Class HMWSoln represents a dilute or concentrated liquid electrolyte phase which obeys the Pitzer formulation for nonideality. More...
#include <HMWSoln.h>
Public Member Functions | |
| HMWSoln () | |
| Default Constructor. More... | |
| HMWSoln (const std::string &inputFile, const std::string &id="") | |
| Construct and initialize an HMWSoln ThermoPhase object directly from an ASCII input file. More... | |
| HMWSoln (XML_Node &phaseRef, const std::string &id="") | |
| Construct and initialize an HMWSoln ThermoPhase object directly from an XML database. More... | |
| virtual doublereal | satPressure (doublereal T) |
| Get the saturation pressure for a given temperature. More... | |
| void | setBinarySalt (const std::string &sp1, const std::string &sp2, size_t nParams, double *beta0, double *beta1, double *beta2, double *Cphi, double alpha1, double alpha2) |
| void | setTheta (const std::string &sp1, const std::string &sp2, size_t nParams, double *theta) |
| void | setPsi (const std::string &sp1, const std::string &sp2, const std::string &sp3, size_t nParams, double *psi) |
| void | setLambda (const std::string &sp1, const std::string &sp2, size_t nParams, double *lambda) |
| void | setMunnn (const std::string &sp, size_t nParams, double *munnn) |
| void | setZeta (const std::string &sp1, const std::string &sp2, const std::string &sp3, size_t nParams, double *psi) |
| void | setPitzerTempModel (const std::string &model) |
| void | setPitzerRefTemperature (double Tref) |
| void | setA_Debye (double A) |
| Set the A_Debye parameter. More... | |
| void | setMaxIonicStrength (double Imax) |
| void | setCroppingCoefficients (double ln_gamma_k_min, double ln_gamma_k_max, double ln_gamma_o_min, double ln_gamma_o_max) |
| virtual void | initThermo () |
| virtual void | initThermoXML (XML_Node &phaseNode, const std::string &id) |
| Initialize the phase parameters from an XML file. More... | |
| virtual double | A_Debye_TP (double temperature=-1.0, double pressure=-1.0) const |
| Value of the Debye Huckel constant as a function of temperature and pressure. More... | |
| virtual double | dA_DebyedT_TP (double temperature=-1.0, double pressure=-1.0) const |
| Value of the derivative of the Debye Huckel constant with respect to temperature as a function of temperature and pressure. More... | |
| virtual double | dA_DebyedP_TP (double temperature=-1.0, double pressure=-1.0) const |
| Value of the derivative of the Debye Huckel constant with respect to pressure, as a function of temperature and pressure. More... | |
| double | ADebye_L (double temperature=-1.0, double pressure=-1.0) const |
| Return Pitzer's definition of A_L. More... | |
| double | ADebye_J (double temperature=-1.0, double pressure=-1.0) const |
| Return Pitzer's definition of A_J. More... | |
| double | ADebye_V (double temperature=-1.0, double pressure=-1.0) const |
| Return Pitzer's definition of A_V. More... | |
| virtual double | d2A_DebyedT2_TP (double temperature=-1.0, double pressure=-1.0) const |
| Value of the 2nd derivative of the Debye Huckel constant with respect to temperature as a function of temperature and pressure. More... | |
| void | printCoeffs () const |
| Print out all of the input Pitzer coefficients. More... | |
| void | getUnscaledMolalityActivityCoefficients (doublereal *acMolality) const |
| Get the array of unscaled non-dimensional molality based activity coefficients at the current solution temperature, pressure, and solution concentration. More... | |
Utilities | |
| virtual std::string | type () const |
| String indicating the thermodynamic model implemented. More... | |
Molar Thermodynamic Properties of the Solution | |
| virtual doublereal | enthalpy_mole () const |
| Molar enthalpy. Units: J/kmol. More... | |
| virtual doublereal | relative_enthalpy () const |
| Excess molar enthalpy of the solution from the mixing process. More... | |
| virtual doublereal | relative_molal_enthalpy () const |
| Excess molar enthalpy of the solution from the mixing process on a molality basis. More... | |
| virtual doublereal | entropy_mole () const |
| Molar entropy. Units: J/kmol/K. More... | |
| virtual doublereal | gibbs_mole () const |
| Molar Gibbs function. Units: J/kmol. More... | |
| virtual doublereal | cp_mole () const |
| Molar heat capacity at constant pressure. Units: J/kmol/K. More... | |
| virtual doublereal | cv_mole () const |
| Molar heat capacity at constant volume. Units: J/kmol/K. More... | |
Activities, Standard States, and Activity Concentrations | |
The activity \(a_k\) of a species in solution is related to the chemical potential by \[ \mu_k = \mu_k^0(T) + \hat R T \log a_k. \] The quantity \(\mu_k^0(T,P)\) is the chemical potential at unit activity, which depends only on temperature and the pressure. Activity is assumed to be molality-based here. | |
| virtual void | getActivityConcentrations (doublereal *c) const |
| This method returns an array of generalized activity concentrations. More... | |
| virtual doublereal | standardConcentration (size_t k=0) const |
| Return the standard concentration for the kth species. More... | |
| virtual void | getActivities (doublereal *ac) const |
| Get the array of non-dimensional activities at the current solution temperature, pressure, and solution concentration. More... | |
Partial Molar Properties of the Solution | |
| virtual void | getChemPotentials (doublereal *mu) const |
| Get the species chemical potentials. Units: J/kmol. More... | |
| virtual void | getPartialMolarEnthalpies (doublereal *hbar) const |
| Returns an array of partial molar enthalpies for the species in the mixture. More... | |
| virtual void | getPartialMolarEntropies (doublereal *sbar) const |
| Returns an array of partial molar entropies of the species in the solution. More... | |
| virtual void | getPartialMolarVolumes (doublereal *vbar) const |
| Return an array of partial molar volumes for the species in the mixture. More... | |
| virtual void | getPartialMolarCp (doublereal *cpbar) const |
| Return an array of partial molar heat capacities for the species in the mixture. More... | |
 Public Member Functions inherited from MolalityVPSSTP | |
| MolalityVPSSTP () | |
| Default Constructor. More... | |
| virtual void | setStateFromXML (const XML_Node &state) |
| Set equation of state parameter values from XML entries. More... | |
| void | setState_TPM (doublereal t, doublereal p, const doublereal *const molalities) |
| Set the temperature (K), pressure (Pa), and molalities (gmol kg-1) of the solutes. More... | |
| void | setState_TPM (doublereal t, doublereal p, const compositionMap &m) |
| Set the temperature (K), pressure (Pa), and molalities. More... | |
| void | setState_TPM (doublereal t, doublereal p, const std::string &m) |
| Set the temperature (K), pressure (Pa), and molalities. More... | |
| virtual void | getdlnActCoeffdlnN (const size_t ld, doublereal *const dlnActCoeffdlnN) |
| Get the array of derivatives of the log activity coefficients with respect to the log of the species mole numbers. More... | |
| virtual std::string | report (bool show_thermo=true, doublereal threshold=1e-14) const |
| returns a summary of the state of the phase as a string More... | |
| void | setpHScale (const int pHscaleType) |
| Set the pH scale, which determines the scale for single-ion activity coefficients. More... | |
| int | pHScale () const |
| Reports the pH scale, which determines the scale for single-ion activity coefficients. More... | |
| void | setSolvent (size_t k) |
| This routine sets the index number of the solvent for the phase. More... | |
| size_t | solventIndex () const |
| Returns the solvent index. More... | |
| void | setMoleFSolventMin (doublereal xmolSolventMIN) |
| Sets the minimum mole fraction in the molality formulation. More... | |
| doublereal | moleFSolventMin () const |
| Returns the minimum mole fraction in the molality formulation. More... | |
| void | calcMolalities () const |
| Calculates the molality of all species and stores the result internally. More... | |
| void | getMolalities (doublereal *const molal) const |
| This function will return the molalities of the species. More... | |
| void | setMolalities (const doublereal *const molal) |
| Set the molalities of the solutes in a phase. More... | |
| void | setMolalitiesByName (const compositionMap &xMap) |
| Set the molalities of a phase. More... | |
| void | setMolalitiesByName (const std::string &name) |
| Set the molalities of a phase. More... | |
| int | activityConvention () const |
| We set the convention to molality here. More... | |
| virtual void | getActivityCoefficients (doublereal *ac) const |
| Get the array of non-dimensional activity coefficients at the current solution temperature, pressure, and solution concentration. More... | |
| virtual void | getMolalityActivityCoefficients (doublereal *acMolality) const |
| Get the array of non-dimensional molality based activity coefficients at the current solution temperature, pressure, and solution concentration. More... | |
| virtual double | osmoticCoefficient () const |
| Calculate the osmotic coefficient. More... | |
| virtual bool | addSpecies (shared_ptr< Species > spec) |
| Public Member Functions inherited from VPStandardStateTP | |
| VPStandardStateTP () | |
| Constructor. More... | |
| virtual int | standardStateConvention () const |
| This method returns the convention used in specification of the standard state, of which there are currently two, temperature based, and variable pressure based. More... | |
| virtual void | getdlnActCoeffdlnN_diag (doublereal *dlnActCoeffdlnN_diag) const |
| Get the array of log species mole number derivatives of the log activity coefficients. More... | |
| virtual void | getChemPotentials_RT (doublereal *mu) const |
| Get the array of non-dimensional species chemical potentials. More... | |
| virtual void | getStandardChemPotentials (doublereal *mu) const |
| Get the array of chemical potentials at unit activity for the species at their standard states at the current T and P of the solution. More... | |
| virtual void | getEnthalpy_RT (doublereal *hrt) const |
| Get the nondimensional Enthalpy functions for the species at their standard states at the current T and P of the solution. More... | |
| virtual void | getEntropy_R (doublereal *sr) const |
| Get the array of nondimensional Entropy functions for the standard state species at the current T and P of the solution. More... | |
| virtual void | getGibbs_RT (doublereal *grt) const |
| Get the nondimensional Gibbs functions for the species in their standard states at the current T and P of the solution. More... | |
| virtual void | getPureGibbs (doublereal *gpure) const |
| Get the Gibbs functions for the standard state of the species at the current T and P of the solution. More... | |
| virtual void | getIntEnergy_RT (doublereal *urt) const |
| Returns the vector of nondimensional Internal Energies of the standard state species at the current T and P of the solution. More... | |
| virtual void | getCp_R (doublereal *cpr) const |
| Get the nondimensional Heat Capacities at constant pressure for the species standard states at the current T and P of the solution. More... | |
| virtual void | getStandardVolumes (doublereal *vol) const |
| Get the molar volumes of the species standard states at the current T and P of the solution. More... | |
| virtual const vector_fp & | getStandardVolumes () const |
| virtual void | setTemperature (const doublereal temp) |
| Set the temperature of the phase. More... | |
| virtual void | setPressure (doublereal p) |
| Set the internally stored pressure (Pa) at constant temperature and composition. More... | |
| virtual void | setState_TP (doublereal T, doublereal pres) |
| Set the temperature and pressure at the same time. More... | |
| virtual doublereal | pressure () const |
| Returns the current pressure of the phase. More... | |
| virtual void | updateStandardStateThermo () const |
| Updates the standard state thermodynamic functions at the current T and P of the solution. More... | |
| void | installPDSS (size_t k, std::unique_ptr< PDSS > &&pdss) |
| Install a PDSS object for species k More... | |
| PDSS * | providePDSS (size_t k) |
| const PDSS * | providePDSS (size_t k) const |
| virtual bool | addSpecies (shared_ptr< Species > spec) |
| Add a Species to this Phase. More... | |
| virtual void | getEnthalpy_RT_ref (doublereal *hrt) const |
| virtual void | getGibbs_RT_ref (doublereal *grt) const |
| Returns the vector of nondimensional Gibbs Free Energies of the reference state at the current temperature of the solution and the reference pressure for the species. More... | |
| virtual void | getGibbs_ref (doublereal *g) const |
| Returns the vector of the Gibbs function of the reference state at the current temperature of the solution and the reference pressure for the species. More... | |
| virtual void | getEntropy_R_ref (doublereal *er) const |
| Returns the vector of nondimensional entropies of the reference state at the current temperature of the solution and the reference pressure for each species. More... | |
| virtual void | getCp_R_ref (doublereal *cprt) const |
| Returns the vector of nondimensional constant pressure heat capacities of the reference state at the current temperature of the solution and reference pressure for each species. More... | |
| virtual void | getStandardVolumes_ref (doublereal *vol) const |
| Get the molar volumes of the species reference states at the current T and P_ref of the solution. More... | |
| Public Member Functions inherited from ThermoPhase | |
| ThermoPhase () | |
| Constructor. More... | |
| doublereal | RT () const |
| Return the Gas Constant multiplied by the current temperature. More... | |
| virtual doublereal | refPressure () const |
| Returns the reference pressure in Pa. More... | |
| virtual doublereal | minTemp (size_t k=npos) const |
| Minimum temperature for which the thermodynamic data for the species or phase are valid. More... | |
| doublereal | Hf298SS (const size_t k) const |
| Report the 298 K Heat of Formation of the standard state of one species (J kmol-1) More... | |
| virtual void | modifyOneHf298SS (const size_t k, const doublereal Hf298New) |
| Modify the value of the 298 K Heat of Formation of one species in the phase (J kmol-1) More... | |
| virtual void | resetHf298 (const size_t k=npos) |
| Restore the original heat of formation of one or more species. More... | |
| virtual doublereal | maxTemp (size_t k=npos) const |
| Maximum temperature for which the thermodynamic data for the species are valid. More... | |
| bool | chargeNeutralityNecessary () const |
| Returns the chargeNeutralityNecessity boolean. More... | |
| virtual doublereal | intEnergy_mole () const |
| Molar internal energy. Units: J/kmol. More... | |
| virtual doublereal | isothermalCompressibility () const |
| Returns the isothermal compressibility. Units: 1/Pa. More... | |
| virtual doublereal | thermalExpansionCoeff () const |
| Return the volumetric thermal expansion coefficient. Units: 1/K. More... | |
| void | setElectricPotential (doublereal v) |
| Set the electric potential of this phase (V). More... | |
| doublereal | electricPotential () const |
| Returns the electric potential of this phase (V). More... | |
| virtual doublereal | logStandardConc (size_t k=0) const |
| Natural logarithm of the standard concentration of the kth species. More... | |
| virtual void | getLnActivityCoefficients (doublereal *lnac) const |
| Get the array of non-dimensional molar-based ln activity coefficients at the current solution temperature, pressure, and solution concentration. More... | |
| void | getElectrochemPotentials (doublereal *mu) const |
| Get the species electrochemical potentials. More... | |
| virtual void | getPartialMolarIntEnergies (doublereal *ubar) const |
| Return an array of partial molar internal energies for the species in the mixture. More... | |
| virtual void | getIntEnergy_RT_ref (doublereal *urt) const |
| Returns the vector of nondimensional internal Energies of the reference state at the current temperature of the solution and the reference pressure for each species. More... | |
| doublereal | enthalpy_mass () const |
| Specific enthalpy. Units: J/kg. More... | |
| doublereal | intEnergy_mass () const |
| Specific internal energy. Units: J/kg. More... | |
| doublereal | entropy_mass () const |
| Specific entropy. Units: J/kg/K. More... | |
| doublereal | gibbs_mass () const |
| Specific Gibbs function. Units: J/kg. More... | |
| doublereal | cp_mass () const |
