IJ[counterIJ] = 0.0;
m_h2func_IJ[counterIJ] = 0.0;
}
}
} else {
m_gfunc_IJ[counterIJ] = 0.0;
m_hfunc_IJ[counterIJ] = 0.0;
}
if (m_debugCalc) {
writelogf(" %-16s %-16s %9.5f %9.5f \n", speciesName(i),
speciesName(j), m_gfunc_IJ[counterIJ], m_hfunc_IJ[counterIJ]);
}
}
}
// SUBSECTION TO CALCULATE BMX, BprimeMX, BphiMX
// Agrees with Pitzer, Eq. (49), (51), (55)
debuglog(" Step 4: \n"
" Species Species BMX BprimeMX BphiMX\n",
m_debugCalc);
for (size_t i = 1; i < m_kk - 1; i++) {
for (size_t j = i+1; j < m_kk; j++) {
// Find the counterIJ for the symmetric binary interaction
size_t n = m_kk*i + j;
size_t counterIJ = m_CounterIJ[n];
// both species have a non-zero charge, and one is positive and the
// other is negative
if (charge(i)*charge(j) < 0.0) {
m_BMX_IJ[counterIJ] = m_Beta0MX_ij[counterIJ]
+ m_Beta1MX_ij[counterIJ] * m_gfunc_IJ[counterIJ]
+ m_Beta2MX_ij[counterIJ] * m_g2func_IJ[counterIJ];
if (m_debugCalc) {
writelogf("%d %g: %g %g %g %g\n",
counterIJ, m_BMX_IJ[counterIJ], m_Beta0MX_ij[counterIJ],
m_Beta1MX_ij[counterIJ], m_Beta2MX_ij[counterIJ], m_gfunc_IJ[counterIJ]);
}
if (Is > 1.0E-150) {
m_BprimeMX_IJ[counterIJ] = (m_Beta1MX_ij[counterIJ] * m_hfunc_IJ[counterIJ]/Is +
m_Beta2MX_ij[counterIJ] * m_h2func_IJ[counterIJ]/Is);
} else {
m_BprimeMX_IJ[counterIJ] = 0.0;
}
m_BphiMX_IJ[counterIJ] = m_BMX_IJ[counterIJ] + Is*m_BprimeMX_IJ[counterIJ];
} else {
m_BMX_IJ[counterIJ] = 0.0;
m_BprimeMX_IJ[counterIJ] = 0.0;
m_BphiMX_IJ[counterIJ] = 0.0;
}
if (m_debugCalc) {
writelogf(" %-16s %-16s %11.7f %11.7f %11.7f \n",
speciesName(i), speciesName(j),
m_BMX_IJ[counterIJ], m_BprimeMX_IJ[counterIJ], m_BphiMX_IJ[counterIJ]);
}
}
}
// SUBSECTION TO CALCULATE CMX
// Agrees with Pitzer, Eq. (53).
debuglog(" Step 5: \n"
" Species Species CMX\n", m_debugCalc);
for (size_t i = 1; i < m_kk-1; i++) {
for (size_t j = i+1; j < m_kk; j++) {
// Find the counterIJ for the symmetric binary interaction
size_t n = m_kk*i + j;
size_t counterIJ = m_CounterIJ[n];
// both species have a non-zero charge, and one is positive
// and the other is negative
if (charge(i)*charge(j) < 0.0) {
m_CMX_IJ[counterIJ] = m_CphiMX_ij[counterIJ]/
(2.0* sqrt(fabs(charge(i)*charge(j))));
} else {
m_CMX_IJ[counterIJ] = 0.0;
}
if (m_debugCalc) {
writelogf(" %-16s %-16s %11.7f \n",
speciesName(i), speciesName(j), m_CMX_IJ[counterIJ]);
}
}
}
// SUBSECTION TO CALCULATE Phi, PhiPrime, and PhiPhi
// Agrees with Pitzer, Eq. 72, 73, 74
debuglog(" Step 6: \n"
" Species Species Phi_ij Phiprime_ij Phi^phi_ij \n",
m_debugCalc);
for (size_t i = 1; i < m_kk-1; i++) {
for (size_t j = i+1; j < m_kk; j++) {
// Find the counterIJ for the symmetric binary interaction
size_t n = m_kk*i + j;
size_t counterIJ = m_CounterIJ[n];
// both species have a non-zero charge, and one is positive and the
// other is negative
if (charge(i)*charge(j) > 0) {
int z1 = (int) fabs(charge(i));
int z2 = (int) fabs(charge(j));
m_Phi_IJ[counterIJ] = m_Theta_ij[counterIJ] + etheta[z1][z2];
m_Phiprime_IJ[counterIJ] = etheta_prime[z1][z2];
m_PhiPhi_IJ[counterIJ] = m_Phi_IJ[counterIJ] + Is * m_Phiprime_IJ[counterIJ];
} else {
m_Phi_IJ[counterIJ] = 0.0;
m_Phiprime_IJ[counterIJ] = 0.0;
m_PhiPhi_IJ[counterIJ] = 0.0;
}
if (m_debugCalc) {
writelogf(" %-16s %-16s %10.6f %10.6f %10.6f \n",
speciesName(i), speciesName(j),
m_Phi_IJ[counterIJ], m_Phiprime_IJ[counterIJ], m_PhiPhi_IJ[counterIJ]);
}
}
}
// SUBSECTION FOR CALCULATION OF F
// Agrees with Pitzer Eqn. (65)
debuglog(" Step 7: \n", m_debugCalc);
double Aphi = A_Debye_TP() / 3.0;
double F = -Aphi * (sqrt(Is) / (1.0 + 1.2*sqrt(Is))
+ (2.0/1.2) * log(1.0+1.2*(sqrtIs)));
if (m_debugCalc) {
writelogf(" initial value of F = %10.6f \n", F);
}
for (size_t i = 1; i < m_kk-1; i++) {
for (size_t j = i+1; j < m_kk; j++) {
// Find the counterIJ for the symmetric binary interaction
size_t n = m_kk*i + j;
size_t counterIJ = m_CounterIJ[n];
// both species have a non-zero charge, and one is positive and the
// other is negative
if (charge(i)*charge(j) < 0) {
F += molality[i]*molality[j] * m_BprimeMX_IJ[counterIJ];
}
// Both species have a non-zero charge, and they
// have the same sign
if (charge(i)*charge(j) > 0) {
F += molality[i]*molality[j] * m_Phiprime_IJ[counterIJ];
}
if (m_debugCalc) {
writelogf(" F = %10.6f \n", F);
}
}
}
debuglog(" Step 8: Summing in All Contributions to Activity Coefficients \n",
m_debugCalc);
for (size_t i = 1; i < m_kk; i++) {
// SUBSECTION FOR CALCULATING THE ACTCOEFF FOR CATIONS
// equations agree with my notes, Eqn. (118).
// Equations agree with Pitzer, eqn.(63)
if (charge(i) > 0.0) {
if (m_debugCalc) {
writelogf(" Contributions to ln(ActCoeff_%s):\n", speciesName(i));
}
// species i is the cation (positive) to calc the actcoeff
double zsqF = charge(i)*charge(i)*F;
if (m_debugCalc) {
writelogf(" Unary term: z*z*F = %10.5f\n", zsqF);
}
double sum1 = 0.0;
double sum2 = 0.0;
double sum3 = 0.0;
double sum4 = 0.0;
double sum5 = 0.0;
for (size_t j = 1; j < m_kk; j++) {
// Find the counterIJ for the symmetric binary interaction
size_t n = m_kk*i + j;
size_t counterIJ = m_CounterIJ[n];
if (charge(j) < 0.0) {
// sum over all anions
sum1 += molality[j] *
(2.0*m_BMX_IJ[counterIJ] + molarcharge*m_CMX_IJ[counterIJ]);
if (m_debugCalc) {
std::string snj = speciesName(j) + ":";
writelogf(" Bin term with %-13s 2 m_j BMX = %10.5f\n", snj,
molality[j]*2.0*m_BMX_IJ[counterIJ]);
writelogf(" m_j Z CMX = %10.5f\n",
molality[j]* molarcharge*m_CMX_IJ[counterIJ]);
}
if (j < m_kk-1) {
// This term is the ternary interaction involving the
// non-duplicate sum over double anions, j, k, with
// respect to the cation, i.
for (size_t k = j+1; k < m_kk; k++) {
// an inner sum over all anions
if (charge(k) < 0.0) {
n = k + j * m_kk + i * m_kk * m_kk;
sum3 += molality[j]*molality[k]*m_Psi_ijk[n];
if (m_debugCalc && m_Psi_ijk[n] != 0.0) {
std::string snj = speciesName(j) + "," + speciesName(k) + ":";
writelogf(" Psi term on %-16s m_j m_k psi_ijk = %10.5f\n", snj,
molality[j]*molality[k]*m_Psi_ijk[n]);
}
}
}
}
}
if (charge(j) > 0.0) {
// sum over all cations
if (j != i) {
sum2 += molality[j]*(2.0*m_Phi_IJ[counterIJ]);
if (m_debugCalc && (molality[j] * m_Phi_IJ[counterIJ])!= 0.0) {
std::string snj = speciesName(j) + ":";
writelogf(" Phi term with %-12s 2 m_j Phi_cc = %10.5f\n", snj,
molality[j]*(2.0*m_Phi_IJ[counterIJ]));
}
}
for (size_t k = 1; k < m_kk; k++) {
if (charge(k) < 0.0) {
// two inner sums over anions
n = k + j * m_kk + i * m_kk * m_kk;
sum2 += molality[j]*molality[k]*m_Psi_ijk[n];
if (m_debugCalc && m_Psi_ijk[n] != 0.0) {
std::string snj = speciesName(j) + "," + speciesName(k) + ":";
writelogf(" Psi term on %-16s m_j m_k psi_ijk = %10.5f\n", snj,
molality[j]*molality[k]*m_Psi_ijk[n]);
}
// Find the counterIJ for the j,k interaction
n = m_kk*j + k;
size_t counterIJ2 = m_CounterIJ[n];
sum4 += (fabs(charge(i))*
molality[j]*molality[k]*m_CMX_IJ[counterIJ2]);
if (m_debugCalc && (molality[j]*molality[k]*m_CMX_IJ[counterIJ2]) != 0.0) {
std::string snj = speciesName(j) + "," + speciesName(k) + ":";
writelogf(" Tern CMX term on %-16s abs(z_i) m_j m_k CMX = %10.5f\n", snj,
fabs(charge(i))* molality[j]*molality[k]*m_CMX_IJ[counterIJ2]);
}
}
}
}
// Handle neutral j species
if (charge(j) == 0) {
sum5 += molality[j]*2.0*m_Lambda_nj(j,i);
if (m_debugCalc && (molality[j]*2.0*m_Lambda_nj(j,i)) != 0.0) {
std::string snj = speciesName(j) + ":";
writelogf(" Lambda term with %-12s 2 m_j lam_ji = %10.5f\n", snj,
molality[j]*2.0*m_Lambda_nj(j,i));
}
// Zeta interaction term
for (size_t k = 1; k < m_kk; k++) {
if (charge(k) < 0.0) {
size_t izeta = j;
size_t jzeta = i;
n = izeta * m_kk * m_kk + jzeta * m_kk + k;
double zeta = m_Psi_ijk[n];
if (zeta != 0.0) {
sum5 += molality[j]*molality[k]*zeta;
if (m_debugCalc) {
std::string snj = speciesName(j) + "," + speciesName(k) + ":";
writelogf(" Zeta term on %-16s m_n m_a zeta_nMa = %10.5f\n", snj,
molality[j]*molality[k]*m_Psi_ijk[n]);
}
}
}
}
}
}
// Add all of the contributions up to yield the log of the solute
// activity coefficients (molality scale)
m_lnActCoeffMolal_Unscaled[i] = zsqF + sum1 + sum2 + sum3 + sum4 + sum5;
gamma_Unscaled[i] = exp(m_lnActCoeffMolal_Unscaled[i]);
if (m_debugCalc) {
writelogf(" Net %-16s lngamma[i] = %9.5f gamma[i]=%10.6f \n",
speciesName(i), m_lnActCoeffMolal_Unscaled[i], gamma_Unscaled[i]);
}
}
// SUBSECTION FOR CALCULATING THE ACTCOEFF FOR ANIONS
// equations agree with my notes, Eqn. (119).
