/** * @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(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, ðeta[z1][z2], ðeta_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, ðeta[z1][z2], ðeta_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, ðeta[z1][z2], ðeta_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, ðeta[z1][z2], ðeta_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; } }