| Specific heat at constant pressure. Units: J/kg/K. More... | |
| doublereal | cv_mass () const |
| Specific heat at constant volume. Units: J/kg/K. More... | |
| virtual void | setState_TPX (doublereal t, doublereal p, const doublereal *x) |
| Set the temperature (K), pressure (Pa), and mole fractions. More... | |
| virtual void | setState_TPX (doublereal t, doublereal p, const compositionMap &x) |
| Set the temperature (K), pressure (Pa), and mole fractions. More... | |
| virtual void | setState_TPX (doublereal t, doublereal p, const std::string &x) |
| Set the temperature (K), pressure (Pa), and mole fractions. More... | |
| virtual void | setState_TPY (doublereal t, doublereal p, const doublereal *y) |
| Set the internally stored temperature (K), pressure (Pa), and mass fractions of the phase. More... | |
| virtual void | setState_TPY (doublereal t, doublereal p, const compositionMap &y) |
| Set the internally stored temperature (K), pressure (Pa), and mass fractions of the phase. More... | |
| virtual void | setState_TPY (doublereal t, doublereal p, const std::string &y) |
| Set the internally stored temperature (K), pressure (Pa), and mass fractions of the phase. More... | |
| virtual void | setState_PX (doublereal p, doublereal *x) |
| Set the pressure (Pa) and mole fractions. More... | |
| virtual void | setState_PY (doublereal p, doublereal *y) |
| Set the internally stored pressure (Pa) and mass fractions. More... | |
| virtual void | setState_HP (double h, double p, double tol=1e-9) |
| Set the internally stored specific enthalpy (J/kg) and pressure (Pa) of the phase. More... | |
| virtual void | setState_UV (double u, double v, double tol=1e-9) |
| Set the specific internal energy (J/kg) and specific volume (m^3/kg). More... | |
| virtual void | setState_SP (double s, double p, double tol=1e-9) |
| Set the specific entropy (J/kg/K) and pressure (Pa). More... | |
| virtual void | setState_SV (double s, double v, double tol=1e-9) |
| Set the specific entropy (J/kg/K) and specific volume (m^3/kg). More... | |
| virtual void | setState_ST (double s, double t, double tol=1e-9) |
| Set the specific entropy (J/kg/K) and temperature (K). More... | |
| virtual void | setState_TV (double t, double v, double tol=1e-9) |
| Set the temperature (K) and specific volume (m^3/kg). More... | |
| virtual void | setState_PV (double p, double v, double tol=1e-9) |
| Set the pressure (Pa) and specific volume (m^3/kg). More... | |
| virtual void | setState_UP (double u, double p, double tol=1e-9) |
| Set the specific internal energy (J/kg) and pressure (Pa). More... | |
| virtual void | setState_VH (double v, double h, double tol=1e-9) |
| Set the specific volume (m^3/kg) and the specific enthalpy (J/kg) More... | |
| virtual void | setState_TH (double t, double h, double tol=1e-9) |
| Set the temperature (K) and the specific enthalpy (J/kg) More... | |
| virtual void | setState_SH (double s, double h, double tol=1e-9) |
| Set the specific entropy (J/kg/K) and the specific enthalpy (J/kg) More... | |
| virtual void | setState_RP (doublereal rho, doublereal p) |
| Set the density (kg/m**3) and pressure (Pa) at constant composition. More... | |
| virtual void | setState_RPX (doublereal rho, doublereal p, const doublereal *x) |
| Set the density (kg/m**3), pressure (Pa) and mole fractions. More... | |
| virtual void | setState_RPX (doublereal rho, doublereal p, const compositionMap &x) |
| Set the density (kg/m**3), pressure (Pa) and mole fractions. More... | |
| virtual void | setState_RPX (doublereal rho, doublereal p, const std::string &x) |
| Set the density (kg/m**3), pressure (Pa) and mole fractions. More... | |
| virtual void | setState_RPY (doublereal rho, doublereal p, const doublereal *y) |
| Set the density (kg/m**3), pressure (Pa) and mass fractions. More... | |
| virtual void | setState_RPY (doublereal rho, doublereal p, const compositionMap &y) |
| Set the density (kg/m**3), pressure (Pa) and mass fractions. More... | |
| virtual void | setState_RPY (doublereal rho, doublereal p, const std::string &y) |
| Set the density (kg/m**3), pressure (Pa) and mass fractions. More... | |
| void | equilibrate (const std::string &XY, const std::string &solver="auto", double rtol=1e-9, int max_steps=50000, int max_iter=100, int estimate_equil=0, int log_level=0) |
| Equilibrate a ThermoPhase object. More... | |
| virtual void | setToEquilState (const doublereal *lambda_RT) |
| This method is used by the ChemEquil equilibrium solver. More... | |
| void | setElementPotentials (const vector_fp &lambda) |
| Stores the element potentials in the ThermoPhase object. More... | |
| bool | getElementPotentials (doublereal *lambda) const |
| Returns the element potentials stored in the ThermoPhase object. More... | |
| virtual bool | compatibleWithMultiPhase () const |
| Indicates whether this phase type can be used with class MultiPhase for equilibrium calculations. More... | |
| virtual doublereal | critTemperature () const |
| Critical temperature (K). More... | |
| virtual doublereal | critPressure () const |
| Critical pressure (Pa). More... | |
| virtual doublereal | critVolume () const |
| Critical volume (m3/kmol). More... | |
| virtual doublereal | critCompressibility () const |
| Critical compressibility (unitless). More... | |
| virtual doublereal | critDensity () const |
| Critical density (kg/m3). More... | |
| virtual doublereal | satTemperature (doublereal p) const |
| Return the saturation temperature given the pressure. More... | |
| virtual doublereal | vaporFraction () const |
| Return the fraction of vapor at the current conditions. More... | |
| virtual void | setState_Tsat (doublereal t, doublereal x) |
| Set the state to a saturated system at a particular temperature. More... | |
| virtual void | setState_Psat (doublereal p, doublereal x) |
| Set the state to a saturated system at a particular pressure. More... | |
| virtual void | modifySpecies (size_t k, shared_ptr< Species > spec) |
| Modify the thermodynamic data associated with a species. More... | |
| void | saveSpeciesData (const size_t k, const XML_Node *const data) |
| Store a reference pointer to the XML tree containing the species data for this phase. More... | |
| const std::vector< const XML_Node * > & | speciesData () const |
| Return a pointer to the vector of XML nodes containing the species data for this phase. More... | |
| virtual MultiSpeciesThermo & | speciesThermo (int k=-1) |
| Return a changeable reference to the calculation manager for species reference-state thermodynamic properties. More... | |
| virtual void | initThermoFile (const std::string &inputFile, const std::string &id) |
| virtual void | setParameters (int n, doublereal *const c) |
| Set the equation of state parameters. More... | |
| virtual void | getParameters (int &n, doublereal *const c) const |
| Get the equation of state parameters in a vector. More... | |
| virtual void | setParametersFromXML (const XML_Node &eosdata) |
| Set equation of state parameter values from XML entries. More... | |
| virtual void | getdlnActCoeffds (const doublereal dTds, const doublereal *const dXds, doublereal *dlnActCoeffds) const |
| Get the change in activity coefficients wrt changes in state (temp, mole fraction, etc) along a line in parameter space or along a line in physical space. More... | |
| virtual void | getdlnActCoeffdlnX_diag (doublereal *dlnActCoeffdlnX_diag) const |
| Get the array of ln mole fraction derivatives of the log activity coefficients - diagonal component only. More... | |
| virtual void | getdlnActCoeffdlnN_numderiv (const size_t ld, doublereal *const dlnActCoeffdlnN) |
| virtual void | reportCSV (std::ofstream &csvFile) const |
| returns a summary of the state of the phase to a comma separated file. More... | |
| Public Member Functions inherited from Phase | |
| Phase () | |
| Default constructor. More... | |
| Phase (const Phase &)=delete | |
| Phase & | operator= (const Phase &)=delete |
| XML_Node & | xml () const |
| Returns a const reference to the XML_Node that describes the phase. More... | |
| void | setXMLdata (XML_Node &xmlPhase) |
| Stores the XML tree information for the current phase. More... | |
| void | saveState (vector_fp &state) const |
| Save the current internal state of the phase. More... | |
| void | saveState (size_t lenstate, doublereal *state) const |
| Write to array 'state' the current internal state. More... | |
| void | restoreState (const vector_fp &state) |
| Restore a state saved on a previous call to saveState. More... | |
| void | restoreState (size_t lenstate, const doublereal *state) |
| Restore the state of the phase from a previously saved state vector. More... | |
| doublereal | molecularWeight (size_t k) const |
Molecular weight of species k. More... | |
| void | getMolecularWeights (vector_fp &weights) const |
| Copy the vector of molecular weights into vector weights. More... | |
| void | getMolecularWeights (doublereal *weights) const |
| Copy the vector of molecular weights into array weights. More... | |
| const vector_fp & | molecularWeights () const |
| Return a const reference to the internal vector of molecular weights. More... | |
| virtual double | size (size_t k) const |
| doublereal | charge (size_t k) const |
| Dimensionless electrical charge of a single molecule of species k The charge is normalized by the the magnitude of the electron charge. More... | |
| doublereal | chargeDensity () const |
| Charge density [C/m^3]. More... | |
| size_t | nDim () const |
| Returns the number of spatial dimensions (1, 2, or 3) More... | |
| void | setNDim (size_t ndim) |
| Set the number of spatial dimensions (1, 2, or 3). More... | |
| virtual bool | ready () const |
| Returns a bool indicating whether the object is ready for use. More... | |
| int | stateMFNumber () const |
| Return the State Mole Fraction Number. More... | |
| std::string | id () const |
| Return the string id for the phase. More... | |
| void | setID (const std::string &id) |
| Set the string id for the phase. More... | |
| std::string | name () const |
| Return the name of the phase. More... | |
| void | setName (const std::string &nm) |
| Sets the string name for the phase. More... | |
| std::string | elementName (size_t m) const |
| Name of the element with index m. More... | |
| size_t | elementIndex (const std::string &name) const |
| Return the index of element named 'name'. More... | |
| const std::vector< std::string > & | elementNames () const |
| Return a read-only reference to the vector of element names. More... | |
| doublereal | atomicWeight (size_t m) const |
| Atomic weight of element m. More... | |
| doublereal | entropyElement298 (size_t m) const |
| Entropy of the element in its standard state at 298 K and 1 bar. More... | |
| int | atomicNumber (size_t m) const |
| Atomic number of element m. More... | |
| int | elementType (size_t m) const |
| Return the element constraint type Possible types include: More... | |
| int | changeElementType (int m, int elem_type) |
| Change the element type of the mth constraint Reassigns an element type. More... | |
| const vector_fp & | atomicWeights () const |
| Return a read-only reference to the vector of atomic weights. More... | |
| size_t | nElements () const |
| Number of elements. More... | |
| void | checkElementIndex (size_t m) const |
| Check that the specified element index is in range. More... | |
| void | checkElementArraySize (size_t mm) const |
| Check that an array size is at least nElements(). More... | |
| doublereal | nAtoms (size_t k, size_t m) const |
Number of atoms of element m in species k. More... | |
| void | getAtoms (size_t k, double *atomArray) const |
| Get a vector containing the atomic composition of species k. More... | |
| size_t | speciesIndex (const std::string &name) const |
| Returns the index of a species named 'name' within the Phase object. More... | |
| std::string | speciesName (size_t k) const |
| Name of the species with index k. More... | |
| std::string | speciesSPName (int k) const |
| Returns the expanded species name of a species, including the phase name This is guaranteed to be unique within a Cantera problem. More... | |
| const std::vector< std::string > & | speciesNames () const |
| Return a const reference to the vector of species names. More... | |
| size_t | nSpecies () const |
| Returns the number of species in the phase. More... | |
| void | checkSpeciesIndex (size_t k) const |
| Check that the specified species index is in range. More... | |
| void | checkSpeciesArraySize (size_t kk) const |
| Check that an array size is at least nSpecies(). More... | |
| void | setMoleFractionsByName (const compositionMap &xMap) |
| Set the species mole fractions by name. More... | |
| void | setMoleFractionsByName (const std::string &x) |
| Set the mole fractions of a group of species by name. More... | |
| void | setMassFractionsByName (const compositionMap &yMap) |
| Set the species mass fractions by name. More... | |
| void | setMassFractionsByName (const std::string &x) |
| Set the species mass fractions by name. More... | |
| void | setState_TRX (doublereal t, doublereal dens, const doublereal *x) |
| Set the internally stored temperature (K), density, and mole fractions. More... | |
| void | setState_TRX (doublereal t, doublereal dens, const compositionMap &x) |
| Set the internally stored temperature (K), density, and mole fractions. More... | |
| void | setState_TRY (doublereal t, doublereal dens, const doublereal *y) |
| Set the internally stored temperature (K), density, and mass fractions. More... | |
| void | setState_TRY (doublereal t, doublereal dens, const compositionMap &y) |
| Set the internally stored temperature (K), density, and mass fractions. More... | |
| void | setState_TNX (doublereal t, doublereal n, const doublereal *x) |
| Set the internally stored temperature (K), molar density (kmol/m^3), and mole fractions. More... | |
| void | setState_TR (doublereal t, doublereal rho) |
| Set the internally stored temperature (K) and density (kg/m^3) More... | |
| void | setState_TX (doublereal t, doublereal *x) |
| Set the internally stored temperature (K) and mole fractions. More... | |
| void | setState_TY (doublereal t, doublereal *y) |
| Set the internally stored temperature (K) and mass fractions. More... | |
| void | setState_RX (doublereal rho, doublereal *x) |
| Set the density (kg/m^3) and mole fractions. More... | |
| void | setState_RY (doublereal rho, doublereal *y) |
| Set the density (kg/m^3) and mass fractions. More... | |
| compositionMap | getMoleFractionsByName (double threshold=0.0) const |
| Get the mole fractions by name. More... | |
| doublereal | moleFraction (size_t k) const |
| Return the mole fraction of a single species. More... | |
| doublereal | moleFraction (const std::string &name) const |
| Return the mole fraction of a single species. More... | |
| compositionMap | getMassFractionsByName (double threshold=0.0) const |
| Get the mass fractions by name. More... | |
| doublereal | massFraction (size_t k) const |
| Return the mass fraction of a single species. More... | |
| doublereal | massFraction (const std::string &name) const |
| Return the mass fraction of a single species. More... | |
| void | getMoleFractions (doublereal *const x) const |
| Get the species mole fraction vector. More... | |
| virtual void | setMoleFractions (const doublereal *const x) |
| Set the mole fractions to the specified values. More... | |
| virtual void | setMoleFractions_NoNorm (const doublereal *const x) |
| Set the mole fractions to the specified values without normalizing. More... | |
| void | getMassFractions (doublereal *const y) const |
| Get the species mass fractions. More... | |
| const doublereal * | massFractions () const |
| Return a const pointer to the mass fraction array. More... | |
| virtual void | setMassFractions (const doublereal *const y) |
| Set the mass fractions to the specified values and normalize them. More... | |
| virtual void | setMassFractions_NoNorm (const doublereal *const y) |
| Set the mass fractions to the specified values without normalizing. More... | |
| void | getConcentrations (doublereal *const c) const |
| Get the species concentrations (kmol/m^3). More... | |
| doublereal | concentration (const size_t k) const |
| Concentration of species k. More... | |
| virtual void | setConcentrations (const doublereal *const conc) |
| Set the concentrations to the specified values within the phase. More... | |
| virtual void | setConcentrationsNoNorm (const double *const conc) |