// Equations agree with Pitzer, eqn.(64)
if (charge(i) < 0) {
if (m_debugCalc) {
writelogf(" Contributions to ln(ActCoeff_%s):\n", speciesName(i));
}
// species i is an anion (negative)
double zsqF = charge(i)*charge(i)*F;
if (m_debugCalc) {
writelogf(" Unary term: z*z*F = %10.5f\n", zsqF);
}
double sum1 = 0.0;
double sum2 = 0.0;
double sum3 = 0.0;
double sum4 = 0.0;
double sum5 = 0.0;
for (size_t j = 1; j < m_kk; j++) {
// Find the counterIJ for the symmetric binary interaction
size_t n = m_kk*i + j;
size_t counterIJ = m_CounterIJ[n];
// For Anions, do the cation interactions.
if (charge(j) > 0) {
sum1 += molality[j]*
(2.0*m_BMX_IJ[counterIJ]+molarcharge*m_CMX_IJ[counterIJ]);
if (m_debugCalc) {
std::string snj = speciesName(j) + ":";
writelogf(" Bin term with %-13s 2 m_j BMX = %10.5f\n", snj,
molality[j]*2.0*m_BMX_IJ[counterIJ]);
writelogf(" m_j Z CMX = %10.5f\n",
molality[j]* molarcharge*m_CMX_IJ[counterIJ]);
}
if (j < m_kk-1) {
for (size_t k = j+1; k < m_kk; k++) {
// an inner sum over all cations
if (charge(k) > 0) {
n = k + j * m_kk + i * m_kk * m_kk;
sum3 += molality[j]*molality[k]*m_Psi_ijk[n];
if (m_debugCalc && m_Psi_ijk[n] != 0.0) {
std::string snj = speciesName(j) + "," + speciesName(k) + ":";
writelogf(" Psi term on %-16s m_j m_k psi_ijk = %10.5f\n", snj,
molality[j]*molality[k]*m_Psi_ijk[n]);
}
}
}
}
}
// For Anions, do the other anion interactions.
if (charge(j) < 0.0) {
// sum over all anions
if (j != i) {
sum2 += molality[j]*(2.0*m_Phi_IJ[counterIJ]);
if (m_debugCalc && (molality[j] * m_Phi_IJ[counterIJ])!= 0.0) {
std::string snj = speciesName(j) + ":";
writelogf(" Phi term with %-12s 2 m_j Phi_aa = %10.5f\n", snj,
molality[j]*(2.0*m_Phi_IJ[counterIJ]));
}
}
for (size_t k = 1; k < m_kk; k++) {
if (charge(k) > 0.0) {
// two inner sums over cations
n = k + j * m_kk + i * m_kk * m_kk;
sum2 += molality[j]*molality[k]*m_Psi_ijk[n];
if (m_debugCalc && m_Psi_ijk[n] != 0.0) {
std::string snj = speciesName(j) + "," + speciesName(k) + ":";
writelogf(" Psi term on %-16s m_j m_k psi_ijk = %10.5f\n", snj,
molality[j]*molality[k]*m_Psi_ijk[n]);
}
// Find the counterIJ for the symmetric binary interaction
n = m_kk*j + k;
size_t counterIJ2 = m_CounterIJ[n];
sum4 += fabs(charge(i))*
molality[j]*molality[k]*m_CMX_IJ[counterIJ2];
if (m_debugCalc && (molality[j]*molality[k]*m_CMX_IJ[counterIJ2]) != 0.0) {
std::string snj = speciesName(j) + "," + speciesName(k) + ":";
writelogf(" Tern CMX term on %-16s abs(z_i) m_j m_k CMX = %10.5f\n", snj,
fabs(charge(i))* molality[j]*molality[k]*m_CMX_IJ[counterIJ2]);
}
}
}
}
// for Anions, do the neutral species interaction
if (charge(j) == 0.0) {
sum5 += molality[j]*2.0*m_Lambda_nj(j,i);
if (m_debugCalc && (molality[j]*2.0*m_Lambda_nj(j,i)) != 0.0) {
std::string snj = speciesName(j) + ":";
writelogf(" Lambda term with %-12s 2 m_j lam_ji = %10.5f\n", snj,
molality[j]*2.0*m_Lambda_nj(j,i));
}
// Zeta interaction term
for (size_t k = 1; k < m_kk; k++) {
if (charge(k) > 0.0) {
size_t izeta = j;
size_t jzeta = k;
size_t kzeta = i;
n = izeta * m_kk * m_kk + jzeta * m_kk + kzeta;
double zeta = m_Psi_ijk[n];
if (zeta != 0.0) {
sum5 += molality[j]*molality[k]*zeta;
if (m_debugCalc) {
std::string snj = speciesName(j) + "," + speciesName(k) + ":";
writelogf(" Zeta term on %-16s m_n m_c zeta_ncX = %10.5f\n", snj,
molality[j]*molality[k]*m_Psi_ijk[n]);
}
}
}
}
}
}
m_lnActCoeffMolal_Unscaled[i] = zsqF + sum1 + sum2 + sum3 + sum4 + sum5;
gamma_Unscaled[i] = exp(m_lnActCoeffMolal_Unscaled[i]);
if (m_debugCalc) {
writelogf(" Net %-16s lngamma[i] = %9.5f gamma[i]=%10.6f\n",
speciesName(i), m_lnActCoeffMolal_Unscaled[i], gamma_Unscaled[i]);
}
}
// SUBSECTION FOR CALCULATING NEUTRAL SOLUTE ACT COEFF
// equations agree with my notes,
// Equations agree with Pitzer,
if (charge(i) == 0.0) {
if (m_debugCalc) {
writelogf(" Contributions to ln(ActCoeff_%s):\n", speciesName(i));
}
double sum1 = 0.0;
double sum3 = 0.0;
for (size_t j = 1; j < m_kk; j++) {
sum1 += molality[j]*2.0*m_Lambda_nj(i,j);
if (m_debugCalc && m_Lambda_nj(i,j) != 0.0) {
std::string snj = speciesName(j) + ":";
writelogf(" Lambda_n term on %-16s 2 m_j lambda_n_j = %10.5f\n", snj,
molality[j]*2.0*m_Lambda_nj(i,j));
}
// Zeta term -> we piggyback on the psi term
if (charge(j) > 0.0) {
for (size_t k = 1; k < m_kk; k++) {
if (charge(k) < 0.0) {
size_t n = k + j * m_kk + i * m_kk * m_kk;
sum3 += molality[j]*molality[k]*m_Psi_ijk[n];
if (m_debugCalc && m_Psi_ijk[n] != 0.0) {
std::string snj = speciesName(j) + "," + speciesName(k) + ":";
writelogf(" Zeta term on %-16s m_j m_k psi_ijk = %10.5f\n", snj,
molality[j]*molality[k]*m_Psi_ijk[n]);
}
}
}
}
}
double sum2 = 3.0 * molality[i]* molality[i] * m_Mu_nnn[i];
if (m_debugCalc && m_Mu_nnn[i] != 0.0) {
writelogf(" Mu_nnn term 3 m_n m_n Mu_n_n = %10.5f\n",
3.0 * molality[i]* molality[i] * m_Mu_nnn[i]);
}
m_lnActCoeffMolal_Unscaled[i] = sum1 + sum2 + sum3;
gamma_Unscaled[i] = exp(m_lnActCoeffMolal_Unscaled[i]);
if (m_debugCalc) {
writelogf(" Net %-16s lngamma[i] = %9.5f gamma[i]=%10.6f\n",
speciesName(i), m_lnActCoeffMolal_Unscaled[i], gamma_Unscaled[i]);
}
}
}
debuglog(" Step 9: \n", m_debugCalc);
// SUBSECTION FOR CALCULATING THE OSMOTIC COEFF
// equations agree with my notes, Eqn. (117).
// Equations agree with Pitzer, eqn.(62)
double sum1 = 0.0;
double sum2 = 0.0;
double sum3 = 0.0;
double sum4 = 0.0;
double sum5 = 0.0;
double sum6 = 0.0;
double sum7 = 0.0;
// term1 is the DH term in the osmotic coefficient expression
// b = 1.2 sqrt(kg/gmol) <- arbitrarily set in all Pitzer
// implementations.
// Is = Ionic strength on the molality scale (units of (gmol/kg))
// Aphi = A_Debye / 3 (units of sqrt(kg/gmol))
double term1 = -Aphi * pow(Is,1.5) / (1.0 + 1.2 * sqrt(Is));
for (size_t j = 1; j < m_kk; j++) {
// Loop Over Cations
if (charge(j) > 0.0) {
for (size_t k = 1; k < m_kk; k++) {
if (charge(k) < 0.0) {
// Find the counterIJ for the symmetric j,k binary interaction
size_t n = m_kk*j + k;
size_t counterIJ = m_CounterIJ[n];
sum1 += molality[j]*molality[k]*
(m_BphiMX_IJ[counterIJ] + molarcharge*m_CMX_IJ[counterIJ]);
}
}
for (size_t k = j+1; k < m_kk; k++) {
if (j == (m_kk-1)) {
// we should never reach this step
throw CanteraError("HMWSoln::s_updatePitzer_lnMolalityActCoeff",
"logic error 1 in Step 9 of hmw_act");
}
if (charge(k) > 0.0) {
// Find the counterIJ for the symmetric j,k binary interaction
// between 2 cations.
size_t n = m_kk*j + k;
size_t counterIJ = m_CounterIJ[n];
sum2 += molality[j]*molality[k]*m_PhiPhi_IJ[counterIJ];
for (size_t m = 1; m < m_kk; m++) {
if (charge(m) < 0.0) {
// species m is an anion
n = m + k * m_kk + j * m_kk * m_kk;
sum2 += molality[j]*molality[k]*molality[m]*m_Psi_ijk[n];
}
}
}
}
}
// Loop Over Anions
if (charge(j) < 0) {
for (size_t k = j+1; k < m_kk; k++) {
if (j == m_kk-1) {
// we should never reach this step
throw CanteraError("HMWSoln::s_updatePitzer_lnMolalityActCoeff",
"logic error 2 in Step 9 of hmw_act");
}
if (charge(k) < 0) {
// Find the counterIJ for the symmetric j,k binary interaction
// between two anions
size_t n = m_kk*j + k;
size_t counterIJ = m_CounterIJ[n];
sum3 += molality[j]*molality[k]*m_PhiPhi_IJ[counterIJ];
for (size_t m = 1; m < m_kk; m++) {
if (charge(m) > 0.0) {
n = m + k * m_kk + j * m_kk * m_kk;
sum3 += molality[j]*molality[k]*molality[m]*m_Psi_ijk[n];
}
}
}
}
}
// Loop Over Neutral Species
if (charge(j) == 0) {
for (size_t k = 1; k < m_kk; k++) {
if (charge(k) < 0.0) {
sum4 += molality[j]*molality[k]*m_Lambda_nj(j,k);
}
if (charge(k) > 0.0) {
sum5 += molality[j]*molality[k]*m_Lambda_nj(j,k);
}
if (charge(k) == 0.0) {
if (k > j) {
sum6 += molality[j]*molality[k]*m_Lambda_nj(j,k);
} else if (k == j) {
sum6 += 0.5 * molality[j]*molality[k]*m_Lambda_nj(j,k);
}
}
if (charge(k) < 0.0) {
size_t izeta = j;
for (size_t m = 1; m < m_kk; m++) {
if (charge(m) > 0.0) {
size_t jzeta = m;
size_t n = k + jzeta * m_kk + izeta * m_kk * m_kk;
double zeta = m_Psi_ijk[n];
if (zeta != 0.0) {
sum7 += molality[izeta]*molality[jzeta]*molality[k]*zeta;
}
}
}
}
}
sum7 += molality[j]*molality[j]*molality[j]*m_Mu_nnn[j];
}
}
double sum_m_phi_minus_1 = 2.0 *
(term1 + sum1 + sum2 + sum3 + sum4 + sum5 + sum6 + sum7);
// Calculate the osmotic coefficient from
// osmotic_coeff = 1 + dGex/d(M0noRT) / sum(molality_i)
double osmotic_coef;
if (molalitysumUncropped > 1.0E-150) {
osmotic_coef = 1.0 + (sum_m_phi_minus_1 / molalitysumUncropped);
} else {
osmotic_coef = 1.0;
}
if (m_debugCalc) {
writelogf(" term1=%10.6f sum1=%10.6f sum2=%10.6f "
"sum3=%10.6f sum4=%10.6f sum5=%10.6f\n",
term1, sum1, sum2, sum3, sum4, sum5);
writelogf(" sum_m_phi_minus_1=%10.6f osmotic_coef=%10.6f\n",
sum_m_phi_minus_1, osmotic_coef);
writelog(" Step 10: \n");
}
double lnwateract = -(m_weightSolvent/1000.0) * molalitysumUncropped * osmotic_coef;
// In Cantera, we define the activity coefficient of the solvent as
//
// act_0 = actcoeff_0 * Xmol_0
//
// We have just computed act_0. However, this routine returns
// ln(actcoeff[]). Therefore, we must calculate ln(actcoeff_0).
double xmolSolvent = moleFraction(m_indexSolvent);
double xx = std::max(m_xmolSolventMIN, xmolSolvent);
m_lnActCoeffMolal_Unscaled[0] = lnwateract - log(xx);
if (m_debugCalc) {
double wateract = exp(lnwateract);
writelogf(" Weight of Solvent = %16.7g\n", m_weightSolvent);
writelogf(" molalitySumUncropped = %16.7g\n", molalitysumUncropped);
writelogf(" ln_a_water=%10.6f a_water=%10.6f\n\n",
lnwateract, wateract);
}
}
void HMWSoln::s_update_dlnMolalityActCoeff_dT() const
{
static const int cacheId = m_cache.getId();
CachedScalar cached = m_cache.getScalar(cacheId);
if( cached.validate(temperature(), pressure(), stateMFNumber()) ) {
return;
}
// Zero the unscaled 2nd derivatives
m_dlnActCoeffMolaldT_Unscaled.assign(m_kk, 0.0);
// Do the actual calculation of the unscaled temperature derivatives
s_updatePitzer_dlnMolalityActCoeff_dT();
for (size_t k = 1; k < m_kk; k++) {
if (CROP_speciesCropped_[k] == 2) {
m_dlnActCoeffMolaldT_Unscaled[k] = 0.0;
}
}
if (CROP_speciesCropped_[0]) {
m_dlnActCoeffMolaldT_Unscaled[0] = 0.0;
}
// Do the pH scaling to the derivatives
s_updateScaling_pHScaling_dT();
}
void HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT() const
{
// It may be assumed that the Pitzer activity coefficient routine is called
// immediately preceding the calling of this routine. Therefore, some
// quantities do not need to be recalculated in this routine.