| Set the concentrations without ignoring negative concentrations. More... | |
| doublereal | elementalMassFraction (const size_t m) const |
| Elemental mass fraction of element m. More... | |
| doublereal | elementalMoleFraction (const size_t m) const |
| Elemental mole fraction of element m. More... | |
| const doublereal * | moleFractdivMMW () const |
| Returns a const pointer to the start of the moleFraction/MW array. More... | |
| doublereal | temperature () const |
| Temperature (K). More... | |
| virtual doublereal | density () const |
| Density (kg/m^3). More... | |
| doublereal | molarDensity () const |
| Molar density (kmol/m^3). More... | |
| doublereal | molarVolume () const |
| Molar volume (m^3/kmol). More... | |
| doublereal | mean_X (const doublereal *const Q) const |
| Evaluate the mole-fraction-weighted mean of an array Q. More... | |
| doublereal | mean_X (const vector_fp &Q) const |
| Evaluate the mole-fraction-weighted mean of an array Q. More... | |
| doublereal | meanMolecularWeight () const |
| The mean molecular weight. Units: (kg/kmol) More... | |
| doublereal | sum_xlogx () const |
| Evaluate \( \sum_k X_k \log X_k \). More... | |
| size_t | addElement (const std::string &symbol, doublereal weight=-12345.0, int atomicNumber=0, doublereal entropy298=ENTROPY298_UNKNOWN, int elem_type=CT_ELEM_TYPE_ABSPOS) |
| Add an element. More... | |
| shared_ptr< Species > | species (const std::string &name) const |
| Return the Species object for the named species. More... | |
| shared_ptr< Species > | species (size_t k) const |
| Return the Species object for species whose index is k. More... | |
| void | ignoreUndefinedElements () |
| Set behavior when adding a species containing undefined elements to just skip the species. More... | |
| void | addUndefinedElements () |
| Set behavior when adding a species containing undefined elements to add those elements to the phase. More... | |
| void | throwUndefinedElements () |
| Set the behavior when adding a species containing undefined elements to throw an exception. More... | |
Public Attributes | |
| int | m_form_A_Debye |
| Form of the constant outside the Debye-Huckel term called A. More... | |
Private Member Functions | |
| void | s_updateScaling_pHScaling () const |
| Apply the current phScale to a set of activity Coefficients. More... | |
| void | s_updateScaling_pHScaling_dT () const |
| Apply the current phScale to a set of derivatives of the activity Coefficients wrt temperature. More... | |
| void | s_updateScaling_pHScaling_dT2 () const |
| Apply the current phScale to a set of 2nd derivatives of the activity Coefficients wrt temperature. More... | |
| void | s_updateScaling_pHScaling_dP () const |
| Apply the current phScale to a set of derivatives of the activity Coefficients wrt pressure. More... | |
| doublereal | s_NBS_CLM_lnMolalityActCoeff () const |
| Calculate the Chlorine activity coefficient on the NBS scale. More... | |
| doublereal | s_NBS_CLM_dlnMolalityActCoeff_dT () const |
| Calculate the temperature derivative of the Chlorine activity coefficient on the NBS scale. More... | |
| doublereal | s_NBS_CLM_d2lnMolalityActCoeff_dT2 () const |
| Calculate the second temperature derivative of the Chlorine activity coefficient on the NBS scale. More... | |
| doublereal | s_NBS_CLM_dlnMolalityActCoeff_dP () const |
| Calculate the pressure derivative of the Chlorine activity coefficient. More... | |
| void | initLengths () |
| Initialize all of the species-dependent lengths in the object. More... | |
| virtual void | applyphScale (doublereal *acMolality) const |
| Apply the current phScale to a set of activity Coefficients or activities. More... | |
| void | s_update_lnMolalityActCoeff () const |
| void | s_update_dlnMolalityActCoeff_dT () const |
| This function calculates the temperature derivative of the natural logarithm of the molality activity coefficients. More... | |
| void | s_update_d2lnMolalityActCoeff_dT2 () const |
| This function calculates the temperature second derivative of the natural logarithm of the molality activity coefficients. More... | |
| void | s_update_dlnMolalityActCoeff_dP () const |
| This function calculates the pressure derivative of the natural logarithm of the molality activity coefficients. More... | |
| void | s_updateIMS_lnMolalityActCoeff () const |
| This function will be called to update the internally stored natural logarithm of the molality activity coefficients. More... | |
| void | s_updatePitzer_lnMolalityActCoeff () const |
| Calculate the Pitzer portion of the activity coefficients. More... | |
| void | s_updatePitzer_dlnMolalityActCoeff_dT () const |
| Calculates the temperature derivative of the natural logarithm of the molality activity coefficients. More... | |
| void | s_updatePitzer_d2lnMolalityActCoeff_dT2 () const |
| This function calculates the temperature second derivative of the natural logarithm of the molality activity coefficients. More... | |
| void | s_updatePitzer_dlnMolalityActCoeff_dP () const |
| Calculates the Pressure derivative of the natural logarithm of the molality activity coefficients. More... | |
| void | s_updatePitzer_CoeffWRTemp (int doDerivs=2) const |
| Calculates the Pitzer coefficients' dependence on the temperature. More... | |
| void | calc_lambdas (double is) const |
| Calculate the lambda interactions. More... | |
| void | calc_thetas (int z1, int z2, double *etheta, double *etheta_prime) const |
| Calculate etheta and etheta_prime. More... | |
| void | counterIJ_setup () const |
| Set up a counter variable for keeping track of symmetric binary interactions amongst the solute species. More... | |
| void | calcMolalitiesCropped () const |
| Calculate the cropped molalities. More... | |
| void | readXMLBinarySalt (XML_Node &BinSalt) |
| Process an XML node called "binarySaltParameters". More... | |
| void | readXMLTheta (XML_Node &BinSalt) |
| Process an XML node called "thetaAnion" or "thetaCation". More... | |
| void | readXMLPsi (XML_Node &BinSalt) |
| Process an XML node called "psiCommonAnion" or "psiCommonCation". More... | |
| void | readXMLLambdaNeutral (XML_Node &BinSalt) |
| Process an XML node called "lambdaNeutral". More... | |
| void | readXMLMunnnNeutral (XML_Node &BinSalt) |
| Process an XML node called "MunnnNeutral". More... | |
| void | readXMLZetaCation (const XML_Node &BinSalt) |
| Process an XML node called "zetaCation". More... | |
| void | calcIMSCutoffParams_ () |
| Precalculate the IMS Cutoff parameters for typeCutoff = 2. More... | |
| void | calcMCCutoffParams_ () |
| Calculate molality cut-off parameters. More... | |
Private Attributes | |
| int | m_formPitzerTemp |
| This is the form of the temperature dependence of Pitzer parameterization used in the model. More... | |
| double | m_IionicMolality |
| Current value of the ionic strength on the molality scale Associated Salts, if present in the mechanism, don't contribute to the value of the ionic strength in this version of the Ionic strength. More... | |
| double | m_maxIionicStrength |
| Maximum value of the ionic strength allowed in the calculation of the activity coefficients. More... | |
| double | m_TempPitzerRef |
| Reference Temperature for the Pitzer formulations. More... | |
| double | m_A_Debye |
| A_Debye: this expression appears on the top of the ln actCoeff term in the general Debye-Huckel expression It depends on temperature. More... | |
| PDSS * | m_waterSS |
| Water standard state calculator. More... | |
| std::unique_ptr< WaterProps > | m_waterProps |
| Pointer to the water property calculator. More... | |
| vector_fp | m_tmpV |
| vector of size m_kk, used as a temporary holding area. More... | |
| vector_fp | m_Beta0MX_ij |
| Array of 2D data used in the Pitzer/HMW formulation. More... | |
| vector_fp | m_Beta0MX_ij_L |
| Derivative of Beta0_ij[i][j] wrt T. Vector index is counterIJ. More... | |
| vector_fp | m_Beta0MX_ij_LL |
| Derivative of Beta0_ij[i][j] wrt TT. Vector index is counterIJ. More... | |
| vector_fp | m_Beta0MX_ij_P |
| Derivative of Beta0_ij[i][j] wrt P. Vector index is counterIJ. More... | |
| Array2D | m_Beta0MX_ij_coeff |
| Array of coefficients for Beta0, a variable in Pitzer's papers. More... | |
| vector_fp | m_Beta1MX_ij |
| Array of 2D data used in the Pitzer/HMW formulation. More... | |
| vector_fp | m_Beta1MX_ij_L |
| Derivative of Beta1_ij[i][j] wrt T. Vector index is counterIJ. More... | |
| vector_fp | m_Beta1MX_ij_LL |
| Derivative of Beta1_ij[i][j] wrt TT. Vector index is counterIJ. More... | |
| vector_fp | m_Beta1MX_ij_P |
| Derivative of Beta1_ij[i][j] wrt P. Vector index is counterIJ. More... | |
| Array2D | m_Beta1MX_ij_coeff |
| Array of coefficients for Beta1, a variable in Pitzer's papers. More... | |
| vector_fp | m_Beta2MX_ij |
| Array of 2D data used in the Pitzer/HMW formulation. More... | |
| vector_fp | m_Beta2MX_ij_L |
| Derivative of Beta2_ij[i][j] wrt T. Vector index is counterIJ. More... | |
| vector_fp | m_Beta2MX_ij_LL |
| Derivative of Beta2_ij[i][j] wrt TT. Vector index is counterIJ. More... | |
| vector_fp | m_Beta2MX_ij_P |
| Derivative of Beta2_ij[i][j] wrt P. Vector index is counterIJ. More... | |
| Array2D | m_Beta2MX_ij_coeff |
| Array of coefficients for Beta2, a variable in Pitzer's papers. More... | |
| vector_fp | m_Alpha1MX_ij |
| vector_fp | m_Alpha2MX_ij |
| Array of 2D data used in the Pitzer/HMW formulation. More... | |
| vector_fp | m_CphiMX_ij |
| Array of 2D data used in the Pitzer/HMW formulation. More... | |
| vector_fp | m_CphiMX_ij_L |
| Derivative of Cphi_ij[i][j] wrt T. Vector index is counterIJ. More... | |
| vector_fp | m_CphiMX_ij_LL |
| Derivative of Cphi_ij[i][j] wrt TT. Vector index is counterIJ. More... | |
| vector_fp | m_CphiMX_ij_P |
| Derivative of Cphi_ij[i][j] wrt P. Vector index is counterIJ. More... | |
| Array2D | m_CphiMX_ij_coeff |
| Array of coefficients for CphiMX, a parameter in the activity coefficient formulation. More... | |
| vector_fp | m_Theta_ij |
| Array of 2D data for Theta_ij[i][j] in the Pitzer/HMW formulation. More... | |
| vector_fp | m_Theta_ij_L |
| Derivative of Theta_ij[i][j] wrt T. Vector index is counterIJ. More... | |
| vector_fp | m_Theta_ij_LL |
| Derivative of Theta_ij[i][j] wrt TT. Vector index is counterIJ. More... | |
| vector_fp | m_Theta_ij_P |
| Derivative of Theta_ij[i][j] wrt P. Vector index is counterIJ. More... | |
| Array2D | m_Theta_ij_coeff |
| Array of coefficients for Theta_ij[i][j] in the Pitzer/HMW formulation. More... | |
| vector_fp | m_Psi_ijk |
| Array of 3D data used in the Pitzer/HMW formulation. More... | |
| vector_fp | m_Psi_ijk_L |
| Derivative of Psi_ijk[n] wrt T. More... | |
| vector_fp | m_Psi_ijk_LL |
| Derivative of Psi_ijk[n] wrt TT. More... | |
| vector_fp | m_Psi_ijk_P |
| Derivative of Psi_ijk[n] wrt P. More... | |
| Array2D | m_Psi_ijk_coeff |
| Array of coefficients for Psi_ijk[n] in the Pitzer/HMW formulation. More... | |
| Array2D | m_Lambda_nj |
| Lambda coefficient for the ij interaction. More... | |
| Array2D | m_Lambda_nj_L |
| Derivative of Lambda_nj[i][j] wrt T. see m_Lambda_ij. More... | |
| Array2D | m_Lambda_nj_LL |
| Derivative of Lambda_nj[i][j] wrt TT. More... | |
| Array2D | m_Lambda_nj_P |
| Derivative of Lambda_nj[i][j] wrt P. More... | |
| Array2D | m_Lambda_nj_coeff |
| Array of coefficients for Lambda_nj[i][j] in the Pitzer/HMW formulation. More... | |
| vector_fp | m_Mu_nnn |
| Mu coefficient for the self-ternary neutral coefficient. More... | |
| vector_fp | m_Mu_nnn_L |
| Mu coefficient temperature derivative for the self-ternary neutral coefficient. More... | |
| vector_fp | m_Mu_nnn_LL |
| Mu coefficient 2nd temperature derivative for the self-ternary neutral coefficient. More... | |
| vector_fp | m_Mu_nnn_P |
| Mu coefficient pressure derivative for the self-ternary neutral coefficient. More... | |
| Array2D | m_Mu_nnn_coeff |
| Array of coefficients form_Mu_nnn term. More... | |
| vector_fp | m_lnActCoeffMolal_Scaled |
| Logarithm of the activity coefficients on the molality scale. More... | |
| vector_fp | m_lnActCoeffMolal_Unscaled |
| Logarithm of the activity coefficients on the molality scale. More... | |
| vector_fp | m_dlnActCoeffMolaldT_Scaled |
| Derivative of the Logarithm of the activity coefficients on the molality scale wrt T. More... | |
| vector_fp | m_dlnActCoeffMolaldT_Unscaled |
| Derivative of the Logarithm of the activity coefficients on the molality scale wrt T. More... | |
| vector_fp | m_d2lnActCoeffMolaldT2_Scaled |
| Derivative of the Logarithm of the activity coefficients on the molality scale wrt TT. More... | |
| vector_fp | m_d2lnActCoeffMolaldT2_Unscaled |
| Derivative of the Logarithm of the activity coefficients on the molality scale wrt TT. More... | |
| vector_fp | m_dlnActCoeffMolaldP_Scaled |
| Derivative of the Logarithm of the activity coefficients on the molality scale wrt P. More... | |
| vector_fp | m_dlnActCoeffMolaldP_Unscaled |
| Derivative of the Logarithm of the activity coefficients on the molality scale wrt P. More... | |
| vector_fp | m_molalitiesCropped |
| Cropped and modified values of the molalities used in activity coefficient calculations. More... | |
| bool | m_molalitiesAreCropped |
| Boolean indicating whether the molalities are cropped or are modified. More... | |
| vector_int | m_CounterIJ |
| a counter variable for keeping track of symmetric binary interactions amongst the solute species. More... | |
| double | elambda [17] |
| This is elambda, MEC. More... | |
| double | elambda1 [17] |
| This is elambda1, MEC. More... | |
| vector_fp | m_gfunc_IJ |
| Various temporary arrays used in the calculation of the Pitzer activity coefficients. More... | |
| vector_fp | m_g2func_IJ |
| This is the value of g2(x2) in Pitzer's papers. Vector index is counterIJ. More... | |
| vector_fp | m_hfunc_IJ |
| hfunc, was called gprime in Pitzer's paper. More... | |
| vector_fp | m_h2func_IJ |
| hfunc2, was called gprime in Pitzer's paper. More... | |
| vector_fp | m_BMX_IJ |
| Intermediate variable called BMX in Pitzer's paper. More... | |
| vector_fp | m_BMX_IJ_L |
| Derivative of BMX_IJ wrt T. Vector index is counterIJ. More... | |
| vector_fp | m_BMX_IJ_LL |
| Derivative of BMX_IJ wrt TT. Vector index is counterIJ. More... | |
| vector_fp | m_BMX_IJ_P |
| Derivative of BMX_IJ wrt P. Vector index is counterIJ. More... | |
| vector_fp | m_BprimeMX_IJ |
| Intermediate variable called BprimeMX in Pitzer's paper. More... | |
| vector_fp | m_BprimeMX_IJ_L |
| Derivative of BprimeMX wrt T. Vector index is counterIJ. More... | |
| vector_fp | m_BprimeMX_IJ_LL |
| Derivative of BprimeMX wrt TT. Vector index is counterIJ. More... | |
| vector_fp | m_BprimeMX_IJ_P |
| Derivative of BprimeMX wrt P. Vector index is counterIJ. More... | |
| vector_fp | m_BphiMX_IJ |
| Intermediate variable called BphiMX in Pitzer's paper. More... | |
| vector_fp | m_BphiMX_IJ_L |
| Derivative of BphiMX_IJ wrt T. Vector index is counterIJ. More... | |
| vector_fp | m_BphiMX_IJ_LL |
| Derivative of BphiMX_IJ wrt TT. Vector index is counterIJ. More... | |
| vector_fp | m_BphiMX_IJ_P |
| Derivative of BphiMX_IJ wrt P. Vector index is counterIJ. More... | |
| vector_fp | m_Phi_IJ |
| Intermediate variable called Phi in Pitzer's paper. More... | |
| vector_fp | m_Phi_IJ_L |
| Derivative of m_Phi_IJ wrt T. Vector index is counterIJ. More... | |
| vector_fp | m_Phi_IJ_LL |
| Derivative of m_Phi_IJ wrt TT. Vector index is counterIJ. More... | |
| vector_fp | m_Phi_IJ_P |
| Derivative of m_Phi_IJ wrt P. Vector index is counterIJ. More... | |
| vector_fp | m_Phiprime_IJ |
| Intermediate variable called Phiprime in Pitzer's paper. More... | |
| vector_fp | m_PhiPhi_IJ |
| Intermediate variable called PhiPhi in Pitzer's paper. More... | |
| vector_fp | m_PhiPhi_IJ_L |
| Derivative of m_PhiPhi_IJ wrt T. Vector index is counterIJ. More... | |
| vector_fp | m_PhiPhi_IJ_LL |
| Derivative of m_PhiPhi_IJ wrt TT. Vector index is counterIJ. More... | |
| vector_fp | m_PhiPhi_IJ_P |
| Derivative of m_PhiPhi_IJ wrt P. Vector index is counterIJ. More... | |
| vector_fp | m_CMX_IJ |
| Intermediate variable called CMX in Pitzer's paper. More... | |
| vector_fp | m_CMX_IJ_L |
| Derivative of m_CMX_IJ wrt T. Vector index is counterIJ. More... | |
| vector_fp | m_CMX_IJ_LL |
| Derivative of m_CMX_IJ wrt TT. Vector index is counterIJ. More... | |
| vector_fp | m_CMX_IJ_P |
| Derivative of m_CMX_IJ wrt P. Vector index is counterIJ. More... | |
| vector_fp | m_gamma_tmp |
| Intermediate storage of the activity coefficient itself. More... | |
| vector_fp | IMS_lnActCoeffMolal_ |
| Logarithm of the molal activity coefficients. More... | |
| doublereal | IMS_X_o_cutoff_ |
| value of the solute mole fraction that centers the cutoff polynomials for the cutoff =1 process; More... | |
| doublereal | IMS_cCut_ |
| Parameter in the polyExp cutoff treatment having to do with rate of exp decay. More... | |
| doublereal | IMS_slopegCut_ |
| Parameter in the polyExp cutoff treatment. More... | |
| doublereal | MC_X_o_cutoff_ |
| value of the solvent mole fraction that centers the cutoff polynomials for the cutoff =1 process; More... | |
| doublereal | m_last_is |
Parameters in the polyExp cutoff treatment having to do with rate of exp decay | |
| doublereal | IMS_dfCut_ |
| doublereal | IMS_efCut_ |
| doublereal | IMS_afCut_ |
| doublereal | IMS_bfCut_ |
| doublereal | IMS_dgCut_ |
| doublereal | IMS_egCut_ |
| doublereal | IMS_agCut_ |
| doublereal | IMS_bgCut_ |
Parameters in the Molality Exp cutoff treatment | |
| doublereal | MC_dpCut_ |
| doublereal | MC_epCut_ |
| doublereal | MC_apCut_ |
| doublereal | MC_bpCut_ |
| doublereal | MC_cpCut_ |
| doublereal | CROP_ln_gamma_o_min |
| doublereal | CROP_ln_gamma_o_max |
| doublereal | CROP_ln_gamma_k_min |
| doublereal | CROP_ln_gamma_k_max |
| vector_int | CROP_speciesCropped_ |
| This is a boolean-type vector indicating whether a species's activity coefficient is in the cropped regime. More... | |
Mechanical Equation of State Properties | |
| virtual void | setDensity (const doublereal rho) |
| Set the internally stored density (kg/m^3) of the phase. More... | |
| virtual void | setMolarDensity (const doublereal conc) |
| Set the internally stored molar density (kmol/m^3) for the phase. More... | |
| void | calcDensity () |
| Calculate the density of the mixture using the partial molar volumes and mole fractions as input. More... | |
Additional Inherited Members | |
| Protected Member Functions inherited from MolalityVPSSTP | |
| virtual void | getCsvReportData (std::vector< std::string > &names, std::vector< vector_fp > &data) const |
Fills names and data with the column names and species thermo properties to be included in the output of the reportCSV method. More... | |
| Protected Member Functions inherited from VPStandardStateTP | |
| virtual void | _updateStandardStateThermo () const |
| Updates the standard state thermodynamic functions at the current T and P of the solution. More... | |
| virtual void | invalidateCache () |
| Invalidate any cached values which are normally updated only when a change in state is detected. More... | |
| const vector_fp & | Gibbs_RT_ref () const |
| Protected Member Functions inherited from Phase | |
| void | setMolecularWeight (const int k, const double mw) |
| Set the molecular weight of a single species to a given value. More... | |
| virtual void | compositionChanged () |
| Apply changes to the state which are needed after the composition changes. More... | |
| Protected Attributes inherited from MolalityVPSSTP | |
| int | m_pHScalingType |
| Scaling to be used for output of single-ion species activity coefficients. More... | |
| size_t | m_indexCLM |
| Index of the phScale species. More... | |
| doublereal | m_weightSolvent |
| Molecular weight of the Solvent. More... | |
| doublereal | m_xmolSolventMIN |
| doublereal | m_Mnaught |
| This is the multiplication factor that goes inside log expressions involving the molalities of species. More... | |
| vector_fp | m_molalities |
| Current value of the molalities of the species in the phase. More... | |
| Protected Attributes inherited from VPStandardStateTP | |
| doublereal | m_Pcurrent |
| Current value of the pressure - state variable. More... | |
| doublereal | m_Tlast_ss |
| The last temperature at which the standard statethermodynamic properties were calculated at. More... | |
| doublereal | m_Plast_ss |
| The last pressure at which the Standard State thermodynamic properties were calculated at. More... | |
| std::vector< std::unique_ptr< PDSS > > | m_PDSS_storage |
| Storage for the PDSS objects for the species. More... | |
| vector_fp | m_h0_RT |
| Vector containing the species reference enthalpies at T = m_tlast and P = p_ref. More... | |
| vector_fp | m_cp0_R |
| Vector containing the species reference constant pressure heat capacities at T = m_tlast and P = p_ref. More... | |
| vector_fp | m_g0_RT |
| Vector containing the species reference Gibbs functions at T = m_tlast and P = p_ref. More... | |
| vector_fp | m_s0_R |
| Vector containing the species reference entropies at T = m_tlast and P = p_ref. More... | |
| vector_fp | m_V0 |
| Vector containing the species reference molar volumes. More... | |
| vector_fp | m_hss_RT |
| Vector containing the species Standard State enthalpies at T = m_tlast and P = m_plast. More... | |
| vector_fp | m_cpss_R |
| Vector containing the species Standard State constant pressure heat capacities at T = m_tlast and P = m_plast. More... | |
| vector_fp | m_gss_RT |
| Vector containing the species Standard State Gibbs functions at T = m_tlast and P = m_plast. More... | |
| vector_fp | m_sss_R |
| Vector containing the species Standard State entropies at T = m_tlast and P = m_plast. More... | |
| vector_fp | m_Vss |
| Vector containing the species standard state volumes at T = m_tlast and P = m_plast. More... | |
| Protected Attributes inherited from ThermoPhase | |
| MultiSpeciesThermo | m_spthermo |
| Pointer to the calculation manager for species reference-state thermodynamic properties. More... | |
| std::vector< const XML_Node * > | m_speciesData |
| Vector of pointers to the species databases. More... | |
| doublereal | m_phi |
| Stored value of the electric potential for this phase. Units are Volts. More... | |
| vector_fp | m_lambdaRRT |
| Vector of element potentials. More... | |
| bool | m_hasElementPotentials |
| Boolean indicating whether there is a valid set of saved element potentials for this phase. More... | |
| bool | m_chargeNeutralityNecessary |
| Boolean indicating whether a charge neutrality condition is a necessity. More... | |
| int | m_ssConvention |
| Contains the standard state convention. More... | |
| doublereal | m_tlast |
| last value of the temperature processed by reference state More... | |
| Protected Attributes inherited from Phase | |
| ValueCache | m_cache |
| Cached for saved calculations within each ThermoPhase. More... | |
| size_t | m_kk |
| Number of species in the phase. More... | |
| size_t | m_ndim |
| Dimensionality of the phase. More... | |
| vector_fp | m_speciesComp |
| Atomic composition of the species. More... | |
| vector_fp | m_speciesCharge |
| Vector of species charges. length m_kk. More... | |
| std::map< std::string, shared_ptr< Species > > | m_species |
| UndefElement::behavior | m_undefinedElementBehavior |
| Flag determining behavior when adding species with an undefined element. More... | |
Detailed Description
Class HMWSoln represents a dilute or concentrated liquid electrolyte phase which obeys the Pitzer formulation for nonideality.
As a prerequisite to the specification of thermodynamic quantities, The concentrations of the ionic species are assumed to obey the electroneutrality condition.
Specification of Species Standard State Properties
The solvent is assumed to be liquid water. A real model for liquid water (IAPWS 1995 formulation) is used as its standard state. All standard state properties for the solvent are based on this real model for water, and involve function calls to the object that handles the real water model, Cantera::WaterPropsIAPWS.
The standard states for solutes are on the unit molality basis. Therefore, in the documentation below, the normal \( o \) superscript is replaced with the \( \triangle \) symbol. The reference state symbol is now \( \triangle, ref \).
It is assumed that the reference state thermodynamics may be obtained by a pointer to a populated species thermodynamic property manager class (see ThermoPhase::m_spthermo). How to relate pressure changes to the reference state thermodynamics is resolved at this level.
For solutes that rely on ThermoPhase::m_spthermo, are assumed to have an incompressible standard state mechanical property. In other words, the molar volumes are independent of temperature and pressure.
For these incompressible, standard states, the molar internal energy is independent of pressure. Since the thermodynamic properties are specified by giving the standard-state enthalpy, the term \( P_0 \hat v\) is subtracted from the specified molar enthalpy to compute the molar internal energy. The entropy is assumed to be independent of the pressure.
The enthalpy function is given by the following relation.
\[ h^\triangle_k(T,P) = h^{\triangle,ref}_k(T) + \tilde{v}_k \left( P - P_{ref} \right) \]
For an incompressible, stoichiometric substance, the molar internal energy is independent of pressure. Since the thermodynamic properties are specified by giving the standard-state enthalpy, the term \( P_{ref} \tilde v\) is subtracted from the specified reference molar enthalpy to compute the molar internal energy.
\[ u^\triangle_k(T,P) = h^{\triangle,ref}_k(T) - P_{ref} \tilde{v}_k \]
The solute standard state heat capacity and entropy are independent of pressure. The solute standard state Gibbs free energy is obtained from the enthalpy and entropy functions.
The current model assumes that an incompressible molar volume for all solutes. The molar volume for the water solvent, however, is obtained from a pure water equation of state, waterSS. Therefore, the water standard state varies with both T and P. It is an error to request standard state water properties at a T and P where the water phase is not a stable phase, i.e., beyond its spinodal curve.
Specification of Solution Thermodynamic Properties
Chemical potentials of the solutes, \( \mu_k \), and the solvent, \( \mu_o \), which are based on the molality form, have the following general format:
\[ \mu_k = \mu^{\triangle}_k(T,P) + R T ln(\gamma_k^{\triangle} \frac{m_k}{m^\triangle}) \]
\[ \mu_o = \mu^o_o(T,P) + RT ln(a_o) \]
where \( \gamma_k^{\triangle} \) is the molality based activity coefficient for species \(k\).
Individual activity coefficients of ions can not be independently measured. Instead, only binary pairs forming electroneutral solutions can be measured. This problem leads to a redundancy in the evaluation of species standard state properties. The redundancy issue is resolved by setting the standard state chemical potential enthalpy, entropy, and volume for the hydrogen ion, H+, to zero, for every temperature and pressure. After this convention is applied, all other standard state properties of ionic species contain meaningful information.
Ionic Strength
Most of the parameterizations within the model use the ionic strength as a key variable. The ionic strength, \( I\) is defined as follows
\[ I = \frac{1}{2} \sum_k{m_k z_k^2} \]
\( m_k \) is the molality of the kth species. \( z_k \) is the charge of the kth species. Note, the ionic strength is a defined units quantity. The molality has defined units of gmol kg-1, and therefore the ionic strength has units of sqrt(gmol/kg).
Specification of the Excess Gibbs Free Energy
Pitzer's formulation may best be represented as a specification of the excess Gibbs free energy, \( G^{ex} \), defined as the deviation of the total Gibbs free energy from that of an ideal molal solution.
\[ G = G^{id} + G^{ex} \]
The ideal molal solution contribution, not equal to an ideal solution contribution and in fact containing a singularity at the zero solvent mole fraction limit, is given below.
\[ G^{id} = n_o \mu^o_o + \sum_{k\ne o} n_k \mu_k^{\triangle} + \tilde{M}_o n_o ( RT (\sum{m_i(\ln(m_i)-1)})) \]
From the excess Gibbs free energy formulation, the activity coefficient expression and the osmotic coefficient expression for the solvent may be defined, by taking the appropriate derivatives. Using this approach guarantees that the entire system will obey the Gibbs-Duhem relations.
Pitzer employs the following general expression for the excess Gibbs free energy
\[ \begin{array}{cclc} \frac{G^{ex}}{\tilde{M}_o n_o RT} &= & \left( \frac{4A_{Debye}I}{3b} \right) \ln(1 + b \sqrt{I}) + 2 \sum_c \sum_a m_c m_a B_{ca} + \sum_c \sum_a m_c m_a Z C_{ca} \\&& + \sum_{c < c'} \sum m_c m_{c'} \left[ 2 \Phi_{c{c'}} + \sum_a m_a \Psi_{c{c'}a} \right] + \sum_{a < a'} \sum m_a m_{a'} \left[ 2 \Phi_{a{a'}} + \sum_c m_c \Psi_{a{a'}c} \right] \\&& + 2 \sum_n \sum_c m_n m_c \lambda_{nc} + 2 \sum_n \sum_a m_n m_a \lambda_{na} + 2 \sum_{n < n'} \sum m_n m_{n'} \lambda_{n{n'}} + \sum_n m^2_n \lambda_{nn} \end{array} \]
a is a subscript over all anions, c is a subscript extending over all cations, and i is a subscript that extends over all anions and cations. n is a subscript that extends only over neutral solute molecules. The second line contains cross terms where cations affect cations and/or cation/anion pairs, and anions affect anions or cation/anion pairs. Note part of the coefficients, \( \Phi_{c{c'}} \) and \( \Phi_{a{a'}} \) stem from the theory of unsymmetrical mixing of electrolytes with different charges. This theory depends on the total ionic strength of the solution, and therefore, \( \Phi_{c{c'}} \) and \( \Phi_{a{a'}} \) will depend on I, the ionic strength. \( B_{ca}\) is a strong function of the total ionic strength, I, of the electrolyte. The rest of the coefficients are assumed to be independent of the molalities or ionic strengths. However, all coefficients are potentially functions of the temperature and pressure of the solution.
A is the Debye-Huckel constant. Its specification is described in its own section below.
\( I\) is the ionic strength of the solution, and is given by:
\[ I = \frac{1}{2} \sum_k{m_k z_k^2} \]
In contrast to several other Debye-Huckel implementations (see DebyeHuckel), the parameter \( b\) in the above equation is a constant that does not vary with respect to ion identity. This is an important simplification as it avoids troubles with satisfaction of the Gibbs-Duhem analysis.
The function \( Z \) is given by
\[ Z = \sum_i m_i \left| z_i \right| \]
The value of \( B_{ca}\) is given by the following function
\[ B_{ca} = \beta^{(0)}_{ca} + \beta^{(1)}_{ca} g(\alpha^{(1)}_{ca} \sqrt{I}) + \beta^{(2)}_{ca} g(\alpha^{(2)}_{ca} \sqrt{I}) \]
where
\[ g(x) = 2 \frac{(1 - (1 + x)\exp[-x])}{x^2} \]
The formulation for \( B_{ca}\) combined with the formulation of the Debye- Huckel term in the eqn. for the excess Gibbs free energy stems essentially from an empirical fit to the ionic strength dependent data based over a wide sampling of binary electrolyte systems. \( C_{ca} \), \( \lambda_{nc} \), \( \lambda_{na} \), \( \lambda_{nn} \), \( \Psi_{c{c'}a} \), \( \Psi_{a{a'}c} \) are experimentally derived coefficients that may have pressure and/or temperature dependencies.
The \( \Phi_{c{c'}} \) and \( \Phi_{a{a'}} \) formulations are slightly more complicated. \( b \) is a universal constant defined to be equal to \( 1.2\ kg^{1/2}\ gmol^{-1/2} \). The exponential coefficient \( \alpha^{(1)}_{ca} \) is usually fixed at \( \alpha^{(1)}_{ca} = 2.0\ kg^{1/2} gmol^{-1/2}\) except for 2-2 electrolytes, while other parameters were fit to experimental data. For 2-2 electrolytes, \( \alpha^{(1)}_{ca} = 1.4\ kg^{1/2}\ gmol^{-1/2}\) is used in combination with either \( \alpha^{(2)}_{ca} = 12\ kg^{1/2}\ gmol^{-1/2}\) or \( \alpha^{(2)}_{ca} = k A_\psi \), where k is a constant. For electrolytes other than 2-2 electrolytes the \( \beta^{(2)}_{ca} g(\alpha^{(2)}_{ca} \sqrt{I}) \) term is not used in the fitting procedure; it is only used for divalent metal solfates and other high-valence electrolytes which exhibit significant association at low ionic strengths.
The \( \beta^{(0)}_{ca} \), \( \beta^{(1)}_{ca}\), \( \beta^{(2)}_{ca} \), and \( C_{ca} \) binary coefficients are referred to as ion- interaction or Pitzer parameters. These Pitzer parameters may vary with temperature and pressure but they do not depend on the ionic strength. Their values and temperature derivatives of their values have been tabulated for a range of electrolytes
The \( \Phi_{c{c'}} \) and \( \Phi_{a{a'}} \) contributions, which capture cation-cation and anion-anion interactions, also have an ionic strength dependence.
Ternary contributions \( \Psi_{c{c'}a} \) and \( \Psi_{a{a'}c} \) have been measured also for some systems. The success of the Pitzer method lies in its ability to model nonlinear activity coefficients of complex multicomponent systems with just binary and minor ternary contributions, which can be independently measured in binary or ternary subsystems.