// HKM -> Assumption is made that the solvent is species 0.
if (m_indexSolvent != 0) {
throw CanteraError("HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT",
"Wrong index solvent value!");
}
const vector_fp& molality = m_molalitiesCropped;
double* d_gamma_dT_Unscaled = m_gamma_tmp.data();
// Local variables defined by Coltrin
double etheta[5][5], etheta_prime[5][5], sqrtIs;
// Molality based ionic strength of the solution
double Is = 0.0;
// Molarcharge of the solution: In Pitzer's notation, this is his variable
// called "Z".
double molarcharge = 0.0;
// molalitysum is the sum of the molalities over all solutes, even those
// with zero charge.
double molalitysum = 0.0;
debuglog("\n Debugging information from s_Pitzer_dlnMolalityActCoeff_dT()\n",
m_debugCalc);
// Make sure the counter variables are setup
counterIJ_setup();
// ---------- Calculate common sums over solutes ---------------------
for (size_t n = 1; n < m_kk; n++) {
// ionic strength
Is += charge(n) * charge(n) * molality[n];
// total molar charge
molarcharge += fabs(charge(n)) * molality[n];
molalitysum += molality[n];
}
Is *= 0.5;
// Store the ionic molality in the object for reference.
m_IionicMolality = Is;
sqrtIs = sqrt(Is);
if (m_debugCalc) {
writelog(" Step 1: \n");
writelogf(" ionic strenth = %14.7le \n total molar "
"charge = %14.7le \n", Is, molarcharge);
}
// The following call to calc_lambdas() calculates all 16 elements of the
// elambda and elambda1 arrays, given the value of the ionic strength (Is)
calc_lambdas(Is);
// Step 2: Find the coefficients E-theta and E-thetaprime for all
// combinations of positive unlike charges up to 4
debuglog(" Step 2: \n", m_debugCalc);
for (int z1 = 1; z1 <=4; z1++) {
for (int z2 =1; z2 <=4; z2++) {
calc_thetas(z1, z2, &etheta[z1][z2], &etheta_prime[z1][z2]);
if (m_debugCalc) {
writelogf(" z1=%3d z2=%3d E-theta(I) = %f, E-thetaprime(I) = %f\n",
z1, z2, etheta[z1][z2], etheta_prime[z1][z2]);
}
}
}
debuglog(" Step 3: \n"
" Species Species g(x) hfunc(x) \n",
m_debugCalc);
// calculate g(x) and hfunc(x) for each cation-anion pair MX
// In the original literature, hfunc, was called gprime. However,
// it's not the derivative of g(x), so I renamed it.
for (size_t i = 1; i < (m_kk - 1); i++) {
for (size_t j = (i+1); j < m_kk; j++) {
// Find the counterIJ for the symmetric binary interaction
size_t n = m_kk*i + j;
size_t counterIJ = m_CounterIJ[n];
// Only loop over oppositely charge species
if (charge(i)*charge(j) < 0) {
// x is a reduced function variable
double x1 = sqrtIs * m_Alpha1MX_ij[counterIJ];
if (x1 > 1.0E-100) {
m_gfunc_IJ[counterIJ] = 2.0*(1.0-(1.0 + x1) * exp(-x1)) / (x1 * x1);
m_hfunc_IJ[counterIJ] = -2.0 *
(1.0-(1.0 + x1 + 0.5 * x1 *x1) * exp(-x1)) / (x1 * x1);
} else {
m_gfunc_IJ[counterIJ] = 0.0;
m_hfunc_IJ[counterIJ] = 0.0;
}
if (m_Beta2MX_ij_L[counterIJ] != 0.0) {
double x2 = sqrtIs * m_Alpha2MX_ij[counterIJ];
if (x2 > 1.0E-100) {
m_g2func_IJ[counterIJ] = 2.0*(1.0-(1.0 + x2) * exp(-x2)) / (x2 * x2);
m_h2func_IJ[counterIJ] = -2.0 *
(1.0-(1.0 + x2 + 0.5 * x2 * x2) * exp(-x2)) / (x2 * x2);
} else {
m_g2func_IJ[counterIJ] = 0.0;
m_h2func_IJ[counterIJ] = 0.0;
}
}
} else {
m_gfunc_IJ[counterIJ] = 0.0;
m_hfunc_IJ[counterIJ] = 0.0;
}
if (m_debugCalc) {
std::string sni = speciesName(i);
std::string snj = speciesName(j);
writelogf(" %-16s %-16s %9.5f %9.5f \n", sni.c_str(), snj.c_str(),
m_gfunc_IJ[counterIJ], m_hfunc_IJ[counterIJ]);
}
}
}
// SUBSECTION TO CALCULATE BMX_L, BprimeMX_L, BphiMX_L
// These are now temperature derivatives of the previously calculated
// quantities.
debuglog(" Step 4: \n"
" Species Species BMX BprimeMX BphiMX \n",
m_debugCalc);
for (size_t i = 1; i < m_kk - 1; i++) {
for (size_t j = i+1; j < m_kk; j++) {
// Find the counterIJ for the symmetric binary interaction
size_t n = m_kk*i + j;
size_t counterIJ = m_CounterIJ[n];
// both species have a non-zero charge, and one is positive
// and the other is negative
if (charge(i)*charge(j) < 0.0) {
m_BMX_IJ_L[counterIJ] = m_Beta0MX_ij_L[counterIJ]
+ m_Beta1MX_ij_L[counterIJ] * m_gfunc_IJ[counterIJ]
+ m_Beta2MX_ij_L[counterIJ] * m_gfunc_IJ[counterIJ];
if (m_debugCalc) {
writelogf("%d %g: %g %g %g %g\n",
counterIJ, m_BMX_IJ_L[counterIJ], m_Beta0MX_ij_L[counterIJ],
m_Beta1MX_ij_L[counterIJ], m_Beta2MX_ij_L[counterIJ], m_gfunc_IJ[counterIJ]);
}
if (Is > 1.0E-150) {
m_BprimeMX_IJ_L[counterIJ] = (m_Beta1MX_ij_L[counterIJ] * m_hfunc_IJ[counterIJ]/Is +
m_Beta2MX_ij_L[counterIJ] * m_h2func_IJ[counterIJ]/Is);
} else {
m_BprimeMX_IJ_L[counterIJ] = 0.0;
}
m_BphiMX_IJ_L[counterIJ] = m_BMX_IJ_L[counterIJ] + Is*m_BprimeMX_IJ_L[counterIJ];
} else {
m_BMX_IJ_L[counterIJ] = 0.0;
m_BprimeMX_IJ_L[counterIJ] = 0.0;
m_BphiMX_IJ_L[counterIJ] = 0.0;
}
if (m_debugCalc) {
writelogf(" %-16s %-16s %11.7f %11.7f %11.7f \n",
speciesName(i), speciesName(j),
m_BMX_IJ_L[counterIJ], m_BprimeMX_IJ_L[counterIJ], m_BphiMX_IJ_L[counterIJ]);
}
}
}
// --------- SUBSECTION TO CALCULATE CMX_L ----------
debuglog(" Step 5: \n"
" Species Species CMX \n", m_debugCalc);
for (size_t i = 1; i < m_kk-1; i++) {
for (size_t j = i+1; j < m_kk; j++) {
// Find the counterIJ for the symmetric binary interaction
size_t n = m_kk*i + j;
size_t counterIJ = m_CounterIJ[n];
// both species have a non-zero charge, and one is positive
// and the other is negative
if (charge(i)*charge(j) < 0.0) {
m_CMX_IJ_L[counterIJ] = m_CphiMX_ij_L[counterIJ]/
(2.0* sqrt(fabs(charge(i)*charge(j))));
} else {
m_CMX_IJ_L[counterIJ] = 0.0;
}
if (m_debugCalc) {
writelogf(" %-16s %-16s %11.7f \n",
speciesName(i), speciesName(j), m_CMX_IJ_L[counterIJ]);
}
}
}
// ------- SUBSECTION TO CALCULATE Phi, PhiPrime, and PhiPhi ----------
debuglog(" Step 6: \n"
" Species Species Phi_ij Phiprime_ij Phi^phi_ij \n",
m_debugCalc);
for (size_t i = 1; i < m_kk-1; i++) {
for (size_t j = i+1; j < m_kk; j++) {
// Find the counterIJ for the symmetric binary interaction
size_t n = m_kk*i + j;
size_t counterIJ = m_CounterIJ[n];
// both species have a non-zero charge, and one is positive
// and the other is negative
if (charge(i)*charge(j) > 0) {
m_Phi_IJ_L[counterIJ] = m_Theta_ij_L[counterIJ];
m_Phiprime_IJ[counterIJ] = 0.0;
m_PhiPhi_IJ_L[counterIJ] = m_Phi_IJ_L[counterIJ] + Is * m_Phiprime_IJ[counterIJ];
} else {
m_Phi_IJ_L[counterIJ] = 0.0;
m_Phiprime_IJ[counterIJ] = 0.0;
m_PhiPhi_IJ_L[counterIJ] = 0.0;
}
if (m_debugCalc) {
writelogf(" %-16s %-16s %10.6f %10.6f %10.6f \n",
speciesName(i), speciesName(j),
m_Phi_IJ_L[counterIJ], m_Phiprime_IJ[counterIJ], m_PhiPhi_IJ_L[counterIJ]);
}
}
}
// ----------- SUBSECTION FOR CALCULATION OF dFdT ---------------------
debuglog(" Step 7: \n", m_debugCalc);
double dA_DebyedT = dA_DebyedT_TP();
double dAphidT = dA_DebyedT /3.0;
double dFdT = -dAphidT * (sqrt(Is) / (1.0 + 1.2*sqrt(Is))
+ (2.0/1.2) * log(1.0+1.2*(sqrtIs)));
if (m_debugCalc) {
writelogf(" initial value of dFdT = %10.6f \n", dFdT);
}
for (size_t i = 1; i < m_kk-1; i++) {
for (size_t j = i+1; j < m_kk; j++) {
// Find the counterIJ for the symmetric binary interaction
size_t n = m_kk*i + j;
size_t counterIJ = m_CounterIJ[n];
// both species have a non-zero charge, and one is positive
// and the other is negative
if (charge(i)*charge(j) < 0) {
dFdT += molality[i]*molality[j] * m_BprimeMX_IJ_L[counterIJ];
}
// Both species have a non-zero charge, and they
// have the same sign, e.g., both positive or both negative.
if (charge(i)*charge(j) > 0) {
dFdT += molality[i]*molality[j] * m_Phiprime_IJ[counterIJ];
}
if (m_debugCalc) {
writelogf(" dFdT = %10.6f \n", dFdT);
}
}
}
debuglog(" Step 8: \n", m_debugCalc);
for (size_t i = 1; i < m_kk; i++) {
// -------- SUBSECTION FOR CALCULATING THE dACTCOEFFdT FOR CATIONS -----
if (charge(i) > 0) {
// species i is the cation (positive) to calc the actcoeff
double zsqdFdT = charge(i)*charge(i)*dFdT;
double sum1 = 0.0;
double sum2 = 0.0;
double sum3 = 0.0;
double sum4 = 0.0;
double sum5 = 0.0;
for (size_t j = 1; j < m_kk; j++) {
// Find the counterIJ for the symmetric binary interaction
size_t n = m_kk*i + j;
size_t counterIJ = m_CounterIJ[n];
if (charge(j) < 0.0) {
// sum over all anions
sum1 += molality[j]*
(2.0*m_BMX_IJ_L[counterIJ] + molarcharge*m_CMX_IJ_L[counterIJ]);
if (j < m_kk-1) {
// This term is the ternary interaction involving the
// non-duplicate sum over double anions, j, k, with
// respect to the cation, i.
for (size_t k = j+1; k < m_kk; k++) {
// an inner sum over all anions
if (charge(k) < 0.0) {
n = k + j * m_kk + i * m_kk * m_kk;
sum3 += molality[j]*molality[k]*m_Psi_ijk_L[n];
}
}
}
}
if (charge(j) > 0.0) {
// sum over all cations
if (j != i) {
sum2 += molality[j]*(2.0*m_Phi_IJ_L[counterIJ]);
}
for (size_t k = 1; k < m_kk; k++) {
if (charge(k) < 0.0) {
// two inner sums over anions
n = k + j * m_kk + i * m_kk * m_kk;
sum2 += molality[j]*molality[k]*m_Psi_ijk_L[n];
// Find the counterIJ for the j,k interaction
n = m_kk*j + k;
size_t counterIJ2 = m_CounterIJ[n];
sum4 += fabs(charge(i))*
molality[j]*molality[k]*m_CMX_IJ_L[counterIJ2];
}
}
}
// Handle neutral j species
if (charge(j) == 0) {
sum5 += molality[j]*2.0*m_Lambda_nj_L(j,i);
}
// Zeta interaction term
for (size_t k = 1; k < m_kk; k++) {
if (charge(k) < 0.0) {
size_t izeta = j;
size_t jzeta = i;
n = izeta * m_kk * m_kk + jzeta * m_kk + k;
double zeta_L = m_Psi_ijk_L[n];
if (zeta_L != 0.0) {
sum5 += molality[j]*molality[k]*zeta_L;
}
}
}
}
// Add all of the contributions up to yield the log of the
// solute activity coefficients (molality scale)
m_dlnActCoeffMolaldT_Unscaled[i] =
zsqdFdT + sum1 + sum2 + sum3 + sum4 + sum5;
d_gamma_dT_Unscaled[i] = exp(m_dlnActCoeffMolaldT_Unscaled[i]);
if (m_debugCalc) {
writelogf(" %-16s lngamma[i]=%10.6f gamma[i]=%10.6f \n",
speciesName(i), m_dlnActCoeffMolaldT_Unscaled[i], d_gamma_dT_Unscaled[i]);
writelogf(" %12g %12g %12g %12g %12g %12g\n",
zsqdFdT, sum1, sum2, sum3, sum4, sum5);
}
}
// ------ SUBSECTION FOR CALCULATING THE dACTCOEFFdT FOR ANIONS ------
if (charge(i) < 0) {
// species i is an anion (negative)
double zsqdFdT = charge(i)*charge(i)*dFdT;
double sum1 = 0.0;
double sum2 = 0.0;
double sum3 = 0.0;
double sum4 = 0.0;
double sum5 = 0.0;
for (size_t j = 1; j < m_kk; j++) {
// Find the counterIJ for the symmetric binary interaction
size_t n = m_kk*i + j;
size_t counterIJ = m_CounterIJ[n];
// For Anions, do the cation interactions.
if (charge(j) > 0) {
sum1 += molality[j]*
(2.0*m_BMX_IJ_L[counterIJ] + molarcharge*m_CMX_IJ_L[counterIJ]);
if (j < m_kk-1) {
for (size_t k = j+1; k < m_kk; k++) {
// an inner sum over all cations
if (charge(k) > 0) {
n = k + j * m_kk + i * m_kk * m_kk;
sum3 += molality[j]*molality[k]*m_Psi_ijk_L[n];
}
}
}
}
// For Anions, do the other anion interactions.
if (charge(j) < 0.0) {
// sum over all anions
if (j != i) {
sum2 += molality[j]*(2.0*m_Phi_IJ_L[counterIJ]);
}
for (size_t k = 1; k < m_kk; k++) {
if (charge(k) > 0.0) {
// two inner sums over cations
n = k + j * m_kk + i * m_kk * m_kk;
sum2 += molality[j]*molality[k]*m_Psi_ijk_L[n];
// Find the counterIJ for the symmetric binary interaction
n = m_kk*j + k;
size_t counterIJ2 = m_CounterIJ[n];
sum4 += fabs(charge(i)) *
molality[j]*molality[k]*m_CMX_IJ_L[counterIJ2];
}
}
}
// for Anions, do the neutral species interaction
if (charge(j) == 0.0) {
sum5 += molality[j]*2.0*m_Lambda_nj_L(j,i);
for (size_t k = 1; k < m_kk; k++) {
if (charge(k) > 0.0) {
size_t izeta = j;
size_t jzeta = k;
size_t kzeta = i;
n = izeta * m_kk * m_kk + jzeta * m_kk + kzeta;
double zeta_L = m_Psi_ijk_L[n];
if (zeta_L != 0.0) {
sum5 += molality[j]*molality[k]*zeta_L;
}
}
}
}
}
m_dlnActCoeffMolaldT_Unscaled[i] =
zsqdFdT + sum1 + sum2 + sum3 + sum4 + sum5;
d_gamma_dT_Unscaled[i] = exp(m_dlnActCoeffMolaldT_Unscaled[i]);
if (m_debugCalc) {
writelogf(" %-16s lngamma[i]=%10.6f gamma[i]=%10.6f\n",
speciesName(i), m_dlnActCoeffMolaldT_Unscaled[i], d_gamma_dT_Unscaled[i]);
writelogf(" %12g %12g %12g %12g %12g %12g\n",
zsqdFdT, sum1, sum2, sum3, sum4, sum5);
}
}
// SUBSECTION FOR CALCULATING NEUTRAL SOLUTE ACT COEFF
// equations agree with my notes,
// Equations agree with Pitzer,
if (charge(i) == 0.0) {
double sum1 = 0.0;
double sum3 = 0.0;
for (size_t j = 1; j < m_kk; j++) {
sum1 += molality[j]*2.0*m_Lambda_nj_L(i,j);
// Zeta term -> we piggyback on the psi term
if (charge(j) > 0.0) {
for (size_t k = 1; k < m_kk; k++) {
if (charge(k) < 0.0) {
size_t n = k + j * m_kk + i * m_kk * m_kk;
sum3 += molality[j]*molality[k]*m_Psi_ijk_L[n];
}
}
}
}
double sum2 = 3.0 * molality[i] * molality[i] * m_Mu_nnn_L[i];
m_dlnActCoeffMolaldT_Unscaled[i] = sum1 + sum2 + sum3;
d_gamma_dT_Unscaled[i] = exp(m_dlnActCoeffMolaldT_Unscaled[i]);
if (m_debugCalc) {
writelogf(" %-16s lngamma[i]=%10.6f gamma[i]=%10.6f \n",
speciesName(i), m_dlnActCoeffMolaldT_Unscaled[i], d_gamma_dT_Unscaled[i]);
}
}
}
debuglog(" Step 9: \n", m_debugCalc);
// ------ SUBSECTION FOR CALCULATING THE d OSMOTIC COEFF dT ---------
double sum1 = 0.0;
double sum2 = 0.0;
double sum3 = 0.0;
double sum4 = 0.0;
double sum5 = 0.0;
double sum6 = 0.0;
double sum7 = 0.0;
// term1 is the temperature derivative of the DH term in the osmotic
// coefficient expression
// b = 1.2 sqrt(kg/gmol) <- arbitrarily set in all Pitzer implementations.
// Is = Ionic strength on the molality scale (units of (gmol/kg))
// Aphi = A_Debye / 3 (units of sqrt(kg/gmol))
double term1 = -dAphidT * Is * sqrt(Is) / (1.0 + 1.2 * sqrt(Is));
for (size_t j = 1; j < m_kk; j++) {
// Loop Over Cations
if (charge(j) > 0.0) {
for (size_t k = 1; k < m_kk; k++) {
if (charge(k) < 0.0) {
// Find the counterIJ for the symmetric j,k binary interaction
size_t n = m_kk*j + k;
size_t counterIJ = m_CounterIJ[n];
sum1 += molality[j]*molality[k]*
(m_BphiMX_IJ_L[counterIJ] + molarcharge*m_CMX_IJ_L[counterIJ]);
}
}
for (size_t k = j+1; k < m_kk; k++) {
if (j == (m_kk-1)) {
// we should never reach this step
throw CanteraError("HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT",
"logic error 1 in Step 9 of hmw_act");
}
if (charge(k) > 0.0) {
// Find the counterIJ for the symmetric j,k binary interaction
// between 2 cations.
size_t n = m_kk*j + k;
size_t counterIJ = m_CounterIJ[n];
sum2 += molality[j]*molality[k]*m_PhiPhi_IJ_L[counterIJ];
for (size_t m = 1; m < m_kk; m++) {
if (charge(m) < 0.0) {
// species m is an anion
n = m + k * m_kk + j * m_kk * m_kk;
sum2 += molality[j]*molality[k]*molality[m]*m_Psi_ijk_L[n];
}
}
}
}
}
// Loop Over Anions
if (charge(j) < 0) {
for (size_t k = j+1; k < m_kk; k++) {
if (j == m_kk-1) {
// we should never reach this step
throw CanteraError("HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT",
"logic error 2 in Step 9 of hmw_act");
}
if (charge(k) < 0) {
// Find the counterIJ for the symmetric j,k binary interaction
// between two anions
size_t n = m_kk*j + k;
size_t counterIJ = m_CounterIJ[n];
sum3 += molality[j]*molality[k]*m_PhiPhi_IJ_L[counterIJ];
for (size_t m = 1; m < m_kk; m++) {
if (charge(m) > 0.0) {
n = m + k * m_kk + j * m_kk * m_kk;
sum3 += molality[j]*molality[k]*molality[m]*m_Psi_ijk_L[n];
}
}
}
}
}
// Loop Over Neutral Species
if (charge(j) == 0) {
for (size_t k = 1; k < m_kk; k++) {
if (charge(k) < 0.0) {
sum4 += molality[j]*molality[k]*m_Lambda_nj_L(j,k);
}
if (charge(k) > 0.0) {
sum5 += molality[j]*molality[k]*m_Lambda_nj_L(j,k);
}
if (charge(k) == 0.0) {
if (k > j) {
sum6 += molality[j]*molality[k]*m_Lambda_nj_L(j,k);
} else if (k == j) {
sum6 += 0.5 * molality[j]*molality[k]*m_Lambda_nj_L(j,k);
}
}
if (charge(k) < 0.0) {
size_t izeta = j;
for (size_t m = 1; m < m_kk; m++) {
if (charge(m) > 0.0) {
size_t jzeta = m;
size_t n = k + jzeta * m_kk + izeta * m_kk * m_kk;
double zeta_L = m_Psi_ijk_L[n];
if (zeta_L != 0.0) {
sum7 += molality[izeta]*molality[jzeta]*molality[k]*zeta_L;
}
}
}
}
}
sum7 += molality[j]*molality[j]*molality[j]*m_Mu_nnn_L[j];
}
}
double sum_m_phi_minus_1 = 2.0 *
(term1 + sum1 + sum2 + sum3 + sum4 + sum5 + sum6 + sum7);
// Calculate the osmotic coefficient from
// osmotic_coeff = 1 + dGex/d(M0noRT) / sum(molality_i)
double d_osmotic_coef_dT;
if (molalitysum > 1.0E-150) {
d_osmotic_coef_dT = 0.0 + (sum_m_phi_minus_1 / molalitysum);
} else {
d_osmotic_coef_dT = 0.0;
}
if (m_debugCalc) {
writelogf(" term1=%10.6f sum1=%10.6f sum2=%10.6f "
"sum3=%10.6f sum4=%10.6f sum5=%10.6f\n",
term1, sum1, sum2, sum3, sum4, sum5);
writelogf(" sum_m_phi_minus_1=%10.6f d_osmotic_coef_dT =%10.6f\n",
sum_m_phi_minus_1, d_osmotic_coef_dT);
writelog(" Step 10: \n");
}
double d_lnwateract_dT = -(m_weightSolvent/1000.0) * molalitysum * d_osmotic_coef_dT;
// In Cantera, we define the activity coefficient of the solvent as
//
// act_0 = actcoeff_0 * Xmol_0
//
// We have just computed act_0. However, this routine returns
// ln(actcoeff[]). Therefore, we must calculate ln(actcoeff_0).
m_dlnActCoeffMolaldT_Unscaled[0] = d_lnwateract_dT;
if (m_debugCalc) {
double d_wateract_dT = exp(d_lnwateract_dT);
writelogf(" d_ln_a_water_dT = %10.6f d_a_water_dT=%10.6f\n\n",
d_lnwateract_dT, d_wateract_dT);
}
}
void HMWSoln::s_update_d2lnMolalityActCoeff_dT2() const
{
static const int cacheId = m_cache.getId();
CachedScalar cached = m_cache.getScalar(cacheId);
if( cached.validate(temperature(), pressure(), stateMFNumber()) ) {
return;
}
// Zero the unscaled 2nd derivatives
m_d2lnActCoeffMolaldT2_Unscaled.assign(m_kk, 0.0);
//! Calculate the unscaled 2nd derivatives
s_updatePitzer_d2lnMolalityActCoeff_dT2();
for (size_t k = 1; k < m_kk; k++) {
if (CROP_speciesCropped_[k] == 2) {
m_d2lnActCoeffMolaldT2_Unscaled[k] = 0.0;
}
}
if (CROP_speciesCropped_[0]) {
m_d2lnActCoeffMolaldT2_Unscaled[0] = 0.0;
}
// Scale the 2nd derivatives
s_updateScaling_pHScaling_dT2();
}
void HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2() const
{
// HKM -> Assumption is made that the solvent is species 0.
if (m_indexSolvent != 0) {
throw CanteraError("HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2",
"Wrong index solvent value!");
}
const double* molality = m_molalitiesCropped.data();
// Local variables defined by Coltrin
double etheta[5][5], etheta_prime[5][5], sqrtIs;
// Molality based ionic strength of the solution
double Is = 0.0;
// Molarcharge of the solution: In Pitzer's notation, this is his variable
// called "Z".
double molarcharge = 0.0;
// molalitysum is the sum of the molalities over all solutes, even those
// with zero charge.
double molalitysum = 0.0;
debuglog("\n Debugging information from s_Pitzer_d2lnMolalityActCoeff_dT2()\n",
m_debugCalc);
// Make sure the counter variables are setup
counterIJ_setup();
// ---------- Calculate common sums over solutes ---------------------
for (size_t n = 1; n < m_kk; n++) {
// ionic strength
Is += charge(n) * charge(n) * molality[n];
// total molar charge
molarcharge += fabs(charge(n)) * molality[n];
molalitysum += molality[n];
}
Is *= 0.5;
// Store the ionic molality in the object for reference.
m_IionicMolality = Is;
sqrtIs = sqrt(Is);
if (m_debugCalc) {
writelog(" Step 1: \n");
writelogf(" ionic strenth = %14.7le \n total molar "
"charge = %14.7le \n", Is, molarcharge);
}
// The following call to calc_lambdas() calculates all 16 elements of the
// elambda and elambda1 arrays, given the value of the ionic strength (Is)
calc_lambdas(Is);
// Step 2: Find the coefficients E-theta and E-thetaprime for all
// combinations of positive unlike charges up to 4
debuglog(" Step 2: \n", m_debugCalc);
for (int z1 = 1; z1 <=4; z1++) {
for (int z2 =1; z2 <=4; z2++) {
calc_thetas(z1, z2, &etheta[z1][z2], &etheta_prime[z1][z2]);
if (m_debugCalc) {
writelogf(" z1=%3d z2=%3d E-theta(I) = %f, E-thetaprime(I) = %f\n",
z1, z2, etheta[z1][z2], etheta_prime[z1][z2]);
}
}
}
debuglog(" Step 3: \n"
" Species Species g(x) hfunc(x) \n",
m_debugCalc);
// calculate gfunc(x) and hfunc(x) for each cation-anion pair MX. In the
// original literature, hfunc, was called gprime. However, it's not the
// derivative of gfunc(x), so I renamed it.
for (size_t i = 1; i < (m_kk - 1); i++) {
for (size_t j = (i+1); j < m_kk; j++) {
// Find the counterIJ for the symmetric binary interaction
size_t n = m_kk*i + j;
size_t counterIJ = m_CounterIJ[n];
// Only loop over oppositely charge species
if (charge(i)*charge(j) < 0) {
// x is a reduced function variable
double x1 = sqrtIs * m_Alpha1MX_ij[counterIJ];
if (x1 > 1.0E-100) {
m_gfunc_IJ[counterIJ] = 2.0*(1.0-(1.0 + x1) * exp(-x1)) / (x1 *x1);
m_hfunc_IJ[counterIJ] = -2.0*
(1.0-(1.0 + x1 + 0.5*x1 * x1) * exp(-x1)) / (x1 * x1);
} else {
m_gfunc_IJ[counterIJ] = 0.0;
m_hfunc_IJ[counterIJ] = 0.0;
}
if (m_Beta2MX_ij_LL[counterIJ] != 0.0) {
double x2 = sqrtIs * m_Alpha2MX_ij[counterIJ];
if (x2 > 1.0E-100) {
m_g2func_IJ[counterIJ] = 2.0*(1.0-(1.0 + x2) * exp(-x2)) / (x2 * x2);
m_h2func_IJ[counterIJ] = -2.0 *
(1.0-(1.0 + x2 + 0.5 * x2 * x2) * exp(-x2)) / (x2 * x2);
} else {
m_g2func_IJ[counterIJ] = 0.0;
m_h2func_IJ[counterIJ] = 0.0;
}
}
} else {
m_gfunc_IJ[counterIJ] = 0.0;
m_hfunc_IJ[counterIJ] = 0.0;
}
if (m_debugCalc) {
writelogf(" %-16s %-16s %9.5f %9.5f \n", speciesName(i), speciesName(j),
m_gfunc_IJ[counterIJ], m_hfunc_IJ[counterIJ]);
}
}
}
// SUBSECTION TO CALCULATE BMX_L, BprimeMX_LL, BphiMX_L
// These are now temperature derivatives of the previously calculated
// quantities.