Multicomponent Activity Coefficients for Solutes
The formulas for activity coefficients of solutes may be obtained by taking the following derivative of the excess Gibbs Free Energy formulation described above:
\[ \ln(\gamma_k^\triangle) = \frac{d\left( \frac{G^{ex}}{M_o n_o RT} \right)}{d(m_k)}\Bigg|_{n_i} \]
In the formulas below the following conventions are used. The subscript M refers to a particular cation. The subscript X refers to a particular anion, whose activity is being currently evaluated. the subscript a refers to a summation over all anions in the solution, while the subscript c refers to a summation over all cations in the solutions.
The activity coefficient for a particular cation M is given by
\[ \ln(\gamma_M^\triangle) = -z_M^2(F) + \sum_a m_a \left( 2 B_{Ma} + Z C_{Ma} \right) + z_M \left( \sum_a \sum_c m_a m_c C_{ca} \right) + \sum_c m_c \left[ 2 \Phi_{Mc} + \sum_a m_a \Psi_{Mca} \right] + \sum_{a < a'} \sum m_a m_{a'} \Psi_{Ma{a'}} + 2 \sum_n m_n \lambda_{nM} \]
The activity coefficient for a particular anion X is given by
\[ \ln(\gamma_X^\triangle) = -z_X^2(F) + \sum_a m_c \left( 2 B_{cX} + Z C_{cX} \right) + \left|z_X \right| \left( \sum_a \sum_c m_a m_c C_{ca} \right) + \sum_a m_a \left[ 2 \Phi_{Xa} + \sum_c m_c \Psi_{cXa} \right] + \sum_{c < c'} \sum m_c m_{c'} \Psi_{c{c'}X} + 2 \sum_n m_n \lambda_{nM} \]
where the function \( F \) is given by
\[ F = - A_{\phi} \left[ \frac{\sqrt{I}}{1 + b \sqrt{I}} + \frac{2}{b} \ln{\left(1 + b\sqrt{I}\right)} \right] + \sum_a \sum_c m_a m_c B'_{ca} + \sum_{c < c'} \sum m_c m_{c'} \Phi'_{c{c'}} + \sum_{a < a'} \sum m_a m_{a'} \Phi'_{a{a'}} \]
We have employed the definition of \( A_{\phi} \), also used by Pitzer which is equal to
\[ A_{\phi} = \frac{A_{Debye}}{3} \]
In the above formulas, \( \Phi'_{c{c'}} \) and \( \Phi'_{a{a'}} \) are the ionic strength derivatives of \( \Phi_{c{c'}} \) and \( \Phi_{a{a'}} \), respectively.
The function \( B'_{MX} \) is defined as:
\[ B'_{MX} = \left( \frac{\beta^{(1)}_{MX} h(\alpha^{(1)}_{MX} \sqrt{I})}{I} \right) \left( \frac{\beta^{(2)}_{MX} h(\alpha^{(2)}_{MX} \sqrt{I})}{I} \right) \]
where \( h(x) \) is defined as
\[ h(x) = g'(x) \frac{x}{2} = \frac{2\left(1 - \left(1 + x + \frac{x^2}{2} \right)\exp(-x) \right)}{x^2} \]
The activity coefficient for neutral species N is given by
\[ \ln(\gamma_N^\triangle) = 2 \left( \sum_i m_i \lambda_{iN}\right) \]
Activity of the Water Solvent
The activity for the solvent water, \( a_o \), is not independent and must be determined either from the Gibbs-Duhem relation or from taking the appropriate derivative of the same excess Gibbs free energy function as was used to formulate the solvent activity coefficients. Pitzer's description follows the later approach to derive a formula for the osmotic coefficient, \( \phi \).
\[ \phi - 1 = - \left( \frac{d\left(\frac{G^{ex}}{RT} \right)}{d(\tilde{M}_o n_o)} \right) \frac{1}{\sum_{i \ne 0} m_i} \]
The osmotic coefficient may be related to the water activity by the following relation:
\[ \phi = - \frac{1}{\tilde{M}_o \sum_{i \neq o} m_i} \ln(a_o) = - \frac{n_o}{\sum_{i \neq o}n_i} \ln(a_o) \]
The result is the following
\[ \begin{array}{ccclc} \phi - 1 &= & \frac{2}{\sum_{i \ne 0} m_i} \bigg[ & - A_{\phi} \frac{I^{3/2}}{1 + b \sqrt{I}} + \sum_c \sum_a m_c m_a \left( B^{\phi}_{ca} + Z C_{ca}\right) \\&&& + \sum_{c < c'} \sum m_c m_{c'} \left[ \Phi^{\phi}_{c{c'}} + \sum_a m_a \Psi_{c{c'}a} \right] + \sum_{a < a'} \sum m_a m_{a'} \left[ \Phi^{\phi}_{a{a'}} + \sum_c m_c \Psi_{a{a'}c} \right] \\&&& + \sum_n \sum_c m_n m_c \lambda_{nc} + \sum_n \sum_a m_n m_a \lambda_{na} + \sum_{n < n'} \sum m_n m_{n'} \lambda_{n{n'}} + \frac{1}{2} \left( \sum_n m^2_n \lambda_{nn}\right) \bigg] \end{array} \]
It can be shown that the expression
\[ B^{\phi}_{ca} = \beta^{(0)}_{ca} + \beta^{(1)}_{ca} \exp{(- \alpha^{(1)}_{ca} \sqrt{I})} + \beta^{(2)}_{ca} \exp{(- \alpha^{(2)}_{ca} \sqrt{I} )} \]
is consistent with the expression \( B_{ca} \) in the \( G^{ex} \) expression after carrying out the derivative wrt \( m_M \).
Also taking into account that \( {\Phi}_{c{c'}} \) and \( {\Phi}_{a{a'}} \) has an ionic strength dependence.
\[ \Phi^{\phi}_{c{c'}} = {\Phi}_{c{c'}} + I \frac{d{\Phi}_{c{c'}}}{dI} \]
\[ \Phi^{\phi}_{a{a'}} = \Phi_{a{a'}} + I \frac{d\Phi_{a{a'}}}{dI} \]
Temperature and Pressure Dependence of the Pitzer Parameters
In general most of the coefficients introduced in the previous section may have a temperature and pressure dependence. The temperature and pressure dependence of these coefficients strongly influence the value of the excess Enthalpy and excess Volumes of Pitzer solutions. Therefore, these are readily measurable quantities. HMWSoln provides several different methods for putting these dependencies into the coefficients. HMWSoln has an implementation described by Silverter and Pitzer (1977), which was used to fit experimental data for NaCl over an extensive range, below the critical temperature of water. They found a temperature functional form for fitting the 3 following coefficients that describe the Pitzer parameterization for a single salt to be adequate to describe how the excess Gibbs free energy values for the binary salt changes with respect to temperature. The following functional form was used to fit the temperature dependence of the Pitzer Coefficients for each cation - anion pair, M X.
\[ \beta^{(0)}_{MX} = q^{b0}_0 + q^{b0}_1 \left( T - T_r \right) + q^{b0}_2 \left( T^2 - T_r^2 \right) + q^{b0}_3 \left( \frac{1}{T} - \frac{1}{T_r}\right) + q^{b0}_4 \ln \left( \frac{T}{T_r} \right) \]
\[ \beta^{(1)}_{MX} = q^{b1}_0 + q^{b1}_1 \left( T - T_r \right) + q^{b1}_{2} \left( T^2 - T_r^2 \right) \]
\[ C^{\phi}_{MX} = q^{Cphi}_0 + q^{Cphi}_1 \left( T - T_r \right) + q^{Cphi}_2 \left( T^2 - T_r^2 \right) + q^{Cphi}_3 \left( \frac{1}{T} - \frac{1}{T_r}\right) + q^{Cphi}_4 \ln \left( \frac{T}{T_r} \right) \]
where
\[ C^{\phi}_{MX} = 2 {\left| z_M z_X \right|}^{1/2} C_{MX} \]
In later papers, Pitzer has added additional temperature dependencies to all of the other remaining second and third order virial coefficients. Some of these dependencies are justified and motivated by theory. Therefore, a formalism wherein all of the coefficients in the base theory have temperature dependencies associated with them has been implemented within the HMWSoln object. Much of the formalism, however, has been unexercised.
In the HMWSoln object, the temperature dependence of the Pitzer parameters are specified in the following way.
- PIZTER_TEMP_CONSTANT - string name "CONSTANT"
- Assumes that all coefficients are independent of temperature and pressure
- PIZTER_TEMP_COMPLEX1 - string name "COMPLEX" or "COMPLEX1"
- Uses the full temperature dependence for the \(\beta^{(0)}_{MX} \) (5 coeffs), the \(\beta^{(1)}_{MX} \) (3 coeffs), and \( C^{\phi}_{MX} \) (5 coeffs) parameters described above.
- PITZER_TEMP_LINEAR - string name "LINEAR"
- Uses just the temperature dependence for the \(\beta^{(0)}_{MX} \), the \(\beta^{(1)}_{MX} \), and \( C^{\phi}_{MX} \) coefficients described above. There are 2 coefficients for each term.
The temperature dependence is specified in an attributes field in the activityCoefficients XML block, called TempModel. Permissible values for that attribute are CONSTANT, COMPLEX1, and LINEAR.
The specification of the binary interaction between a cation and an anion is given by the coefficients, \( B_{MX}\) and \( C_{MX}\) The specification of \( B_{MX}\) is a function of \(\beta^{(0)}_{MX} \), \(\beta^{(1)}_{MX} \), \(\beta^{(2)}_{MX} \), \(\alpha^{(1)}_{MX} \), and \(\alpha^{(2)}_{MX} \). \( C_{MX}\) is calculated from \(C^{\phi}_{MX} \) from the formula above. All of the underlying coefficients are specified in the XML element block binarySaltParameters, which has the attribute cation and anion to identify the interaction. XML elements named beta0, beta1, beta2, Cphi, Alpha1, Alpha2 within each binarySaltParameters block specify the parameters. Within each of these blocks multiple parameters describing temperature or pressure dependence are serially listed in the order that they appear in the equation in this document. An example of the beta0 block that fits the COMPLEX1 temperature dependence given above is
The parameters for \( \beta^{(0)}\) fit the following equation:
\[ \beta^{(0)} = q_0^{{\beta}0} + q_1^{{\beta}0} \left( T - T_r \right) + q_2^{{\beta}0} \left( T^2 - T_r^2 \right) + q_3^{{\beta}0} \left( \frac{1}{T} - \frac{1}{T_r} \right) + q_4^{{\beta}0} \ln \left( \frac{T}{T_r} \right) \]
This same COMPLEX1 temperature dependence given above is used for the following parameters: \( \beta^{(0)}_{MX} \), \( \beta^{(1)}_{MX} \), \( \beta^{(2)}_{MX} \), \( \Theta_{cc'} \), \(\Theta_{aa'} \), \( \Psi_{c{c'}a} \) and \( \Psi_{ca{a'}} \).
Like-Charged Binary Ion Parameters and the Mixing Parameters
The previous section contained the functions, \( \Phi_{c{c'}} \), \( \Phi_{a{a'}} \) and their derivatives wrt the ionic strength, \( \Phi'_{c{c'}} \) and \( \Phi'_{a{a'}} \). Part of these terms come from theory.
Since like charged ions repel each other and are generally not near each other, the virial coefficients for same-charged ions are small. However, Pitzer doesn't ignore these in his formulation. Relatively larger and longer range terms between like-charged ions exist however, which appear only for unsymmetrical mixing of same-sign charged ions with different charges. \( \Phi_{ij} \), where \( ij \) is either \( a{a'} \) or \( c{c'} \) is given by
\[ {\Phi}_{ij} = \Theta_{ij} + \,^E \Theta_{ij}(I) \]
\( \Theta_{ij} \) is the small virial coefficient expansion term. Dependent in general on temperature and pressure, its ionic strength dependence is ignored in Pitzer's approach. \( \,^E\Theta_{ij}(I) \) accounts for the electrostatic unsymmetrical mixing effects and is dependent only on the charges of the ions i, j, the total ionic strength and on the dielectric constant and density of the solvent. This seems to be a relatively well- documented part of the theory. They theory below comes from Pitzer summation (Pitzer) in the appendix. It's also mentioned in Bethke's book (Bethke), and the equations are summarized in Harvie & Weare (1980). Within the code, \( \,^E\Theta_{ij}(I) \) is evaluated according to the algorithm described in Appendix B [Pitzer] as
\[ \,^E\Theta_{ij}(I) = \left( \frac{z_i z_j}{4I} \right) \left( J(x_{ij}) - \frac{1}{2} J(x_{ii}) - \frac{1}{2} J(x_{jj}) \right) \]
where \( x_{ij} = 6 z_i z_j A_{\phi} \sqrt{I} \) and
\[ J(x) = \frac{1}{x} \int_0^{\infty}{\left( 1 + q + \frac{1}{2} q^2 - e^q \right) y^2 dy} \]
and \( q = - (\frac{x}{y}) e^{-y} \). \( J(x) \) is evaluated by numerical integration.
The \( \Theta_{ij} \) term is a constant that is specified by the XML element thetaCation and thetaAnion, which has the attribute cation1, cation2 and anion1, anion2 respectively to identify the interaction. No temperature or pressure dependence of this parameter is currently allowed. An example of the block is presented below.
Ternary Pitzer Parameters
The \( \Psi_{c{c'}a} \) and \( \Psi_{ca{a'}} \) terms represent ternary interactions between two cations and an anion and two anions and a cation, respectively. In Pitzer's implementation these terms are usually small in absolute size. Currently these parameters do not have any dependence on temperature, pressure, or ionic strength.
Their values are input using the XML element psiCommonCation and psiCommonAnion. The species id's are specified in attribute fields in the XML element. The fields cation, anion1, and anion2 are used for psiCommonCation. The fields anion, cation1 and cation2 are used for psiCommonAnion. An example block is given below. The Theta field below is a duplicate of the thetaAnion field mentioned above. The two fields are input into the same block for convenience, and because their data are highly correlated, in practice. It is an error for the two blocks to specify different information about thetaAnion (or thetaCation) in different blocks. It's ok to specify duplicate but consistent information in multiple blocks.
Treatment of Neutral Species
Binary virial-coefficient-like interactions between two neutral species may be specified in the \( \lambda_{mn} \) terms that appear in the formulas above. Currently these interactions are independent of temperature, pressure, and ionic strength. Also, currently, the neutrality of the species are not checked. Therefore, this interaction may involve charged species in the solution as well. The identity of the species is specified by the species1 and species2 attributes to the XML lambdaNeutral node. These terms are symmetrical; species1 and species2 may be reversed and the term will be the same. An example is given below.
Example of the Specification of Parameters for the Activity Coefficients
An example is given below.
An example activityCoefficients XML block for this formulation is supplied below
Specification of the Debye-Huckel Constant
In the equations above, the formula for \( A_{Debye} \) is needed. The HMWSoln object uses two methods for specifying these quantities. The default method is to assume that \( A_{Debye} \) is a constant, given in the initialization process, and stored in the member double, m_A_Debye. Optionally, a full water treatment may be employed that makes \( A_{Debye} \) a full function of T and P and creates nontrivial entries for the excess heat capacity, enthalpy, and excess volumes of solution.
\[ A_{Debye} = \frac{F e B_{Debye}}{8 \pi \epsilon R T} {\left( C_o \tilde{M}_o \right)}^{1/2} \]
where
\[ B_{Debye} = \frac{F} {{(\frac{\epsilon R T}{2})}^{1/2}} \]
Therefore:
\[ A_{Debye} = \frac{1}{8 \pi} {\left(\frac{2 N_a \rho_o}{1000}\right)}^{1/2} {\left(\frac{N_a e^2}{\epsilon R T }\right)}^{3/2} \]
Units = sqrt(kg/gmol)
where
- \( N_a \) is Avogadro's number
- \( \rho_w \) is the density of water
- \( e \) is the electronic charge
- \( \epsilon = K \epsilon_o \) is the permittivity of water
- \( K \) is the dielectric constant of water,
- \( \epsilon_o \) is the permittivity of free space.
- \( \rho_o \) is the density of the solvent in its standard state.
Nominal value at 298 K and 1 atm = 1.172576 (kg/gmol)^(1/2) based on:
- \( \epsilon / \epsilon_0 \) = 78.54 (water at 25C)
- T = 298.15 K
- B_Debye = 3.28640E9 (kg/gmol)^(1/2) / m
An example of a fixed value implementation is given below.
An example of a variable value implementation within the HMWSoln object is given below. The model attribute, "water", triggers the full implementation.
Temperature and Pressure Dependence of the Activity Coefficients
Temperature dependence of the activity coefficients leads to nonzero terms for the excess enthalpy and entropy of solution. This means that the partial molar enthalpies, entropies, and heat capacities are all non-trivial to compute. The following formulas are used.