debuglog(" Step 4: \n"
" Species Species BMX BprimeMX BphiMX \n",
m_debugCalc);
for (size_t i = 1; i < m_kk - 1; i++) {
for (size_t j = i+1; j < m_kk; j++) {
// Find the counterIJ for the symmetric binary interaction
size_t n = m_kk*i + j;
size_t counterIJ = m_CounterIJ[n];
// both species have a non-zero charge, and one is positive
// and the other is negative
if (charge(i)*charge(j) < 0.0) {
m_BMX_IJ_LL[counterIJ] = m_Beta0MX_ij_LL[counterIJ]
+ m_Beta1MX_ij_LL[counterIJ] * m_gfunc_IJ[counterIJ]
+ m_Beta2MX_ij_LL[counterIJ] * m_g2func_IJ[counterIJ];
if (m_debugCalc) {
writelogf("%d %g: %g %g %g %g\n",
counterIJ, m_BMX_IJ_LL[counterIJ], m_Beta0MX_ij_LL[counterIJ],
m_Beta1MX_ij_LL[counterIJ], m_Beta2MX_ij_LL[counterIJ], m_gfunc_IJ[counterIJ]);
}
if (Is > 1.0E-150) {
m_BprimeMX_IJ_LL[counterIJ] = (m_Beta1MX_ij_LL[counterIJ] * m_hfunc_IJ[counterIJ]/Is +
m_Beta2MX_ij_LL[counterIJ] * m_h2func_IJ[counterIJ]/Is);
} else {
m_BprimeMX_IJ_LL[counterIJ] = 0.0;
}
m_BphiMX_IJ_LL[counterIJ] = m_BMX_IJ_LL[counterIJ] + Is*m_BprimeMX_IJ_LL[counterIJ];
} else {
m_BMX_IJ_LL[counterIJ] = 0.0;
m_BprimeMX_IJ_LL[counterIJ] = 0.0;
m_BphiMX_IJ_LL[counterIJ] = 0.0;
}
if (m_debugCalc) {
writelogf(" %-16s %-16s %11.7f %11.7f %11.7f \n",
speciesName(i), speciesName(j),
m_BMX_IJ_LL[counterIJ], m_BprimeMX_IJ_LL[counterIJ], m_BphiMX_IJ_LL[counterIJ]);
}
}
}
// --------- SUBSECTION TO CALCULATE CMX_LL ----------
debuglog(" Step 5: \n"
" Species Species CMX \n", m_debugCalc);
for (size_t i = 1; i < m_kk-1; i++) {
for (size_t j = i+1; j < m_kk; j++) {
// Find the counterIJ for the symmetric binary interaction
size_t n = m_kk*i + j;
size_t counterIJ = m_CounterIJ[n];
// both species have a non-zero charge, and one is positive
// and the other is negative
if (charge(i)*charge(j) < 0.0) {
m_CMX_IJ_LL[counterIJ] = m_CphiMX_ij_LL[counterIJ]/
(2.0* sqrt(fabs(charge(i)*charge(j))));
} else {
m_CMX_IJ_LL[counterIJ] = 0.0;
}
if (m_debugCalc) {
writelogf(" %-16s %-16s %11.7f \n",
speciesName(i), speciesName(j), m_CMX_IJ_LL[counterIJ]);
}
}
}
// ------- SUBSECTION TO CALCULATE Phi, PhiPrime, and PhiPhi ----------
debuglog(" Step 6: \n"
" Species Species Phi_ij Phiprime_ij Phi^phi_ij \n",
m_debugCalc);
for (size_t i = 1; i < m_kk-1; i++) {
for (size_t j = i+1; j < m_kk; j++) {
// Find the counterIJ for the symmetric binary interaction
size_t n = m_kk*i + j;
size_t counterIJ = m_CounterIJ[n];
// both species have a non-zero charge, and one is positive
// and the other is negative
if (charge(i)*charge(j) > 0) {
m_Phi_IJ_LL[counterIJ] = m_Theta_ij_LL[counterIJ];
m_Phiprime_IJ[counterIJ] = 0.0;
m_PhiPhi_IJ_LL[counterIJ] = m_Phi_IJ_LL[counterIJ];
} else {
m_Phi_IJ_LL[counterIJ] = 0.0;
m_Phiprime_IJ[counterIJ] = 0.0;
m_PhiPhi_IJ_LL[counterIJ] = 0.0;
}
if (m_debugCalc) {
writelogf(" %-16s %-16s %10.6f %10.6f %10.6f \n",
speciesName(i), speciesName(j),
m_Phi_IJ_LL[counterIJ], m_Phiprime_IJ[counterIJ], m_PhiPhi_IJ_LL[counterIJ]);
}
}
}
// ----------- SUBSECTION FOR CALCULATION OF d2FdT2 ---------------------
debuglog(" Step 7: \n", m_debugCalc);
double d2AphidT2 = d2A_DebyedT2_TP() / 3.0;
double d2FdT2 = -d2AphidT2 * (sqrt(Is) / (1.0 + 1.2*sqrt(Is))
+ (2.0/1.2) * log(1.0+1.2*(sqrtIs)));
if (m_debugCalc) {
writelogf(" initial value of d2FdT2 = %10.6f \n", d2FdT2);
}
for (size_t i = 1; i < m_kk-1; i++) {
for (size_t j = i+1; j < m_kk; j++) {
// Find the counterIJ for the symmetric binary interaction
size_t n = m_kk*i + j;
size_t counterIJ = m_CounterIJ[n];
// both species have a non-zero charge, and one is positive
// and the other is negative
if (charge(i)*charge(j) < 0) {
d2FdT2 += molality[i]*molality[j] * m_BprimeMX_IJ_LL[counterIJ];
}
// Both species have a non-zero charge, and they
// have the same sign, e.g., both positive or both negative.
if (charge(i)*charge(j) > 0) {
d2FdT2 += molality[i]*molality[j] * m_Phiprime_IJ[counterIJ];
}
if (m_debugCalc) {
writelogf(" d2FdT2 = %10.6f \n", d2FdT2);
}
}
}
debuglog(" Step 8: \n", m_debugCalc);
for (size_t i = 1; i < m_kk; i++) {
// -------- SUBSECTION FOR CALCULATING THE dACTCOEFFdT FOR CATIONS -----
if (charge(i) > 0) {
// species i is the cation (positive) to calc the actcoeff
double zsqd2FdT2 = charge(i)*charge(i)*d2FdT2;
double sum1 = 0.0;
double sum2 = 0.0;
double sum3 = 0.0;
double sum4 = 0.0;
double sum5 = 0.0;
for (size_t j = 1; j < m_kk; j++) {
// Find the counterIJ for the symmetric binary interaction
size_t n = m_kk*i + j;
size_t counterIJ = m_CounterIJ[n];
if (charge(j) < 0.0) {
// sum over all anions
sum1 += molality[j]*
(2.0*m_BMX_IJ_LL[counterIJ] + molarcharge*m_CMX_IJ_LL[counterIJ]);
if (j < m_kk-1) {
// This term is the ternary interaction involving the
// non-duplicate sum over double anions, j, k, with
// respect to the cation, i.
for (size_t k = j+1; k < m_kk; k++) {
// an inner sum over all anions
if (charge(k) < 0.0) {
n = k + j * m_kk + i * m_kk * m_kk;
sum3 += molality[j]*molality[k]*m_Psi_ijk_LL[n];
}
}
}
}
if (charge(j) > 0.0) {
// sum over all cations
if (j != i) {
sum2 += molality[j]*(2.0*m_Phi_IJ_LL[counterIJ]);
}
for (size_t k = 1; k < m_kk; k++) {
if (charge(k) < 0.0) {
// two inner sums over anions
n = k + j * m_kk + i * m_kk * m_kk;
sum2 += molality[j]*molality[k]*m_Psi_ijk_LL[n];
// Find the counterIJ for the j,k interaction
n = m_kk*j + k;
size_t counterIJ2 = m_CounterIJ[n];
sum4 += fabs(charge(i)) *
molality[j]*molality[k]*m_CMX_IJ_LL[counterIJ2];
}
}
}
// Handle neutral j species
if (charge(j) == 0) {
sum5 += molality[j]*2.0*m_Lambda_nj_LL(j,i);
// Zeta interaction term
for (size_t k = 1; k < m_kk; k++) {
if (charge(k) < 0.0) {
size_t izeta = j;
size_t jzeta = i;
n = izeta * m_kk * m_kk + jzeta * m_kk + k;
double zeta_LL = m_Psi_ijk_LL[n];
if (zeta_LL != 0.0) {
sum5 += molality[j]*molality[k]*zeta_LL;
}
}
}
}
}
// Add all of the contributions up to yield the log of the
// solute activity coefficients (molality scale)
m_d2lnActCoeffMolaldT2_Unscaled[i] =
zsqd2FdT2 + sum1 + sum2 + sum3 + sum4 + sum5;
if (m_debugCalc) {
writelogf(" %-16s d2lngammadT2[i]=%10.6f \n",
speciesName(i), m_d2lnActCoeffMolaldT2_Unscaled[i]);
writelogf(" %12g %12g %12g %12g %12g %12g\n",
zsqd2FdT2, sum1, sum2, sum3, sum4, sum5);
}
}
// ------ SUBSECTION FOR CALCULATING THE d2ACTCOEFFdT2 FOR ANIONS ------
if (charge(i) < 0) {
// species i is an anion (negative)
double zsqd2FdT2 = charge(i)*charge(i)*d2FdT2;
double sum1 = 0.0;
double sum2 = 0.0;
double sum3 = 0.0;
double sum4 = 0.0;
double sum5 = 0.0;
for (size_t j = 1; j < m_kk; j++) {
// Find the counterIJ for the symmetric binary interaction
size_t n = m_kk*i + j;
size_t counterIJ = m_CounterIJ[n];
// For Anions, do the cation interactions.
if (charge(j) > 0) {
sum1 += molality[j]*
(2.0*m_BMX_IJ_LL[counterIJ] + molarcharge*m_CMX_IJ_LL[counterIJ]);
if (j < m_kk-1) {
for (size_t k = j+1; k < m_kk; k++) {
// an inner sum over all cations
if (charge(k) > 0) {
n = k + j * m_kk + i * m_kk * m_kk;
sum3 += molality[j]*molality[k]*m_Psi_ijk_LL[n];
}
}
}
}
// For Anions, do the other anion interactions.
if (charge(j) < 0.0) {
// sum over all anions
if (j != i) {
sum2 += molality[j]*(2.0*m_Phi_IJ_LL[counterIJ]);
}
for (size_t k = 1; k < m_kk; k++) {
if (charge(k) > 0.0) {
// two inner sums over cations
n = k + j * m_kk + i * m_kk * m_kk;
sum2 += molality[j]*molality[k]*m_Psi_ijk_LL[n];
// Find the counterIJ for the symmetric binary interaction
n = m_kk*j + k;
size_t counterIJ2 = m_CounterIJ[n];
sum4 += fabs(charge(i)) *
molality[j]*molality[k]*m_CMX_IJ_LL[counterIJ2];
}
}
}
// for Anions, do the neutral species interaction
if (charge(j) == 0.0) {
sum5 += molality[j]*2.0*m_Lambda_nj_LL(j,i);
// Zeta interaction term
for (size_t k = 1; k < m_kk; k++) {
if (charge(k) > 0.0) {
size_t izeta = j;
size_t jzeta = k;
size_t kzeta = i;
n = izeta * m_kk * m_kk + jzeta * m_kk + kzeta;
double zeta_LL = m_Psi_ijk_LL[n];
if (zeta_LL != 0.0) {
sum5 += molality[j]*molality[k]*zeta_LL;
}
}
}
}
}
m_d2lnActCoeffMolaldT2_Unscaled[i] =
zsqd2FdT2 + sum1 + sum2 + sum3 + sum4 + sum5;
if (m_debugCalc) {
writelogf(" %-16s d2lngammadT2[i]=%10.6f\n",
speciesName(i), m_d2lnActCoeffMolaldT2_Unscaled[i]);
writelogf(" %12g %12g %12g %12g %12g %12g\n",
zsqd2FdT2, sum1, sum2, sum3, sum4, sum5);
}
}
// SUBSECTION FOR CALCULATING NEUTRAL SOLUTE ACT COEFF
// equations agree with my notes,
// Equations agree with Pitzer,
if (charge(i) == 0.0) {
double sum1 = 0.0;
double sum3 = 0.0;
for (size_t j = 1; j < m_kk; j++) {
sum1 += molality[j]*2.0*m_Lambda_nj_LL(i,j);
// Zeta term -> we piggyback on the psi term
if (charge(j) > 0.0) {
for (size_t k = 1; k < m_kk; k++) {
if (charge(k) < 0.0) {
size_t n = k + j * m_kk + i * m_kk * m_kk;
sum3 += molality[j]*molality[k]*m_Psi_ijk_LL[n];
}
}
}
}
double sum2 = 3.0 * molality[i] * molality[i] * m_Mu_nnn_LL[i];
m_d2lnActCoeffMolaldT2_Unscaled[i] = sum1 + sum2 + sum3;
if (m_debugCalc) {
writelog(" %-16s d2lngammadT2[i]=%10.6f \n",
speciesName(i), m_d2lnActCoeffMolaldT2_Unscaled[i]);
}
}
}
debuglog(" Step 9: \n", m_debugCalc);
// ------ SUBSECTION FOR CALCULATING THE d2 OSMOTIC COEFF dT2 ---------
double sum1 = 0.0;
double sum2 = 0.0;
double sum3 = 0.0;
double sum4 = 0.0;
double sum5 = 0.0;
double sum6 = 0.0;
double sum7 = 0.0;
// term1 is the temperature derivative of the DH term in the osmotic
// coefficient expression
// b = 1.2 sqrt(kg/gmol) <- arbitrarily set in all Pitzer implementations.
// Is = Ionic strength on the molality scale (units of (gmol/kg))
// Aphi = A_Debye / 3 (units of sqrt(kg/gmol))
double term1 = -d2AphidT2 * Is * sqrt(Is) / (1.0 + 1.2 * sqrt(Is));
for (size_t j = 1; j < m_kk; j++) {
// Loop Over Cations
if (charge(j) > 0.0) {
for (size_t k = 1; k < m_kk; k++) {
if (charge(k) < 0.0) {
// Find the counterIJ for the symmetric j,k binary interaction
size_t n = m_kk*j + k;
size_t counterIJ = m_CounterIJ[n];
sum1 += molality[j]*molality[k] *
(m_BphiMX_IJ_LL[counterIJ] + molarcharge*m_CMX_IJ_LL[counterIJ]);
}
}
for (size_t k = j+1; k < m_kk; k++) {
if (j == (m_kk-1)) {
// we should never reach this step
throw CanteraError("HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2",
"logic error 1 in Step 9 of hmw_act");
}
if (charge(k) > 0.0) {
// Find the counterIJ for the symmetric j,k binary interaction
// between 2 cations.
size_t n = m_kk*j + k;
size_t counterIJ = m_CounterIJ[n];
sum2 += molality[j]*molality[k]*m_PhiPhi_IJ_LL[counterIJ];
for (size_t m = 1; m < m_kk; m++) {
if (charge(m) < 0.0) {
// species m is an anion
n = m + k * m_kk + j * m_kk * m_kk;
sum2 += molality[j]*molality[k]*molality[m]*m_Psi_ijk_LL[n];
}
}
}
}
}
// Loop Over Anions
if (charge(j) < 0) {
for (size_t k = j+1; k < m_kk; k++) {
if (j == m_kk-1) {
// we should never reach this step
throw CanteraError("HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2",
"logic error 2 in Step 9 of hmw_act");
}
if (charge(k) < 0) {
// Find the counterIJ for the symmetric j,k binary interaction
// between two anions
size_t n = m_kk*j + k;
size_t counterIJ = m_CounterIJ[n];
sum3 += molality[j]*molality[k]*m_PhiPhi_IJ_LL[counterIJ];
for (size_t m = 1; m < m_kk; m++) {
if (charge(m) > 0.0) {
n = m + k * m_kk + j * m_kk * m_kk;
sum3 += molality[j]*molality[k]*molality[m]*m_Psi_ijk_LL[n];
}
}
}
}
}
// Loop Over Neutral Species
if (charge(j) == 0) {
for (size_t k = 1; k < m_kk; k++) {
if (charge(k) < 0.0) {
sum4 += molality[j]*molality[k]*m_Lambda_nj_LL(j,k);
}
if (charge(k) > 0.0) {
sum5 += molality[j]*molality[k]*m_Lambda_nj_LL(j,k);
}
if (charge(k) == 0.0) {
if (k > j) {
sum6 += molality[j]*molality[k]*m_Lambda_nj_LL(j,k);
} else if (k == j) {
sum6 += 0.5 * molality[j]*molality[k]*m_Lambda_nj_LL(j,k);
}
}
if (charge(k) < 0.0) {
size_t izeta = j;
for (size_t m = 1; m < m_kk; m++) {
if (charge(m) > 0.0) {
size_t jzeta = m;
size_t n = k + jzeta * m_kk + izeta * m_kk * m_kk;
double zeta_LL = m_Psi_ijk_LL[n];
if (zeta_LL != 0.0) {
sum7 += molality[izeta]*molality[jzeta]*molality[k]*zeta_LL;
}
}
}
}
}
sum7 += molality[j] * molality[j] * molality[j] * m_Mu_nnn_LL[j];
}
}
double sum_m_phi_minus_1 = 2.0 *
(term1 + sum1 + sum2 + sum3 + sum4 + sum5 + sum6 + sum7);
// Calculate the osmotic coefficient from
// osmotic_coeff = 1 + dGex/d(M0noRT) / sum(molality_i)
double d2_osmotic_coef_dT2;
if (molalitysum > 1.0E-150) {
d2_osmotic_coef_dT2 = 0.0 + (sum_m_phi_minus_1 / molalitysum);
} else {
d2_osmotic_coef_dT2 = 0.0;
}
if (m_debugCalc) {
writelogf(" term1=%10.6f sum1=%10.6f sum2=%10.6f "
"sum3=%10.6f sum4=%10.6f sum5=%10.6f\n",
term1, sum1, sum2, sum3, sum4, sum5);
writelogf(" sum_m_phi_minus_1=%10.6f d2_osmotic_coef_dT2=%10.6f\n",
sum_m_phi_minus_1, d2_osmotic_coef_dT2);
writelog(" Step 10: \n");
}
double d2_lnwateract_dT2 = -(m_weightSolvent/1000.0) * molalitysum * d2_osmotic_coef_dT2;
// In Cantera, we define the activity coefficient of the solvent as
//
// act_0 = actcoeff_0 * Xmol_0
//
// We have just computed act_0. However, this routine returns
// ln(actcoeff[]). Therefore, we must calculate ln(actcoeff_0).
m_d2lnActCoeffMolaldT2_Unscaled[0] = d2_lnwateract_dT2;
if (m_debugCalc) {
double d2_wateract_dT2 = exp(d2_lnwateract_dT2);
writelogf(" d2_ln_a_water_dT2 = %10.6f d2_a_water_dT2=%10.6f\n\n",
d2_lnwateract_dT2, d2_wateract_dT2);
}
}
void HMWSoln::s_update_dlnMolalityActCoeff_dP() const
{
static const int cacheId = m_cache.getId();
CachedScalar cached = m_cache.getScalar(cacheId);
if( cached.validate(temperature(), pressure(), stateMFNumber()) ) {
return;
}
m_dlnActCoeffMolaldP_Unscaled.assign(m_kk, 0.0);
s_updatePitzer_dlnMolalityActCoeff_dP();
for (size_t k = 1; k < m_kk; k++) {
if (CROP_speciesCropped_[k] == 2) {
m_dlnActCoeffMolaldP_Unscaled[k] = 0.0;
}
}
if (CROP_speciesCropped_[0]) {
m_dlnActCoeffMolaldP_Unscaled[0] = 0.0;
}
s_updateScaling_pHScaling_dP();
}
void HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP() const
{
// HKM -> Assumption is made that the solvent is species 0.
if (m_indexSolvent != 0) {
throw CanteraError("HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP",
"Wrong index solvent value!");
}
const double* molality = m_molalitiesCropped.data();
// Local variables defined by Coltrin
double etheta[5][5], etheta_prime[5][5], sqrtIs;
// Molality based ionic strength of the solution
double Is = 0.0;
// Molarcharge of the solution: In Pitzer's notation, this is his variable
// called "Z".
double molarcharge = 0.0;
// molalitysum is the sum of the molalities over all solutes, even those
// with zero charge.
double molalitysum = 0.0;
double currTemp = temperature();
double currPres = pressure();
debuglog("\n Debugging information from s_Pitzer_dlnMolalityActCoeff_dP()\n",
m_debugCalc);
// Make sure the counter variables are setup
counterIJ_setup();
// ---------- Calculate common sums over solutes ---------------------
for (size_t n = 1; n < m_kk; n++) {
// ionic strength
Is += charge(n) * charge(n) * molality[n];
// total molar charge
molarcharge += fabs(charge(n)) * molality[n];
molalitysum += molality[n];
}
Is *= 0.5;
// Store the ionic molality in the object for reference.
m_IionicMolality = Is;
sqrtIs = sqrt(Is);
if (m_debugCalc) {
writelog(" Step 1: \n");
writelogf(" ionic strenth = %14.7le \n total molar "
"charge = %14.7le \n", Is, molarcharge);
}
// The following call to calc_lambdas() calculates all 16 elements of the
// elambda and elambda1 arrays, given the value of the ionic strength (Is)
calc_lambdas(Is);
// Step 2: Find the coefficients E-theta and E-thetaprime for all
// combinations of positive unlike charges up to 4
debuglog(" Step 2: \n", m_debugCalc);
for (int z1 = 1; z1 <=4; z1++) {
for (int z2 =1; z2 <=4; z2++) {
calc_thetas(z1, z2, &etheta[z1][z2], &etheta_prime[z1][z2]);
if (m_debugCalc) {
writelogf(" z1=%3d z2=%3d E-theta(I) = %f, E-thetaprime(I) = %f\n",
z1, z2, etheta[z1][z2], etheta_prime[z1][z2]);
}
}
}
debuglog(" Step 3: \n"
" Species Species g(x) hfunc(x)\n",
m_debugCalc);
// calculate g(x) and hfunc(x) for each cation-anion pair MX
// In the original literature, hfunc, was called gprime. However,
// it's not the derivative of g(x), so I renamed it.
for (size_t i = 1; i < (m_kk - 1); i++) {
for (size_t j = (i+1); j < m_kk; j++) {
// Find the counterIJ for the symmetric binary interaction
size_t n = m_kk*i + j;
size_t counterIJ = m_CounterIJ[n];
// Only loop over oppositely charge species
if (charge(i)*charge(j) < 0) {
// x is a reduced function variable
double x1 = sqrtIs * m_Alpha1MX_ij[counterIJ];
if (x1 > 1.0E-100) {
m_gfunc_IJ[counterIJ] = 2.0*(1.0-(1.0 + x1) * exp(-x1)) / (x1 * x1);
m_hfunc_IJ[counterIJ] = -2.0*
(1.0-(1.0 + x1 + 0.5 * x1 * x1) * exp(-x1)) / (x1 * x1);
} else {
m_gfunc_IJ[counterIJ] = 0.0;
m_hfunc_IJ[counterIJ] = 0.0;
}
if (m_Beta2MX_ij_P[counterIJ] != 0.0) {
double x2 = sqrtIs * m_Alpha2MX_ij[counterIJ];
if (x2 > 1.0E-100) {
m_g2func_IJ[counterIJ] = 2.0*(1.0-(1.0 + x2) * exp(-x2)) / (x2 * x2);
m_h2func_IJ[counterIJ] = -2.0 *
(1.0-(1.0 + x2 + 0.5 * x2 * x2) * exp(-x2)) / (x2 * x2);
} else {
m_g2func_IJ[counterIJ] = 0.0;
m_h2func_IJ[counterIJ] = 0.0;
}
}
} else {
m_gfunc_IJ[counterIJ] = 0.0;
m_hfunc_IJ[counterIJ] = 0.0;
}
if (m_debugCalc) {
writelogf(" %-16s %-16s %9.5f %9.5f \n", speciesName(i),
speciesName(j), m_gfunc_IJ[counterIJ], m_hfunc_IJ[counterIJ]);
}
}
}
// SUBSECTION TO CALCULATE BMX_P, BprimeMX_P, BphiMX_P
// These are now temperature derivatives of the previously calculated
// quantities.
debuglog(" Step 4: \n"
" Species Species BMX BprimeMX BphiMX \n",
m_debugCalc);
for (size_t i = 1; i < m_kk - 1; i++) {
for (size_t j = i+1; j < m_kk; j++) {
// Find the counterIJ for the symmetric binary interaction
size_t n = m_kk*i + j;
size_t counterIJ = m_CounterIJ[n];
// both species have a non-zero charge, and one is positive
// and the other is negative
if (charge(i)*charge(j) < 0.0) {
m_BMX_IJ_P[counterIJ] = m_Beta0MX_ij_P[counterIJ]
+ m_Beta1MX_ij_P[counterIJ] * m_gfunc_IJ[counterIJ]
+ m_Beta2MX_ij_P[counterIJ] * m_g2func_IJ[counterIJ];
if (m_debugCalc) {
writelogf("%d %g: %g %g %g %g\n",
counterIJ, m_BMX_IJ_P[counterIJ], m_Beta0MX_ij_P[counterIJ],
m_Beta1MX_ij_P[counterIJ], m_Beta2MX_ij_P[counterIJ], m_gfunc_IJ[counterIJ]);
}
if (Is > 1.0E-150) {
m_BprimeMX_IJ_P[counterIJ] = (m_Beta1MX_ij_P[counterIJ] * m_hfunc_IJ[counterIJ]/Is +
m_Beta2MX_ij_P[counterIJ] * m_h2func_IJ[counterIJ]/Is);
} else {
m_BprimeMX_IJ_P[counterIJ] = 0.0;
}
m_BphiMX_IJ_P[counterIJ] = m_BMX_IJ_P[counterIJ] + Is*m_BprimeMX_IJ_P[counterIJ];
} else {
m_BMX_IJ_P[counterIJ] = 0.0;
m_BprimeMX_IJ_P[counterIJ] = 0.0;
m_BphiMX_IJ_P[counterIJ] = 0.0;
}
if (m_debugCalc) {
writelogf(" %-16s %-16s %11.7f %11.7f %11.7f \n",
speciesName(i), speciesName(j),
m_BMX_IJ_P[counterIJ], m_BprimeMX_IJ_P[counterIJ], m_BphiMX_IJ_P[counterIJ]);
}
}
}
// --------- SUBSECTION TO CALCULATE CMX_P ----------
debuglog(" Step 5: \n"
" Species Species CMX \n", m_debugCalc);
for (size_t i = 1; i < m_kk-1; i++) {
for (size_t j = i+1; j < m_kk; j++) {
// Find the counterIJ for the symmetric binary interaction
size_t n = m_kk*i + j;
size_t counterIJ = m_CounterIJ[n];
// both species have a non-zero charge, and one is positive
// and the other is negative
if (charge(i)*charge(j) < 0.0) {
m_CMX_IJ_P[counterIJ] = m_CphiMX_ij_P[counterIJ]/
(2.0* sqrt(fabs(charge(i)*charge(j))));
} else {
m_CMX_IJ_P[counterIJ] = 0.0;
}
if (m_debugCalc) {
writelogf(" %-16s %-16s %11.7f \n",
speciesName(i), speciesName(j), m_CMX_IJ_P[counterIJ]);
}
}
}
// ------- SUBSECTION TO CALCULATE Phi, PhiPrime, and PhiPhi ----------
debuglog(" Step 6: \n"
" Species Species Phi_ij Phiprime_ij Phi^phi_ij \n",
m_debugCalc);
for (size_t i = 1; i < m_kk-1; i++) {
for (size_t j = i+1; j < m_kk; j++) {
// Find the counterIJ for the symmetric binary interaction
size_t n = m_kk*i + j;
size_t counterIJ = m_CounterIJ[n];
// both species have a non-zero charge, and one is positive
// and the other is negative
if (charge(i)*charge(j) > 0) {
m_Phi_IJ_P[counterIJ] = m_Theta_ij_P[counterIJ];
m_Phiprime_IJ[counterIJ] = 0.0;
m_PhiPhi_IJ_P[counterIJ] = m_Phi_IJ_P[counterIJ] + Is * m_Phiprime_IJ[counterIJ];
} else {
m_Phi_IJ_P[counterIJ] = 0.0;
m_Phiprime_IJ[counterIJ] = 0.0;
m_PhiPhi_IJ_P[counterIJ] = 0.0;
}
if (m_debugCalc) {
writelogf(" %-16s %-16s %10.6f %10.6f %10.6f \n",
speciesName(i), speciesName(j),
m_Phi_IJ_P[counterIJ], m_Phiprime_IJ[counterIJ], m_PhiPhi_IJ_P[counterIJ]);
}
}
}
// ----------- SUBSECTION FOR CALCULATION OF dFdT ---------------------
debuglog(" Step 7: \n", m_debugCalc);
double dA_DebyedP = dA_DebyedP_TP(currTemp, currPres);
double dAphidP = dA_DebyedP /3.0;
double dFdP = -dAphidP * (sqrt(Is) / (1.0 + 1.2*sqrt(Is))
+ (2.0/1.2) * log(1.0+1.2*(sqrtIs)));
if (m_debugCalc) {
writelogf(" initial value of dFdP = %10.6f \n", dFdP);
}
for (size_t i = 1; i < m_kk-1; i++) {
for (size_t j = i+1; j < m_kk; j++) {
// Find the counterIJ for the symmetric binary interaction
size_t n = m_kk*i + j;
size_t counterIJ = m_CounterIJ[n];
// both species have a non-zero charge, and one is positive
// and the other is negative
if (charge(i)*charge(j) < 0) {
dFdP += molality[i]*molality[j] * m_BprimeMX_IJ_P[counterIJ];
}
// Both species have a non-zero charge, and they
// have the same sign, e.g., both positive or both negative.