The partial molar enthalpy, \( \bar s_k(T,P) \):
\[ \bar h_k(T,P) = h^{\triangle}_k(T,P) - R T^2 \frac{d \ln(\gamma_k^\triangle)}{dT} \]
The solvent partial molar enthalpy is equal to
\[ \bar h_o(T,P) = h^{o}_o(T,P) - R T^2 \frac{d \ln(a_o)}{dT} = h^{o}_o(T,P) + R T^2 (\sum_{k \neq o} m_k) \tilde{M_o} (\frac{d \phi}{dT}) \]
The partial molar entropy, \( \bar s_k(T,P) \):
\[ \bar s_k(T,P) = s^{\triangle}_k(T,P) - R \ln( \gamma^{\triangle}_k \frac{m_k}{m^{\triangle}})) - R T \frac{d \ln(\gamma^{\triangle}_k) }{dT} \]
\[ \bar s_o(T,P) = s^o_o(T,P) - R \ln(a_o) - R T \frac{d \ln(a_o)}{dT} \]
The partial molar heat capacity, \( C_{p,k}(T,P)\):
\[ \bar C_{p,k}(T,P) = C^{\triangle}_{p,k}(T,P) - 2 R T \frac{d \ln( \gamma^{\triangle}_k)}{dT} - R T^2 \frac{d^2 \ln(\gamma^{\triangle}_k) }{{dT}^2} \]
\[ \bar C_{p,o}(T,P) = C^o_{p,o}(T,P) - 2 R T \frac{d \ln(a_o)}{dT} - R T^2 \frac{d^2 \ln(a_o)}{{dT}^2} \]
The pressure dependence of the activity coefficients leads to non-zero terms for the excess Volume of the solution. Therefore, the partial molar volumes are functions of the pressure derivatives of the activity coefficients.
\[ \bar V_k(T,P) = V^{\triangle}_k(T,P) + R T \frac{d \ln(\gamma^{\triangle}_k) }{dP} \]
\[ \bar V_o(T,P) = V^o_o(T,P) + R T \frac{d \ln(a_o)}{dP} \]
The majority of work for these functions take place in the internal routines that calculate the first and second derivatives of the log of the activity coefficients wrt temperature, s_update_dlnMolalityActCoeff_dT(), s_update_d2lnMolalityActCoeff_dT2(), and the first derivative of the log activity coefficients wrt pressure, s_update_dlnMolalityActCoeff_dP().
Application within Kinetics Managers
For the time being, we have set the standard concentration for all solute species in this phase equal to the default concentration of the solvent at the system temperature and pressure multiplied by Mnaught (kg solvent / gmol solvent). The solvent standard concentration is just equal to its standard state concentration.
This means that the kinetics operator essentially works on an generalized concentration basis (kmol / m3), with units for the kinetic rate constant specified as if all reactants (solvent or solute) are on a concentration basis (kmol /m3). The concentration will be modified by the activity coefficients.
For example, a bulk-phase binary reaction between liquid solute species j and k, producing a new liquid solute species l would have the following equation for its rate of progress variable, \( R^1 \), which has units of kmol m-3 s-1.
\[ R^1 = k^1 C_j^a C_k^a = k^1 (C^o_o \tilde{M}_o a_j) (C^o_o \tilde{M}_o a_k) \]
where
\[ C_j^a = C^o_o \tilde{M}_o a_j \quad and \quad C_k^a = C^o_o \tilde{M}_o a_k \]
\( C_j^a \) is the activity concentration of species j, and \( C_k^a \) is the activity concentration of species k. \( C^o_o \) is the concentration of water at 298 K and 1 atm. \( \tilde{M}_o \) has units of kg solvent per gmol solvent and is equal to
\[ \tilde{M}_o = \frac{M_o}{1000} \]
\( a_j \) is the activity of species j at the current temperature and pressure and concentration of the liquid phase is given by the molality based activity coefficient multiplied by the molality of the jth species.
\[ a_j = \gamma_j^\triangle m_j = \gamma_j^\triangle \frac{n_j}{\tilde{M}_o n_o} \]
\(k^1 \) has units of m^3/kmol/s.
Therefore the generalized activity concentration of a solute species has the following form
\[ C_j^a = C^o_o \frac{\gamma_j^\triangle n_j}{n_o} \]
The generalized activity concentration of the solvent has the same units, but it's a simpler form
\[ C_o^a = C^o_o a_o \]
The reverse rate constant can then be obtained from the law of microscopic reversibility and the equilibrium expression for the system.
\[ \frac{a_j a_k}{ a_l} = K^{o,1} = \exp(\frac{\mu^o_l - \mu^o_j - \mu^o_k}{R T} ) \]
\( K^{o,1} \) is the dimensionless form of the equilibrium constant.
\[ R^{-1} = k^{-1} C_l^a = k^{-1} (C_o \tilde{M}_o a_l) \]
where
\[ k^{-1} = k^1 K^{o,1} C_o \tilde{M}_o \]
\( k^{-1} \) has units of 1/s.
Note, this treatment may be modified in the future, as events dictate.
Instantiation of the Class
The constructor for this phase is now located in the default ThermoFactory for Cantera. The following code snippet may be used to initialize the phase using the default construction technique within Cantera.
A new HMWSoln object may be created by the following code snippets:
or
or by the following call to importPhase():
XML Example
The phase model name for this is called StoichSubstance. It must be supplied as the model attribute of the thermo XML element entry. Within the phase XML block, the density of the phase must be specified. An example of an XML file this phase is given below.
Constructor & Destructor Documentation
◆ HMWSoln() [1/3]
| HMWSoln | ( | ) |
Default Constructor.
Definition at line 30 of file HMWSoln.cpp.
◆ HMWSoln() [2/3]
| HMWSoln | ( | const std::string & | inputFile, |
| const std::string & | id = "" |
||
| ) |
Construct and initialize an HMWSoln ThermoPhase object directly from an ASCII input file.
This constructor is a shell that calls the routine initThermo(), with a reference to the XML database to get the info for the phase.
- Parameters
-
inputFile Name of the input file containing the phase XML data to set up the object id ID of the phase in the input file. Defaults to the empty string.
Definition at line 68 of file HMWSoln.cpp.
◆ HMWSoln() [3/3]
Construct and initialize an HMWSoln ThermoPhase object directly from an XML database.
- Parameters
-
phaseRef XML phase node containing the description of the phase id id attribute containing the name of the phase. (default is the empty string)
Definition at line 103 of file HMWSoln.cpp.
Member Function Documentation
◆ type()
|
inlinevirtual |
String indicating the thermodynamic model implemented.
Usually corresponds to the name of the derived class, less any suffixes such as "Phase", TP", "VPSS", etc.
Reimplemented from ThermoPhase.
◆ enthalpy_mole()
|
virtual |
Molar enthalpy. Units: J/kmol.
Molar enthalpy of the solution. Units: J/kmol. (HKM -> Bump up to Parent object)
Reimplemented from ThermoPhase.
Definition at line 140 of file HMWSoln.cpp.
References HMWSoln::getPartialMolarEnthalpies(), HMWSoln::m_tmpV, and Phase::mean_X().
◆ relative_enthalpy()
|
virtual |
Excess molar enthalpy of the solution from the mixing process.
Units: J/ kmol.
Note this is kmol of the total solution.
Definition at line 146 of file HMWSoln.cpp.
References VPStandardStateTP::getEnthalpy_RT(), HMWSoln::getPartialMolarEnthalpies(), HMWSoln::m_gamma_tmp, Phase::m_kk, HMWSoln::m_tmpV, Phase::mean_X(), and ThermoPhase::RT().
Referenced by HMWSoln::relative_molal_enthalpy().
◆ relative_molal_enthalpy()
|
virtual |
Excess molar enthalpy of the solution from the mixing process on a molality basis.
Units: J/ (kmol add salt).
Note this is kmol of the guessed at salt composition
Definition at line 158 of file HMWSoln.cpp.
References Phase::charge(), Phase::getMoleFractions(), Phase::m_kk, HMWSoln::m_tmpV, Cantera::npos, and HMWSoln::relative_enthalpy().
◆ entropy_mole()
|
virtual |
Molar entropy. Units: J/kmol/K.
Molar entropy of the solution. Units: J/kmol/K. For an ideal, constant partial molar volume solution mixture with pure species phases which exhibit zero volume expansivity:
\[ \hat s(T, P, X_k) = \sum_k X_k \hat s^0_k(T) - \hat R \sum_k X_k log(X_k) \]
The reference-state pure-species entropies \( \hat s^0_k(T,p_{ref}) \) are computed by the species thermodynamic property manager. The pure species entropies are independent of temperature since the volume expansivities are equal to zero.
- See also
- MultiSpeciesThermo
(HKM -> Bump up to Parent object)
Reimplemented from ThermoPhase.
Definition at line 198 of file HMWSoln.cpp.
References HMWSoln::getPartialMolarEntropies(), HMWSoln::m_tmpV, and Phase::mean_X().
◆ gibbs_mole()
|
virtual |
Molar Gibbs function. Units: J/kmol.
(HKM -> Bump up to Parent object)
Reimplemented from ThermoPhase.
Definition at line 204 of file HMWSoln.cpp.
References HMWSoln::getChemPotentials(), HMWSoln::m_tmpV, and Phase::mean_X().
◆ cp_mole()
|
virtual |
Molar heat capacity at constant pressure. Units: J/kmol/K.
Reimplemented from ThermoPhase.
Definition at line 210 of file HMWSoln.cpp.
References HMWSoln::getPartialMolarCp(), HMWSoln::m_tmpV, and Phase::mean_X().
◆ cv_mole()
|
virtual |
Molar heat capacity at constant volume. Units: J/kmol/K.
(HKM -> Bump up to Parent object)
Reimplemented from ThermoPhase.
Definition at line 216 of file HMWSoln.cpp.
References ThermoPhase::isothermalCompressibility().
◆ calcDensity()
|
protectedvirtual |
Calculate the density of the mixture using the partial molar volumes and mole fractions as input.
In this equation of state implementation, the density is a function only of the mole fractions. Therefore, it can't be an independent variable. Instead, the pressure is used as the independent variable. Functions which try to set the thermodynamic state by calling setDensity() may cause an exception to be thrown.The formula for this is
\[ \rho = \frac{\sum_k{X_k W_k}}{\sum_k{X_k V_k}} \]
where \(X_k\) are the mole fractions, \(W_k\) are the molecular weights, and \(V_k\) are the pure species molar volumes.
Note, the basis behind this formula is that in an ideal solution the partial molar volumes are equal to the pure species molar volumes. We have additionally specified in this class that the pure species molar volumes are independent of temperature and pressure.
NOTE: This is a non-virtual function, which is not a member of the ThermoPhase base class.
Reimplemented from VPStandardStateTP.
Definition at line 228 of file HMWSoln.cpp.
References ValueCache::getId(), HMWSoln::getPartialMolarVolumes(), ValueCache::getScalar(), Phase::m_cache, HMWSoln::m_tmpV, Phase::mean_X(), Phase::meanMolecularWeight(), VPStandardStateTP::pressure(), Phase::setDensity(), Phase::stateMFNumber(), Phase::temperature(), and CachedValue< T >::validate().
◆ setDensity()
|
virtual |
Set the internally stored density (kg/m^3) of the phase.
Overridden setDensity() function is necessary because the density is not an independent variable.
This function will now throw an error condition.
Note, in general, setting the phase density is now a nonlinear calculation. P and T are the fundamental variables. This routine should be revamped to do the nonlinear problem.
- Todo:
May have to adjust the strategy here to make the eos for these materials slightly compressible, in order to create a condition where the density is a function of the pressure.
Now have a compressible ss equation for liquid water. Therefore, this phase is compressible. May still want to change the independent variable however.
- Parameters
-
rho Input density (kg/m^3).
Reimplemented from Phase.
Definition at line 243 of file HMWSoln.cpp.
References Phase::density().
◆ setMolarDensity()
|
virtual |
Set the internally stored molar density (kmol/m^3) for the phase.
Overridden setMolarDensity() function is necessary because of the underlying water model.
This function will now throw an error condition if the input isn't exactly equal to the current molar density.
- Parameters
-
conc Input molar density (kmol/m^3).
Reimplemented from Phase.
Definition at line 252 of file HMWSoln.cpp.
◆ getActivityConcentrations()
|
virtual |
This method returns an array of generalized activity concentrations.
The generalized activity concentrations, \( C_k^a\), are defined such that \( a_k = C^a_k / C^0_k, \) where \( C^0_k \) is a standard concentration defined below. These generalized concentrations are used by kinetics manager classes to compute the forward and reverse rates of elementary reactions.
The generalized activity concentration of a solute species has the following form
\[ C_j^a = C^o_o \frac{\gamma_j^\triangle n_j}{n_o} \]
The generalized activity concentration of the solvent has the same units, but it's a simpler form
\[ C_o^a = C^o_o a_o \]
- Parameters
-
c Array of generalized concentrations. The units are kmol m-3 for both the solvent and the solute species
Reimplemented from MolalityVPSSTP.
Definition at line 260 of file HMWSoln.cpp.
References HMWSoln::getActivities(), Phase::m_kk, and HMWSoln::standardConcentration().
◆ standardConcentration()
|
virtual |
Return the standard concentration for the kth species.
The standard concentration \( C^0_k \) used to normalize the activity (i.e., generalized) concentration for use
We have set the standard concentration for all solute species in this phase equal to the default concentration of the solvent at the system temperature and pressure multiplied by Mnaught (kg solvent / gmol solvent). The solvent standard concentration is just equal to its standard state concentration.
\[ C_j^0 = C^o_o \tilde{M}_o \quad and C_o^0 = C^o_o \]
The consequence of this is that the standard concentrations have unequal units between the solvent and the solute. However, both the solvent and the solute activity concentrations will have the same units of kmol/kg^3.
This means that the kinetics operator essentially works on an generalized concentration basis (kmol / m3), with units for the kinetic rate constant specified as if all reactants (solvent or solute) are on a concentration basis (kmol /m3). The concentration will be modified by the activity coefficients.
For example, a bulk-phase binary reaction between liquid solute species j and k, producing a new liquid solute species l would have the following equation for its rate of progress variable, \( R^1 \), which has units of kmol m-3 s-1.
\[ R^1 = k^1 C_j^a C_k^a = k^1 (C^o_o \tilde{M}_o a_j) (C^o_o \tilde{M}_o a_k) \]
where
\[ C_j^a = C^o_o \tilde{M}_o a_j \quad and \quad C_k^a = C^o_o \tilde{M}_o a_k \]
\( C_j^a \) is the activity concentration of species j, and \( C_k^a \) is the activity concentration of species k. \( C^o_o \) is the concentration of water at 298 K and 1 atm. \( \tilde{M}_o \) has units of kg solvent per gmol solvent and is equal to
\[ \tilde{M}_o = \frac{M_o}{1000} \]
\( a_j \) is the activity of species j at the current temperature and pressure and concentration of the liquid phase is given by the molality based activity coefficient multiplied by the molality of the jth species.
\[ a_j = \gamma_j^\triangle m_j = \gamma_j^\triangle \frac{n_j}{\tilde{M}_o n_o} \]
\(k^1 \) has units of m^3/kmol/s.
Therefore the generalized activity concentration of a solute species has the following form
\[ C_j^a = C^o_o \frac{\gamma_j^\triangle n_j}{n_o} \]
The generalized activity concentration of the solvent has the same units, but it's a simpler form
\[ C_o^a = C^o_o a_o \]
- Parameters
-
k Optional parameter indicating the species. The default is to assume this refers to species 0.
- Returns
- the standard Concentration in units of m^3/kmol.
- Parameters
-
k Species index
Reimplemented from MolalityVPSSTP.
Definition at line 273 of file HMWSoln.cpp.
References VPStandardStateTP::getStandardVolumes(), MolalityVPSSTP::m_Mnaught, and HMWSoln::m_tmpV.
Referenced by HMWSoln::getActivityConcentrations().
◆ getActivities()
|
virtual |
Get the array of non-dimensional activities at the current solution temperature, pressure, and solution concentration.
We resolve this function at this level by calling on the activityConcentration function. However, derived classes may want to override this default implementation.
(note solvent is on molar scale).
- Parameters
-
ac Output vector of activities. Length: m_kk.
Reimplemented from MolalityVPSSTP.
Definition at line 283 of file HMWSoln.cpp.
References Phase::m_kk, HMWSoln::m_lnActCoeffMolal_Scaled, MolalityVPSSTP::m_molalities, Phase::moleFraction(), and VPStandardStateTP::updateStandardStateThermo().
Referenced by HMWSoln::getActivityConcentrations().