if (charge(i)*charge(j) > 0) {
dFdP += molality[i]*molality[j] * m_Phiprime_IJ[counterIJ];
}
if (m_debugCalc) {
writelogf(" dFdP = %10.6f \n", dFdP);
}
}
}
debuglog(" Step 8: \n", m_debugCalc);
for (size_t i = 1; i < m_kk; i++) {
// -------- SUBSECTION FOR CALCULATING THE dACTCOEFFdP FOR CATIONS -----
if (charge(i) > 0) {
// species i is the cation (positive) to calc the actcoeff
double zsqdFdP = charge(i)*charge(i)*dFdP;
double sum1 = 0.0;
double sum2 = 0.0;
double sum3 = 0.0;
double sum4 = 0.0;
double sum5 = 0.0;
for (size_t j = 1; j < m_kk; j++) {
// Find the counterIJ for the symmetric binary interaction
size_t n = m_kk*i + j;
size_t counterIJ = m_CounterIJ[n];
if (charge(j) < 0.0) {
// sum over all anions
sum1 += molality[j]*
(2.0*m_BMX_IJ_P[counterIJ] + molarcharge*m_CMX_IJ_P[counterIJ]);
if (j < m_kk-1) {
// This term is the ternary interaction involving the
// non-duplicate sum over double anions, j, k, with
// respect to the cation, i.
for (size_t k = j+1; k < m_kk; k++) {
// an inner sum over all anions
if (charge(k) < 0.0) {
n = k + j * m_kk + i * m_kk * m_kk;
sum3 += molality[j]*molality[k]*m_Psi_ijk_P[n];
}
}
}
}
if (charge(j) > 0.0) {
// sum over all cations
if (j != i) {
sum2 += molality[j]*(2.0*m_Phi_IJ_P[counterIJ]);
}
for (size_t k = 1; k < m_kk; k++) {
if (charge(k) < 0.0) {
// two inner sums over anions
n = k + j * m_kk + i * m_kk * m_kk;
sum2 += molality[j]*molality[k]*m_Psi_ijk_P[n];
// Find the counterIJ for the j,k interaction
n = m_kk*j + k;
size_t counterIJ2 = m_CounterIJ[n];
sum4 += fabs(charge(i)) *
molality[j]*molality[k]*m_CMX_IJ_P[counterIJ2];
}
}
}
// for Anions, do the neutral species interaction
if (charge(j) == 0) {
sum5 += molality[j]*2.0*m_Lambda_nj_P(j,i);
// Zeta interaction term
for (size_t k = 1; k < m_kk; k++) {
if (charge(k) < 0.0) {
size_t izeta = j;
size_t jzeta = i;
n = izeta * m_kk * m_kk + jzeta * m_kk + k;
double zeta_P = m_Psi_ijk_P[n];
if (zeta_P != 0.0) {
sum5 += molality[j]*molality[k]*zeta_P;
}
}
}
}
}
// Add all of the contributions up to yield the log of the
// solute activity coefficients (molality scale)
m_dlnActCoeffMolaldP_Unscaled[i] =
zsqdFdP + sum1 + sum2 + sum3 + sum4 + sum5;
if (m_debugCalc) {
writelogf(" %-16s lngamma[i]=%10.6f \n",
speciesName(i), m_dlnActCoeffMolaldP_Unscaled[i]);
writelogf(" %12g %12g %12g %12g %12g %12g\n",
zsqdFdP, sum1, sum2, sum3, sum4, sum5);
}
}
// ------ SUBSECTION FOR CALCULATING THE dACTCOEFFdP FOR ANIONS ------
if (charge(i) < 0) {
// species i is an anion (negative)
double zsqdFdP = charge(i)*charge(i)*dFdP;
double sum1 = 0.0;
double sum2 = 0.0;
double sum3 = 0.0;
double sum4 = 0.0;
double sum5 = 0.0;
for (size_t j = 1; j < m_kk; j++) {
// Find the counterIJ for the symmetric binary interaction
size_t n = m_kk*i + j;
size_t counterIJ = m_CounterIJ[n];
// For Anions, do the cation interactions.
if (charge(j) > 0) {
sum1 += molality[j] *
(2.0*m_BMX_IJ_P[counterIJ] + molarcharge*m_CMX_IJ_P[counterIJ]);
if (j < m_kk-1) {
for (size_t k = j+1; k < m_kk; k++) {
// an inner sum over all cations
if (charge(k) > 0) {
n = k + j * m_kk + i * m_kk * m_kk;
sum3 += molality[j]*molality[k]*m_Psi_ijk_P[n];
}
}
}
}
// For Anions, do the other anion interactions.
if (charge(j) < 0.0) {
// sum over all anions
if (j != i) {
sum2 += molality[j]*(2.0*m_Phi_IJ_P[counterIJ]);
}
for (size_t k = 1; k < m_kk; k++) {
if (charge(k) > 0.0) {
// two inner sums over cations
n = k + j * m_kk + i * m_kk * m_kk;
sum2 += molality[j]*molality[k]*m_Psi_ijk_P[n];
// Find the counterIJ for the symmetric binary interaction
n = m_kk*j + k;
size_t counterIJ2 = m_CounterIJ[n];
sum4 += fabs(charge(i))*
molality[j]*molality[k]*m_CMX_IJ_P[counterIJ2];
}
}
}
// for Anions, do the neutral species interaction
if (charge(j) == 0.0) {
sum5 += molality[j]*2.0*m_Lambda_nj_P(j,i);
// Zeta interaction term
for (size_t k = 1; k < m_kk; k++) {
if (charge(k) > 0.0) {
size_t izeta = j;
size_t jzeta = k;
size_t kzeta = i;
n = izeta * m_kk * m_kk + jzeta * m_kk + kzeta;
double zeta_P = m_Psi_ijk_P[n];
if (zeta_P != 0.0) {
sum5 += molality[j]*molality[k]*zeta_P;
}
}
}
}
}
m_dlnActCoeffMolaldP_Unscaled[i] =
zsqdFdP + sum1 + sum2 + sum3 + sum4 + sum5;
if (m_debugCalc) {
writelogf(" %-16s lndactcoeffmolaldP[i]=%10.6f \n",
speciesName(i), m_dlnActCoeffMolaldP_Unscaled[i]);
writelogf(" %12g %12g %12g %12g %12g %12g\n",
zsqdFdP, sum1, sum2, sum3, sum4, sum5);
}
}
// ------ SUBSECTION FOR CALCULATING d NEUTRAL SOLUTE ACT COEFF dP -----
if (charge(i) == 0.0) {
double sum1 = 0.0;
double sum3 = 0.0;
for (size_t j = 1; j < m_kk; j++) {
sum1 += molality[j]*2.0*m_Lambda_nj_P(i,j);
// Zeta term -> we piggyback on the psi term
if (charge(j) > 0.0) {
for (size_t k = 1; k < m_kk; k++) {
if (charge(k) < 0.0) {
size_t n = k + j * m_kk + i * m_kk * m_kk;
sum3 += molality[j]*molality[k]*m_Psi_ijk_P[n];
}
}
}
}
double sum2 = 3.0 * molality[i] * molality[i] * m_Mu_nnn_P[i];
m_dlnActCoeffMolaldP_Unscaled[i] = sum1 + sum2 + sum3;
if (m_debugCalc) {
writelogf(" %-16s dlnActCoeffMolaldP[i]=%10.6f \n",
speciesName(i), m_dlnActCoeffMolaldP_Unscaled[i]);
}
}
}
debuglog(" Step 9: \n", m_debugCalc);
// ------ SUBSECTION FOR CALCULATING THE d OSMOTIC COEFF dP ---------
double sum1 = 0.0;
double sum2 = 0.0;
double sum3 = 0.0;
double sum4 = 0.0;
double sum5 = 0.0;
double sum6 = 0.0;
double sum7 = 0.0;
// term1 is the temperature derivative of the DH term in the osmotic
// coefficient expression
// b = 1.2 sqrt(kg/gmol) <- arbitrarily set in all Pitzer implementations.
// Is = Ionic strength on the molality scale (units of (gmol/kg))
// Aphi = A_Debye / 3 (units of sqrt(kg/gmol))
double term1 = -dAphidP * Is * sqrt(Is) / (1.0 + 1.2 * sqrt(Is));
for (size_t j = 1; j < m_kk; j++) {
// Loop Over Cations
if (charge(j) > 0.0) {
for (size_t k = 1; k < m_kk; k++) {
if (charge(k) < 0.0) {
// Find the counterIJ for the symmetric j,k binary interaction
size_t n = m_kk*j + k;
size_t counterIJ = m_CounterIJ[n];
sum1 += molality[j]*molality[k]*
(m_BphiMX_IJ_P[counterIJ] + molarcharge*m_CMX_IJ_P[counterIJ]);
}
}
for (size_t k = j+1; k < m_kk; k++) {
if (j == (m_kk-1)) {
// we should never reach this step
throw CanteraError("HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP",
"logic error 1 in Step 9 of hmw_act");
}
if (charge(k) > 0.0) {
// Find the counterIJ for the symmetric j,k binary interaction
// between 2 cations.
size_t n = m_kk*j + k;
size_t counterIJ = m_CounterIJ[n];
sum2 += molality[j]*molality[k]*m_PhiPhi_IJ_P[counterIJ];
for (size_t m = 1; m < m_kk; m++) {
if (charge(m) < 0.0) {
// species m is an anion
n = m + k * m_kk + j * m_kk * m_kk;
sum2 += molality[j]*molality[k]*molality[m]*m_Psi_ijk_P[n];
}
}
}
}
}
// Loop Over Anions
if (charge(j) < 0) {
for (size_t k = j+1; k < m_kk; k++) {
if (j == m_kk-1) {
// we should never reach this step
throw CanteraError("HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP",
"logic error 2 in Step 9 of hmw_act");
}
if (charge(k) < 0) {
// Find the counterIJ for the symmetric j,k binary interaction
// between two anions
size_t n = m_kk*j + k;
size_t counterIJ = m_CounterIJ[n];
sum3 += molality[j]*molality[k]*m_PhiPhi_IJ_P[counterIJ];
for (size_t m = 1; m < m_kk; m++) {
if (charge(m) > 0.0) {
n = m + k * m_kk + j * m_kk * m_kk;
sum3 += molality[j]*molality[k]*molality[m]*m_Psi_ijk_P[n];
}
}
}
}
}
// Loop Over Neutral Species
if (charge(j) == 0) {
for (size_t k = 1; k < m_kk; k++) {
if (charge(k) < 0.0) {
sum4 += molality[j]*molality[k]*m_Lambda_nj_P(j,k);
}
if (charge(k) > 0.0) {
sum5 += molality[j]*molality[k]*m_Lambda_nj_P(j,k);
}
if (charge(k) == 0.0) {
if (k > j) {
sum6 += molality[j]*molality[k]*m_Lambda_nj_P(j,k);
} else if (k == j) {
sum6 += 0.5 * molality[j]*molality[k]*m_Lambda_nj_P(j,k);
}
}
if (charge(k) < 0.0) {
size_t izeta = j;
for (size_t m = 1; m < m_kk; m++) {
if (charge(m) > 0.0) {
size_t jzeta = m;
size_t n = k + jzeta * m_kk + izeta * m_kk * m_kk;
double zeta_P = m_Psi_ijk_P[n];
if (zeta_P != 0.0) {
sum7 += molality[izeta]*molality[jzeta]*molality[k]*zeta_P;
}
}
}
}
}
sum7 += molality[j] * molality[j] * molality[j] * m_Mu_nnn_P[j];
}
}
double sum_m_phi_minus_1 = 2.0 *
(term1 + sum1 + sum2 + sum3 + sum4 + sum5 + sum6 + sum7);
// Calculate the osmotic coefficient from
// osmotic_coeff = 1 + dGex/d(M0noRT) / sum(molality_i)
double d_osmotic_coef_dP;
if (molalitysum > 1.0E-150) {
d_osmotic_coef_dP = 0.0 + (sum_m_phi_minus_1 / molalitysum);
} else {
d_osmotic_coef_dP = 0.0;
}
if (m_debugCalc) {
writelogf(" term1=%10.6f sum1=%10.6f sum2=%10.6f "
"sum3=%10.6f sum4=%10.6f sum5=%10.6f\n",
term1, sum1, sum2, sum3, sum4, sum5);
writelogf(" sum_m_phi_minus_1=%10.6f d_osmotic_coef_dP =%10.6f\n",
sum_m_phi_minus_1, d_osmotic_coef_dP);
writelog(" Step 10: \n");
}
double d_lnwateract_dP = -(m_weightSolvent/1000.0) * molalitysum * d_osmotic_coef_dP;
// In Cantera, we define the activity coefficient of the solvent as
//
// act_0 = actcoeff_0 * Xmol_0
//
// We have just computed act_0. However, this routine returns
// ln(actcoeff[]). Therefore, we must calculate ln(actcoeff_0).
m_dlnActCoeffMolaldP_Unscaled[0] = d_lnwateract_dP;
if (m_debugCalc) {
writelogf(" d_ln_a_water_dP = %10.6f d_a_water_dP=%10.6f\n\n",
d_lnwateract_dP, exp(d_lnwateract_dP));
}
}
void HMWSoln::calc_lambdas(double is) const
{
if( m_last_is == is ) {
return;
}
m_last_is = is;
// Coefficients c1-c4 are used to approximate the integral function "J";
// aphi is the Debye-Huckel constant at 25 C
double c1 = 4.581, c2 = 0.7237, c3 = 0.0120, c4 = 0.528;
double aphi = 0.392; /* Value at 25 C */
if (m_debugCalc) {
writelogf(" Is = %g\n", is);
}
if (is < 1.0E-150) {
for (int i = 0; i < 17; i++) {
elambda[i] = 0.0;
elambda1[i] = 0.0;
}
return;
}
// Calculate E-lambda terms for charge combinations of like sign,
// using method of Pitzer (1975). Charges up to 4 are calculated.
for (int i=1; i<=4; i++) {
for (int j=i; j<=4; j++) {
int ij = i*j;
// calculate the product of the charges
double zprod = (double)ij;
// calculate Xmn (A1) from Harvie, Weare (1980).