◆ getChemPotentials()
|
virtual |
Get the species chemical potentials. Units: J/kmol.
This function returns a vector of chemical potentials of the species in solution.
\[ \mu_k = \mu^{\triangle}_k(T,P) + R T ln(\gamma_k^{\triangle} m_k) \]
- Parameters
-
mu Output vector of species chemical potentials. Length: m_kk. Units: J/kmol
Reimplemented from ThermoPhase.
Definition at line 312 of file HMWSoln.cpp.
References VPStandardStateTP::getStandardChemPotentials(), Phase::m_kk, HMWSoln::m_lnActCoeffMolal_Scaled, MolalityVPSSTP::m_molalities, Phase::moleFraction(), ThermoPhase::RT(), and Cantera::SmallNumber.
Referenced by HMWSoln::gibbs_mole().
◆ getPartialMolarEnthalpies()
|
virtual |
Returns an array of partial molar enthalpies for the species in the mixture.
Units (J/kmol)
For this phase, the partial molar enthalpies are equal to the standard state enthalpies modified by the derivative of the molality-based activity coefficient wrt temperature
\[ \bar h_k(T,P) = h^{\triangle}_k(T,P) - R T^2 \frac{d \ln(\gamma_k^\triangle)}{dT} \]
The solvent partial molar enthalpy is equal to
\[ \bar h_o(T,P) = h^{o}_o(T,P) - R T^2 \frac{d \ln(a_o)}{dT} = h^{o}_o(T,P) + R T^2 (\sum_{k \neq o} m_k) \tilde{M_o} (\frac{d \phi}{dT}) \]
- Parameters
-
hbar Output vector of species partial molar enthalpies. Length: m_kk. units are J/kmol.
Reimplemented from ThermoPhase.
Definition at line 332 of file HMWSoln.cpp.
References VPStandardStateTP::getEnthalpy_RT(), HMWSoln::m_dlnActCoeffMolaldT_Scaled, Phase::m_kk, ThermoPhase::RT(), HMWSoln::s_update_dlnMolalityActCoeff_dT(), and Phase::temperature().
Referenced by HMWSoln::enthalpy_mole(), and HMWSoln::relative_enthalpy().
◆ getPartialMolarEntropies()
|
virtual |
Returns an array of partial molar entropies of the species in the solution.
Units: J/kmol/K.
Maxwell's equations provide an answer for how calculate this (p.215 Smith and Van Ness)
d(chemPot_i)/dT = -sbar_i
For this phase, the partial molar entropies are equal to the SS species entropies plus the ideal solution contribution plus complicated functions of the temperature derivative of the activity coefficients.
\[ \bar s_k(T,P) = s^{\triangle}_k(T,P) - R \ln( \gamma^{\triangle}_k \frac{m_k}{m^{\triangle}})) - R T \frac{d \ln(\gamma^{\triangle}_k) }{dT} \]
\[ \bar s_o(T,P) = s^o_o(T,P) - R \ln(a_o) - R T \frac{d \ln(a_o)}{dT} \]
- Parameters
-
sbar Output vector of species partial molar entropies. Length = m_kk. units are J/kmol/K.
Reimplemented from ThermoPhase.
Definition at line 351 of file HMWSoln.cpp.
References Cantera::GasConstant, VPStandardStateTP::getEntropy_R(), HMWSoln::m_dlnActCoeffMolaldT_Scaled, Phase::m_kk, HMWSoln::m_lnActCoeffMolal_Scaled, MolalityVPSSTP::m_molalities, Phase::moleFraction(), ThermoPhase::RT(), HMWSoln::s_update_dlnMolalityActCoeff_dT(), and Cantera::SmallNumber.
Referenced by HMWSoln::entropy_mole().
◆ getPartialMolarVolumes()
|
virtual |
Return an array of partial molar volumes for the species in the mixture.
Units: m^3/kmol.
For this solution, the partial molar volumes are functions of the pressure derivatives of the activity coefficients.
\[ \bar V_k(T,P) = V^{\triangle}_k(T,P) + R T \frac{d \ln(\gamma^{\triangle}_k) }{dP} \]
\[ \bar V_o(T,P) = V^o_o(T,P) + R T \frac{d \ln(a_o)}{dP} \]
- Parameters
-
vbar Output vector of species partial molar volumes. Length = m_kk. units are m^3/kmol.
Reimplemented from ThermoPhase.
Definition at line 386 of file HMWSoln.cpp.
References VPStandardStateTP::getStandardVolumes(), HMWSoln::m_dlnActCoeffMolaldP_Scaled, Phase::m_kk, ThermoPhase::RT(), and HMWSoln::s_update_dlnMolalityActCoeff_dP().
Referenced by HMWSoln::calcDensity().
◆ getPartialMolarCp()
|
virtual |
Return an array of partial molar heat capacities for the species in the mixture.
Units: J/kmol/K
The following formulas are implemented within the code.
\[ \bar C_{p,k}(T,P) = C^{\triangle}_{p,k}(T,P) - 2 R T \frac{d \ln( \gamma^{\triangle}_k)}{dT} - R T^2 \frac{d^2 \ln(\gamma^{\triangle}_k) }{{dT}^2} \]
\[ \bar C_{p,o}(T,P) = C^o_{p,o}(T,P) - 2 R T \frac{d \ln(a_o)}{dT} - R T^2 \frac{d^2 \ln(a_o)}{{dT}^2} \]
- Parameters
-
cpbar Output vector of species partial molar heat capacities at constant pressure. Length = m_kk. units are J/kmol/K.
Reimplemented from ThermoPhase.
Definition at line 399 of file HMWSoln.cpp.
References Cantera::GasConstant, VPStandardStateTP::getCp_R(), HMWSoln::m_d2lnActCoeffMolaldT2_Scaled, HMWSoln::m_dlnActCoeffMolaldT_Scaled, Phase::m_kk, ThermoPhase::RT(), HMWSoln::s_update_d2lnMolalityActCoeff_dT2(), HMWSoln::s_update_dlnMolalityActCoeff_dT(), and Phase::temperature().
Referenced by HMWSoln::cp_mole().
◆ satPressure()
|
virtual |
Get the saturation pressure for a given temperature.
Note the limitations of this function. Stability considerations concerning multiphase equilibrium are ignored in this calculation. Therefore, the call is made directly to the SS of water underneath. The object is put back into its original state at the end of the call.
- Todo:
- This is probably not implemented correctly. The stability of the salt should be added into this calculation. The underlying water model may be called to get the stability of the pure water solution, if needed.
- Parameters
-
T Temperature (kelvin)
Reimplemented from ThermoPhase.
Definition at line 419 of file HMWSoln.cpp.
References HMWSoln::m_waterSS, VPStandardStateTP::pressure(), PDSS::satPressure(), PDSS::setState_TP(), and Phase::temperature().
◆ setA_Debye()
| void setA_Debye | ( | double | A | ) |
Set the A_Debye parameter.
If a negative value is provided, enables calculation of A_Debye using the detailed water equation of state.
Definition at line 641 of file HMWSoln.cpp.
Referenced by HMWSoln::initThermoXML().
◆ initThermo()
|
virtual |
The following methods are used in the process of constructing the phase and setting its parameters from a specification in an input file. They are not normally used in application programs. To see how they are used, see importPhase().
Reimplemented from MolalityVPSSTP.
Definition at line 660 of file HMWSoln.cpp.
References Phase::charge(), HMWSoln::elambda, HMWSoln::elambda1, Phase::getMoleFractions(), HMWSoln::initLengths(), MolalityVPSSTP::initThermo(), Phase::m_kk, HMWSoln::m_waterProps, HMWSoln::m_waterSS, Cantera::npos, and Phase::speciesIndex().
◆ initThermoXML()
|
virtual |
Initialize the phase parameters from an XML file.
This gets called from importPhase(). It processes the XML file after the species are set up. This is the main routine for reading in activity coefficient parameters.
- Parameters
-
phaseNode This object must be the phase node of a complete XML tree description of the phase, including all of the species data. In other words while "phase" must point to an XML phase object, it must have sibling nodes "speciesData" that describe the species in the phase. id ID of the phase. If nonnull, a check is done to see if phaseNode is pointing to the phase with the correct id.
Reimplemented from ThermoPhase.
Definition at line 746 of file HMWSoln.cpp.
References XML_Node::attrib(), Cantera::caseInsensitiveEquals(), XML_Node::child(), XML_Node::children(), Cantera::fpValueCheck(), Cantera::getFloat(), XML_Node::hasChild(), XML_Node::id(), HMWSoln::initLengths(), ThermoPhase::initThermoXML(), HMWSoln::readXMLBinarySalt(), HMWSoln::readXMLLambdaNeutral(), HMWSoln::readXMLPsi(), HMWSoln::readXMLTheta(), HMWSoln::readXMLZetaCation(), and HMWSoln::setA_Debye().
◆ A_Debye_TP()
|
virtual |
Value of the Debye Huckel constant as a function of temperature and pressure.
A_Debye = (F e B_Debye) / (8 Pi epsilon R T)
Units = sqrt(kg/gmol)
- Parameters
-
temperature Temperature of the derivative calculation or -1 to indicate the current temperature pressure Pressure of the derivative calculation or -1 to indicate the current pressure
Definition at line 845 of file HMWSoln.cpp.
Referenced by HMWSoln::getUnscaledMolalityActivityCoefficients().
◆ dA_DebyedT_TP()
|
virtual |
Value of the derivative of the Debye Huckel constant with respect to temperature as a function of temperature and pressure.
A_Debye = (F e B_Debye) / (8 Pi epsilon R T)
Units = sqrt(kg/gmol)
- Parameters
-
temperature Temperature of the derivative calculation or -1 to indicate the current temperature pressure Pressure of the derivative calculation or -1 to indicate the current pressure
Definition at line 877 of file HMWSoln.cpp.
Referenced by HMWSoln::ADebye_L(), and HMWSoln::s_NBS_CLM_dlnMolalityActCoeff_dT().
◆ dA_DebyedP_TP()
|
virtual |
Value of the derivative of the Debye Huckel constant with respect to pressure, as a function of temperature and pressure.
A_Debye = (F e B_Debye) / (8 Pi epsilon R T)
Units = sqrt(kg/gmol)
- Parameters
-
temperature Temperature of the derivative calculation or -1 to indicate the current temperature pressure Pressure of the derivative calculation or -1 to indicate the current pressure
Definition at line 901 of file HMWSoln.cpp.
Referenced by HMWSoln::ADebye_V(), and HMWSoln::s_NBS_CLM_dlnMolalityActCoeff_dP().
◆ ADebye_L()
| double ADebye_L | ( | double | temperature = -1.0, |
| double | pressure = -1.0 |
||
| ) | const |
Return Pitzer's definition of A_L.
This is basically the derivative of the A_phi multiplied by 4 R T**2
A_Debye = (F e B_Debye) / (8 Pi epsilon R T)
dA_phidT = d(A_Debye)/dT / 3.0
A_L = dA_phidT * (4 * R * T * T)
Units = sqrt(kg/gmol) (RT)
- Parameters
-
temperature Temperature of the derivative calculation or -1 to indicate the current temperature pressure Pressure of the derivative calculation or -1 to indicate the current pressure
Definition at line 933 of file HMWSoln.cpp.
References HMWSoln::dA_DebyedT_TP().
◆ ADebye_J()
| double ADebye_J | ( | double | temperature = -1.0, |
| double | pressure = -1.0 |
||
| ) | const |
Return Pitzer's definition of A_J.
This is basically the temperature derivative of A_L, and the second derivative of A_phi
A_Debye = (F e B_Debye) / (8 Pi epsilon R T)
dA_phidT = d(A_Debye)/dT / 3.0
A_J = 2 A_L/T + 4 * R * T * T * d2(A_phi)/dT2
Units = sqrt(kg/gmol) (R)
- Parameters
-
temperature Temperature of the derivative calculation or -1 to indicate the current temperature pressure Pressure of the derivative calculation or -1 to indicate the current pressure
Definition at line 955 of file HMWSoln.cpp.
◆ ADebye_V()
| double ADebye_V | ( | double | temperature = -1.0, |
| double | pressure = -1.0 |
||
| ) | const |
Return Pitzer's definition of A_V.
This is the derivative wrt pressure of A_phi multiplied by - 4 R T
A_Debye = (F e B_Debye) / (8 Pi epsilon R T)
dA_phidT = d(A_Debye)/dP / 3.0
A_V = - dA_phidP * (4 * R * T)
Units = sqrt(kg/gmol) (RT) / Pascal
- Parameters
-
temperature Temperature of the derivative calculation or -1 to indicate the current temperature pressure Pressure of the derivative calculation or -1 to indicate the current pressure
Definition at line 944 of file HMWSoln.cpp.
References HMWSoln::dA_DebyedP_TP().
◆ d2A_DebyedT2_TP()
|
virtual |
Value of the 2nd derivative of the Debye Huckel constant with respect to temperature as a function of temperature and pressure.
A_Debye = (F e B_Debye) / (8 Pi epsilon R T)
Units = sqrt(kg/gmol)
- Parameters
-
temperature Temperature of the derivative calculation or -1 to indicate the current temperature pressure Pressure of the derivative calculation or -1 to indicate the current pressure
Definition at line 967 of file HMWSoln.cpp.
Referenced by HMWSoln::s_NBS_CLM_d2lnMolalityActCoeff_dT2().
◆ printCoeffs()
| void printCoeffs | ( | ) | const |
Print out all of the input Pitzer coefficients.
Definition at line 4051 of file HMWSoln.cpp.
References MolalityVPSSTP::calcMolalities(), Phase::charge(), Phase::getMoleFractions(), HMWSoln::m_Beta0MX_ij, HMWSoln::m_Beta1MX_ij, HMWSoln::m_Beta2MX_ij, HMWSoln::m_CounterIJ, HMWSoln::m_CphiMX_ij, Phase::m_kk, HMWSoln::m_molalitiesCropped, HMWSoln::m_Psi_ijk, HMWSoln::m_Theta_ij, HMWSoln::m_tmpV, HMWSoln::s_updatePitzer_CoeffWRTemp(), Phase::speciesName(), Cantera::writelog(), and Cantera::writelogf().
◆ getUnscaledMolalityActivityCoefficients()
|
virtual |
Get the array of unscaled non-dimensional molality based activity coefficients at the current solution temperature, pressure, and solution concentration.
See Denbigh p. 278 for a thorough discussion. This class must be overridden in classes which derive from MolalityVPSSTP. This function takes over from the molar-based activity coefficient calculation, getActivityCoefficients(), in derived classes.
- Parameters
-
acMolality Output vector containing the molality based activity coefficients. length: m_kk.
Reimplemented from MolalityVPSSTP.
Definition at line 299 of file HMWSoln.cpp.
References HMWSoln::A_Debye_TP(), Phase::m_kk, HMWSoln::m_lnActCoeffMolal_Unscaled, and VPStandardStateTP::updateStandardStateThermo().
◆ s_updateScaling_pHScaling()
|
private |
Apply the current phScale to a set of activity Coefficients.
See the Eq3/6 Manual for a thorough discussion.
Definition at line 4109 of file HMWSoln.cpp.
References AssertTrace, Phase::charge(), MolalityVPSSTP::m_indexCLM, Phase::m_kk, HMWSoln::m_lnActCoeffMolal_Scaled, HMWSoln::m_lnActCoeffMolal_Unscaled, MolalityVPSSTP::m_pHScalingType, Cantera::PHSCALE_NBS, Cantera::PHSCALE_PITZER, and HMWSoln::s_NBS_CLM_lnMolalityActCoeff().
◆ s_updateScaling_pHScaling_dT()
|
private |
Apply the current phScale to a set of derivatives of the activity Coefficients wrt temperature.
See the Eq3/6 Manual for a thorough discussion of the need
Definition at line 4124 of file HMWSoln.cpp.
References AssertTrace, Phase::charge(), HMWSoln::m_dlnActCoeffMolaldT_Scaled, HMWSoln::m_dlnActCoeffMolaldT_Unscaled, MolalityVPSSTP::m_indexCLM, Phase::m_kk, MolalityVPSSTP::m_pHScalingType, Cantera::PHSCALE_NBS, Cantera::PHSCALE_PITZER, and HMWSoln::s_NBS_CLM_dlnMolalityActCoeff_dT().
Referenced by HMWSoln::s_update_dlnMolalityActCoeff_dT().
◆ s_updateScaling_pHScaling_dT2()
|
private |
Apply the current phScale to a set of 2nd derivatives of the activity Coefficients wrt temperature.
See the Eq3/6 Manual for a thorough discussion of the need
Definition at line 4139 of file HMWSoln.cpp.