double x = 6.0* zprod * aphi * sqrt(is); // eqn 23
double jfunc = x / (4.0 + c1*pow(x,-c2)*exp(-c3*pow(x,c4))); // eqn 47
double t = c3 * c4 * pow(x,c4);
double dj = c1* pow(x,(-c2-1.0)) * (c2+t) * exp(-c3*pow(x,c4));
double jprime = (jfunc/x)*(1.0 + jfunc*dj);
elambda[ij] = zprod*jfunc / (4.0*is); // eqn 14
elambda1[ij] = (3.0*zprod*zprod*aphi*jprime/(4.0*sqrt(is))
- elambda[ij])/is;
if (m_debugCalc) {
writelogf(" ij = %d, elambda = %g, elambda1 = %g\n",
ij, elambda[ij], elambda1[ij]);
}
}
}
}
void HMWSoln::calc_thetas(int z1, int z2,
double* etheta, double* etheta_prime) const
{
// Calculate E-theta(i) and E-theta'(I) using method of Pitzer (1987)
int i = abs(z1);
int j = abs(z2);
AssertThrowMsg(i <= 4 && j <= 4, "HMWSoln::calc_thetas",
"we shouldn't be here");
AssertThrowMsg(i != 0 && j != 0, "HMWSoln::calc_thetas",
"called with one species being neutral");
// Check to see if the charges are of opposite sign. If they are of opposite
// sign then their etheta interaction is zero.
if (z1*z2 < 0) {
*etheta = 0.0;
*etheta_prime = 0.0;
} else {
// Actually calculate the interaction.
double f1 = (double)i / (2.0 * j);
double f2 = (double)j / (2.0 * i);
*etheta = elambda[i*j] - f1*elambda[j*j] - f2*elambda[i*i];
*etheta_prime = elambda1[i*j] - f1*elambda1[j*j] - f2*elambda1[i*i];
}
}
void HMWSoln::s_updateIMS_lnMolalityActCoeff() const
{
// Calculate the molalities. Currently, the molalities may not be current
// with respect to the contents of the State objects' data.
calcMolalities();
double xmolSolvent = moleFraction(m_indexSolvent);
double xx = std::max(m_xmolSolventMIN, xmolSolvent);
if (IMS_typeCutoff_ == 0) {
for (size_t k = 1; k < m_kk; k++) {
IMS_lnActCoeffMolal_[k]= 0.0;
}
IMS_lnActCoeffMolal_[m_indexSolvent] = - log(xx) + (xx - 1.0)/xx;
return;
} else if (IMS_typeCutoff_ == 1) {
if (xmolSolvent > 3.0 * IMS_X_o_cutoff_/2.0) {
for (size_t k = 1; k < m_kk; k++) {
IMS_lnActCoeffMolal_[k]= 0.0;
}
IMS_lnActCoeffMolal_[m_indexSolvent] = - log(xx) + (xx - 1.0)/xx;
return;
} else if (xmolSolvent < IMS_X_o_cutoff_/2.0) {
double tmp = log(xx * IMS_gamma_k_min_);
for (size_t k = 1; k < m_kk; k++) {
IMS_lnActCoeffMolal_[k]= tmp;
}
IMS_lnActCoeffMolal_[m_indexSolvent] = log(IMS_gamma_o_min_);
return;
} else {
// If we are in the middle region, calculate the connecting polynomials
double xminus = xmolSolvent - IMS_X_o_cutoff_/2.0;
double xminus2 = xminus * xminus;
double xminus3 = xminus2 * xminus;
double x_o_cut2 = IMS_X_o_cutoff_ * IMS_X_o_cutoff_;
double x_o_cut3 = x_o_cut2 * IMS_X_o_cutoff_;
double h2 = 3.5 * xminus2 / IMS_X_o_cutoff_ - 2.0 * xminus3 / x_o_cut2;
double h2_prime = 7.0 * xminus / IMS_X_o_cutoff_ - 6.0 * xminus2 / x_o_cut2;
double h1 = (1.0 - 3.0 * xminus2 / x_o_cut2 + 2.0 * xminus3/ x_o_cut3);
double h1_prime = (- 6.0 * xminus / x_o_cut2 + 6.0 * xminus2/ x_o_cut3);
double h1_g = h1 / IMS_gamma_o_min_;
double h1_g_prime = h1_prime / IMS_gamma_o_min_;
double alpha = 1.0 / (exp(1.0) * IMS_gamma_k_min_);
double h1_f = h1 * alpha;
double h1_f_prime = h1_prime * alpha;
double f = h2 + h1_f;
double f_prime = h2_prime + h1_f_prime;
double g = h2 + h1_g;
double g_prime = h2_prime + h1_g_prime;
double tmp = (xmolSolvent/ g * g_prime + (1.0-xmolSolvent) / f * f_prime);
double lngammak = -1.0 - log(f) + tmp * xmolSolvent;
double lngammao =-log(g) - tmp * (1.0-xmolSolvent);
tmp = log(xmolSolvent) + lngammak;
for (size_t k = 1; k < m_kk; k++) {
IMS_lnActCoeffMolal_[k]= tmp;
}
IMS_lnActCoeffMolal_[m_indexSolvent] = lngammao;
}
} else if (IMS_typeCutoff_ == 2) {
// Exponentials - trial 2
if (xmolSolvent > IMS_X_o_cutoff_) {
for (size_t k = 1; k < m_kk; k++) {
IMS_lnActCoeffMolal_[k]= 0.0;
}
IMS_lnActCoeffMolal_[m_indexSolvent] = - log(xx) + (xx - 1.0)/xx;
return;
} else {
double xoverc = xmolSolvent/IMS_cCut_;
double eterm = std::exp(-xoverc);
double fptmp = IMS_bfCut_ - IMS_afCut_ / IMS_cCut_ - IMS_bfCut_*xoverc
+ 2.0*IMS_dfCut_*xmolSolvent - IMS_dfCut_*xmolSolvent*xoverc;
double f_prime = 1.0 + eterm*fptmp;
double f = xmolSolvent + IMS_efCut_
+ eterm * (IMS_afCut_ + xmolSolvent * (IMS_bfCut_ + IMS_dfCut_*xmolSolvent));
double gptmp = IMS_bgCut_ - IMS_agCut_ / IMS_cCut_ - IMS_bgCut_*xoverc
+ 2.0*IMS_dgCut_*xmolSolvent - IMS_dgCut_*xmolSolvent*xoverc;
double g_prime = 1.0 + eterm*gptmp;
double g = xmolSolvent + IMS_egCut_
+ eterm * (IMS_agCut_ + xmolSolvent * (IMS_bgCut_ + IMS_dgCut_*xmolSolvent));
double tmp = (xmolSolvent / g * g_prime + (1.0 - xmolSolvent) / f * f_prime);
double lngammak = -1.0 - log(f) + tmp * xmolSolvent;
double lngammao =-log(g) - tmp * (1.0-xmolSolvent);
tmp = log(xx) + lngammak;
for (size_t k = 1; k < m_kk; k++) {
IMS_lnActCoeffMolal_[k]= tmp;
}
IMS_lnActCoeffMolal_[m_indexSolvent] = lngammao;
}
}
return;
}
void HMWSoln::printCoeffs() const
{
calcMolalities();
vector_fp& moleF = m_tmpV;
// Update the coefficients wrt Temperature. Calculate the derivatives as well
s_updatePitzer_CoeffWRTemp(2);
getMoleFractions(moleF.data());
writelog("Index Name MoleF MolalityCropped Charge\n");
for (size_t k = 0; k < m_kk; k++) {
writelogf("%2d %-16s %14.7le %14.7le %5.1f \n",
k, speciesName(k), moleF[k], m_molalitiesCropped[k], charge(k));
}
writelog("\n Species Species beta0MX "
"beta1MX beta2MX CphiMX alphaMX thetaij\n");
for (size_t i = 1; i < m_kk - 1; i++) {
for (size_t j = i+1; j < m_kk; j++) {
size_t n = i * m_kk + j;
size_t ct = m_CounterIJ[n];
writelogf(" %-16s %-16s %9.5f %9.5f %9.5f %9.5f %9.5f %9.5f \n",
speciesName(i), speciesName(j),
m_Beta0MX_ij[ct], m_Beta1MX_ij[ct],
m_Beta2MX_ij[ct], m_CphiMX_ij[ct],
m_Alpha1MX_ij[ct], m_Theta_ij[ct]);
}
}
writelog("\n Species Species Species psi \n");
for (size_t i = 1; i < m_kk; i++) {
for (size_t j = 1; j < m_kk; j++) {
for (size_t k = 1; k < m_kk; k++) {
size_t n = k + j * m_kk + i * m_kk * m_kk;
if (m_Psi_ijk[n] != 0.0) {
writelogf(" %-16s %-16s %-16s %9.5f \n",
speciesName(i), speciesName(j),
speciesName(k), m_Psi_ijk[n]);
}
}
}
}
}
void HMWSoln::applyphScale(doublereal* acMolality) const
{
if (m_pHScalingType == PHSCALE_PITZER) {
return;
}
AssertTrace(m_pHScalingType == PHSCALE_NBS);
doublereal lnGammaClMs2 = s_NBS_CLM_lnMolalityActCoeff();
doublereal lnGammaCLMs1 = m_lnActCoeffMolal_Unscaled[m_indexCLM];
doublereal afac = -1.0 *(lnGammaClMs2 - lnGammaCLMs1);
for (size_t k = 0; k < m_kk; k++) {
acMolality[k] *= exp(charge(k) * afac);
}
}
void HMWSoln::s_updateScaling_pHScaling() const
{
if (m_pHScalingType == PHSCALE_PITZER) {
m_lnActCoeffMolal_Scaled = m_lnActCoeffMolal_Unscaled;
return;
}
AssertTrace(m_pHScalingType == PHSCALE_NBS);
doublereal lnGammaClMs2 = s_NBS_CLM_lnMolalityActCoeff();
doublereal lnGammaCLMs1 = m_lnActCoeffMolal_Unscaled[m_indexCLM];
doublereal afac = -1.0 *(lnGammaClMs2 - lnGammaCLMs1);
for (size_t k = 0; k < m_kk; k++) {
m_lnActCoeffMolal_Scaled[k] = m_lnActCoeffMolal_Unscaled[k] + charge(k) * afac;
}
}
void HMWSoln::s_updateScaling_pHScaling_dT() const
{
if (m_pHScalingType == PHSCALE_PITZER) {
m_dlnActCoeffMolaldT_Scaled = m_dlnActCoeffMolaldT_Unscaled;
return;
}
AssertTrace(m_pHScalingType == PHSCALE_NBS);
doublereal dlnGammaClM_dT_s2 = s_NBS_CLM_dlnMolalityActCoeff_dT();
doublereal dlnGammaCLM_dT_s1 = m_dlnActCoeffMolaldT_Unscaled[m_indexCLM];
doublereal afac = -1.0 *(dlnGammaClM_dT_s2 - dlnGammaCLM_dT_s1);
for (size_t k = 0; k < m_kk; k++) {
m_dlnActCoeffMolaldT_Scaled[k] = m_dlnActCoeffMolaldT_Unscaled[k] + charge(k) * afac;
}
}
void HMWSoln::s_updateScaling_pHScaling_dT2() const
{
if (m_pHScalingType == PHSCALE_PITZER) {
m_d2lnActCoeffMolaldT2_Scaled = m_d2lnActCoeffMolaldT2_Unscaled;
return;
}
AssertTrace(m_pHScalingType == PHSCALE_NBS);
doublereal d2lnGammaClM_dT2_s2 = s_NBS_CLM_d2lnMolalityActCoeff_dT2();
doublereal d2lnGammaCLM_dT2_s1 = m_d2lnActCoeffMolaldT2_Unscaled[m_indexCLM];
doublereal afac = -1.0 *(d2lnGammaClM_dT2_s2 - d2lnGammaCLM_dT2_s1);
for (size_t k = 0; k < m_kk; k++) {
m_d2lnActCoeffMolaldT2_Scaled[k] = m_d2lnActCoeffMolaldT2_Unscaled[k] + charge(k) * afac;
}
}
void HMWSoln::s_updateScaling_pHScaling_dP() const
{
if (m_pHScalingType == PHSCALE_PITZER) {
m_dlnActCoeffMolaldP_Scaled = m_dlnActCoeffMolaldP_Unscaled;
return;
}
AssertTrace(m_pHScalingType == PHSCALE_NBS);
doublereal dlnGammaClM_dP_s2 = s_NBS_CLM_dlnMolalityActCoeff_dP();
doublereal dlnGammaCLM_dP_s1 = m_dlnActCoeffMolaldP_Unscaled[m_indexCLM];
doublereal afac = -1.0 *(dlnGammaClM_dP_s2 - dlnGammaCLM_dP_s1);
for (size_t k = 0; k < m_kk; k++) {
m_dlnActCoeffMolaldP_Scaled[k] = m_dlnActCoeffMolaldP_Unscaled[k] + charge(k) * afac;
}
}
doublereal HMWSoln::s_NBS_CLM_lnMolalityActCoeff() const
{
doublereal sqrtIs = sqrt(m_IionicMolality);
doublereal A = A_Debye_TP();
doublereal lnGammaClMs2 = - A * sqrtIs /(1.0 + 1.5 * sqrtIs);
return lnGammaClMs2;
}
doublereal HMWSoln::s_NBS_CLM_dlnMolalityActCoeff_dT() const
{
doublereal sqrtIs = sqrt(m_IionicMolality);
doublereal dAdT = dA_DebyedT_TP();
return - dAdT * sqrtIs /(1.0 + 1.5 * sqrtIs);
}
doublereal HMWSoln::s_NBS_CLM_d2lnMolalityActCoeff_dT2() const
{
doublereal sqrtIs = sqrt(m_IionicMolality);
doublereal d2AdT2 = d2A_DebyedT2_TP();
return - d2AdT2 * sqrtIs /(1.0 + 1.5 * sqrtIs);
}
doublereal HMWSoln::s_NBS_CLM_dlnMolalityActCoeff_dP() const
{
doublereal sqrtIs = sqrt(m_IionicMolality);
doublereal dAdP = dA_DebyedP_TP();
return - dAdP * sqrtIs /(1.0 + 1.5 * sqrtIs);
}
int HMWSoln::debugPrinting()
{
return m_debugCalc;
}
}
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