References AssertTrace, Phase::charge(), HMWSoln::m_d2lnActCoeffMolaldT2_Scaled, HMWSoln::m_d2lnActCoeffMolaldT2_Unscaled, MolalityVPSSTP::m_indexCLM, Phase::m_kk, MolalityVPSSTP::m_pHScalingType, Cantera::PHSCALE_NBS, Cantera::PHSCALE_PITZER, and HMWSoln::s_NBS_CLM_d2lnMolalityActCoeff_dT2().
Referenced by HMWSoln::s_update_d2lnMolalityActCoeff_dT2().
◆ s_updateScaling_pHScaling_dP()
|
private |
Apply the current phScale to a set of derivatives of the activity Coefficients wrt pressure.
See the Eq3/6 Manual for a thorough discussion of the need
Definition at line 4154 of file HMWSoln.cpp.
References AssertTrace, Phase::charge(), HMWSoln::m_dlnActCoeffMolaldP_Scaled, HMWSoln::m_dlnActCoeffMolaldP_Unscaled, MolalityVPSSTP::m_indexCLM, Phase::m_kk, MolalityVPSSTP::m_pHScalingType, Cantera::PHSCALE_NBS, Cantera::PHSCALE_PITZER, and HMWSoln::s_NBS_CLM_dlnMolalityActCoeff_dP().
Referenced by HMWSoln::s_update_dlnMolalityActCoeff_dP().
◆ s_NBS_CLM_lnMolalityActCoeff()
|
private |
Calculate the Chlorine activity coefficient on the NBS scale.
We assume here that the m_IionicMolality variable is up to date.
Definition at line 4169 of file HMWSoln.cpp.
References HMWSoln::m_IionicMolality.
Referenced by HMWSoln::applyphScale(), and HMWSoln::s_updateScaling_pHScaling().
◆ s_NBS_CLM_dlnMolalityActCoeff_dT()
|
private |
Calculate the temperature derivative of the Chlorine activity coefficient on the NBS scale.
We assume here that the m_IionicMolality variable is up to date.
Definition at line 4177 of file HMWSoln.cpp.
References HMWSoln::dA_DebyedT_TP(), and HMWSoln::m_IionicMolality.
Referenced by HMWSoln::s_updateScaling_pHScaling_dT().
◆ s_NBS_CLM_d2lnMolalityActCoeff_dT2()
|
private |
Calculate the second temperature derivative of the Chlorine activity coefficient on the NBS scale.
We assume here that the m_IionicMolality variable is up to date.
Definition at line 4184 of file HMWSoln.cpp.
References HMWSoln::d2A_DebyedT2_TP(), and HMWSoln::m_IionicMolality.
Referenced by HMWSoln::s_updateScaling_pHScaling_dT2().
◆ s_NBS_CLM_dlnMolalityActCoeff_dP()
|
private |
Calculate the pressure derivative of the Chlorine activity coefficient.
We assume here that the m_IionicMolality variable is up to date.
Definition at line 4191 of file HMWSoln.cpp.
References HMWSoln::dA_DebyedP_TP(), and HMWSoln::m_IionicMolality.
Referenced by HMWSoln::s_updateScaling_pHScaling_dP().
◆ initLengths()
|
private |
Initialize all of the species-dependent lengths in the object.
Definition at line 995 of file HMWSoln.cpp.
References HMWSoln::m_formPitzerTemp, Phase::m_kk, HMWSoln::m_molalitiesCropped, and HMWSoln::m_tmpV.
Referenced by HMWSoln::initThermo(), and HMWSoln::initThermoXML().
◆ applyphScale()
|
privatevirtual |
Apply the current phScale to a set of activity Coefficients or activities.
See the Eq3/6 Manual for a thorough discussion.
- Parameters
-
acMolality input/Output vector containing the molality based activity coefficients. length: m_kk.
Reimplemented from MolalityVPSSTP.
Definition at line 4095 of file HMWSoln.cpp.
References AssertTrace, Phase::charge(), MolalityVPSSTP::m_indexCLM, Phase::m_kk, HMWSoln::m_lnActCoeffMolal_Unscaled, MolalityVPSSTP::m_pHScalingType, Cantera::PHSCALE_NBS, Cantera::PHSCALE_PITZER, and HMWSoln::s_NBS_CLM_lnMolalityActCoeff().
◆ s_update_dlnMolalityActCoeff_dT()
|
private |
This function calculates the temperature derivative of the natural logarithm of the molality activity coefficients.
This function does all of the direct work. The solvent activity coefficient is on the molality scale. It's derivative is too.
Definition at line 2399 of file HMWSoln.cpp.
References HMWSoln::CROP_speciesCropped_, ValueCache::getId(), ValueCache::getScalar(), Phase::m_cache, HMWSoln::m_dlnActCoeffMolaldT_Unscaled, Phase::m_kk, VPStandardStateTP::pressure(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), HMWSoln::s_updateScaling_pHScaling_dT(), Phase::stateMFNumber(), Phase::temperature(), and CachedValue< T >::validate().
Referenced by HMWSoln::getPartialMolarCp(), HMWSoln::getPartialMolarEnthalpies(), and HMWSoln::getPartialMolarEntropies().
◆ s_update_d2lnMolalityActCoeff_dT2()
|
private |
This function calculates the temperature second derivative of the natural logarithm of the molality activity coefficients.
Definition at line 2918 of file HMWSoln.cpp.
References HMWSoln::CROP_speciesCropped_, ValueCache::getId(), ValueCache::getScalar(), Phase::m_cache, HMWSoln::m_d2lnActCoeffMolaldT2_Unscaled, Phase::m_kk, VPStandardStateTP::pressure(), HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updateScaling_pHScaling_dT2(), Phase::stateMFNumber(), Phase::temperature(), and CachedValue< T >::validate().
Referenced by HMWSoln::getPartialMolarCp().
◆ s_update_dlnMolalityActCoeff_dP()
|
private |
This function calculates the pressure derivative of the natural logarithm of the molality activity coefficients.
Assumes that the activity coefficients are current.
Definition at line 3429 of file HMWSoln.cpp.
References HMWSoln::CROP_speciesCropped_, ValueCache::getId(), ValueCache::getScalar(), Phase::m_cache, HMWSoln::m_dlnActCoeffMolaldP_Unscaled, Phase::m_kk, VPStandardStateTP::pressure(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), HMWSoln::s_updateScaling_pHScaling_dP(), Phase::stateMFNumber(), Phase::temperature(), and CachedValue< T >::validate().
Referenced by HMWSoln::getPartialMolarVolumes().
◆ s_updateIMS_lnMolalityActCoeff()
|
private |
This function will be called to update the internally stored natural logarithm of the molality activity coefficients.
Definition at line 4008 of file HMWSoln.cpp.
References MolalityVPSSTP::calcMolalities(), HMWSoln::IMS_cCut_, HMWSoln::IMS_lnActCoeffMolal_, HMWSoln::IMS_X_o_cutoff_, Phase::m_kk, MolalityVPSSTP::m_xmolSolventMIN, and Phase::moleFraction().
◆ s_updatePitzer_lnMolalityActCoeff()
|
private |
Calculate the Pitzer portion of the activity coefficients.
This is the main routine in the whole module. It calculates the molality based activity coefficients for the solutes, and the activity of water.
Definition at line 1896 of file HMWSoln.cpp.
References HMWSoln::calc_lambdas(), HMWSoln::calc_thetas(), Phase::charge(), HMWSoln::counterIJ_setup(), HMWSoln::m_CounterIJ, HMWSoln::m_gamma_tmp, HMWSoln::m_IionicMolality, Phase::m_kk, MolalityVPSSTP::m_molalities, and HMWSoln::m_molalitiesCropped.
◆ s_updatePitzer_dlnMolalityActCoeff_dT()
|
private |
Calculates the temperature derivative of the natural logarithm of the molality activity coefficients.
Public function makes sure that all dependent data is up to date, before calling a private function
Definition at line 2427 of file HMWSoln.cpp.
References HMWSoln::calc_lambdas(), HMWSoln::calc_thetas(), Phase::charge(), HMWSoln::counterIJ_setup(), HMWSoln::m_CounterIJ, HMWSoln::m_gamma_tmp, HMWSoln::m_IionicMolality, Phase::m_kk, and HMWSoln::m_molalitiesCropped.
Referenced by HMWSoln::s_update_dlnMolalityActCoeff_dT().
◆ s_updatePitzer_d2lnMolalityActCoeff_dT2()
|
private |
This function calculates the temperature second derivative of the natural logarithm of the molality activity coefficients.
It is assumed that the Pitzer activity coefficient and first derivative routine are called immediately preceding the call to this routine.
Definition at line 2946 of file HMWSoln.cpp.
References HMWSoln::calc_lambdas(), HMWSoln::calc_thetas(), Phase::charge(), HMWSoln::counterIJ_setup(), HMWSoln::m_CounterIJ, HMWSoln::m_IionicMolality, Phase::m_kk, and HMWSoln::m_molalitiesCropped.
Referenced by HMWSoln::s_update_d2lnMolalityActCoeff_dT2().
◆ s_updatePitzer_dlnMolalityActCoeff_dP()
|
private |
Calculates the Pressure derivative of the natural logarithm of the molality activity coefficients.
It is assumed that the Pitzer activity coefficient and first derivative routine are called immediately preceding the calling of this routine.
Definition at line 3453 of file HMWSoln.cpp.
References HMWSoln::calc_lambdas(), HMWSoln::calc_thetas(), Phase::charge(), HMWSoln::counterIJ_setup(), HMWSoln::m_CounterIJ, HMWSoln::m_IionicMolality, Phase::m_kk, HMWSoln::m_molalitiesCropped, VPStandardStateTP::pressure(), and Phase::temperature().
Referenced by HMWSoln::s_update_dlnMolalityActCoeff_dP().
◆ s_updatePitzer_CoeffWRTemp()
|
private |
Calculates the Pitzer coefficients' dependence on the temperature.
It will also calculate the temperature derivatives of the coefficients, as they are important in the calculation of the latent heats and the heat capacities of the mixtures.
- Parameters
-
doDerivs If >= 1, then the routine will calculate the first derivative. If >= 2, the routine will calculate the first and second temperature derivative. default = 2
Definition at line 1650 of file HMWSoln.cpp.
Referenced by HMWSoln::printCoeffs().
◆ calc_lambdas()
|
private |
Calculate the lambda interactions.
Calculate E-lambda terms for charge combinations of like sign, using method of Pitzer (1975). This implementation is based on Bethke, Appendix 2.
- Parameters
-
is Ionic strength
Definition at line 3938 of file HMWSoln.cpp.
Referenced by HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
◆ calc_thetas()
|
private |
Calculate etheta and etheta_prime.
This interaction accounts for the mixing effects of like-signed ions with different charges. This interaction will be nonzero for species with the same charge. this routine is not to be called for neutral species; it core dumps or error exits.
MEC implementation routine.
- Parameters
-
z1 charge of the first molecule z2 charge of the second molecule etheta return pointer containing etheta etheta_prime Return pointer containing etheta_prime.
This routine uses the internal variables, elambda[] and elambda1[].
Definition at line 3982 of file HMWSoln.cpp.
References AssertThrowMsg, HMWSoln::elambda, and HMWSoln::elambda1.
Referenced by HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
◆ counterIJ_setup()
|
private |
Set up a counter variable for keeping track of symmetric binary interactions amongst the solute species.
The purpose of this is to squeeze the ij parameters into a compressed single counter.
n = m_kk*i + j m_Counter[n] = counter
Definition at line 1313 of file HMWSoln.cpp.
References HMWSoln::m_CounterIJ, and Phase::m_kk.
Referenced by HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
◆ calcMolalitiesCropped()
|
private |
Calculate the cropped molalities.
This is an internal routine that calculates values of m_molalitiesCropped from m_molalities
Definition at line 1172 of file HMWSoln.cpp.
References Phase::charge(), Phase::m_kk, HMWSoln::m_maxIionicStrength, MolalityVPSSTP::m_molalities, HMWSoln::m_molalitiesAreCropped, HMWSoln::m_molalitiesCropped, and Cantera::npos.
◆ readXMLBinarySalt()
|
private |
Process an XML node called "binarySaltParameters".
This node contains all of the parameters necessary to describe the Pitzer model for that particular binary salt. This function reads the XML file and writes the coefficients it finds to an internal data structures.
- Parameters
-
BinSalt reference to the XML_Node named binarySaltParameters containing the anion - cation interaction
Definition at line 1336 of file HMWSoln.cpp.
References XML_Node::attrib(), Cantera::getFloatArray(), HMWSoln::m_formPitzerTemp, XML_Node::name(), Cantera::npos, and Phase::speciesIndex().
Referenced by HMWSoln::initThermoXML().
◆ readXMLTheta()
|
private |
Process an XML node called "thetaAnion" or "thetaCation".
This node contains all of the parameters necessary to describe the binary interactions between two anions or two cations.
- Parameters
-
BinSalt reference to the XML_Node named thetaAnion containing the anion - anion interaction
Definition at line 1382 of file HMWSoln.cpp.
References XML_Node::attrib(), Cantera::getFloatArray(), HMWSoln::m_formPitzerTemp, XML_Node::name(), Cantera::npos, and Phase::speciesIndex().
Referenced by HMWSoln::initThermoXML().
◆ readXMLPsi()
|
private |
Process an XML node called "psiCommonAnion" or "psiCommonCation".
This node contains all of the parameters necessary to describe the ternary interactions between one anion and two cations or two anions and one cation.
- Parameters
-
BinSalt reference to the XML_Node named psiCommonAnion containing the anion - cation1 - cation2 interaction
Definition at line 1422 of file HMWSoln.cpp.
References XML_Node::attrib(), Cantera::getFloatArray(), HMWSoln::m_formPitzerTemp, XML_Node::name(), Cantera::npos, and Phase::speciesIndex().
Referenced by HMWSoln::initThermoXML().
◆ readXMLLambdaNeutral()
|
private |
Process an XML node called "lambdaNeutral".
This node contains all of the parameters necessary to describe the binary interactions between one neutral species and any other species (neutral or otherwise) in the mechanism.
- Parameters
-
BinSalt reference to the XML_Node named lambdaNeutral containing multiple Neutral - species interactions
Definition at line 1471 of file HMWSoln.cpp.
References XML_Node::attrib(), Cantera::getFloatArray(), HMWSoln::m_formPitzerTemp, XML_Node::name(), Cantera::npos, and Phase::speciesIndex().
Referenced by HMWSoln::initThermoXML().
◆ readXMLMunnnNeutral()
|
private |
Process an XML node called "MunnnNeutral".
This node contains all of the parameters necessary to describe the self-ternary interactions for one neutral species.
- Parameters
-
BinSalt reference to the XML_Node named Munnn containing the self-ternary interaction
Definition at line 1501 of file HMWSoln.cpp.
References XML_Node::attrib(), Cantera::getFloatArray(), HMWSoln::m_formPitzerTemp, XML_Node::name(), Cantera::npos, and Phase::speciesIndex().
◆ readXMLZetaCation()
|
private |
Process an XML node called "zetaCation".
This node contains all of the parameters necessary to describe the ternary interactions between one neutral, one cation, and one anion.
- Parameters
-
BinSalt reference to the XML_Node named psiCommonCation containing the neutral - cation - anion interaction
Definition at line 1526 of file HMWSoln.cpp.
References XML_Node::attrib(), Cantera::getFloatArray(), HMWSoln::m_formPitzerTemp, XML_Node::name(), Cantera::npos, and Phase::speciesIndex().
Referenced by HMWSoln::initThermoXML().
◆ calcIMSCutoffParams_()
|
private |
Precalculate the IMS Cutoff parameters for typeCutoff = 2.
Definition at line 1561 of file HMWSoln.cpp.
References HMWSoln::IMS_cCut_, and HMWSoln::IMS_X_o_cutoff_.
◆ calcMCCutoffParams_()
|
private |
Calculate molality cut-off parameters.
Definition at line 1614 of file HMWSoln.cpp.
References HMWSoln::MC_X_o_cutoff_.
Member Data Documentation
◆ m_formPitzerTemp
|
private |
This is the form of the temperature dependence of Pitzer parameterization used in the model.
PITZER_TEMP_CONSTANT 0 PITZER_TEMP_LINEAR 1 PITZER_TEMP_COMPLEX1 2
Definition at line 1717 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::readXMLBinarySalt(), HMWSoln::readXMLLambdaNeutral(), HMWSoln::readXMLMunnnNeutral(), HMWSoln::readXMLPsi(), HMWSoln::readXMLTheta(), and HMWSoln::readXMLZetaCation().
◆ m_IionicMolality
|
mutableprivate |
Current value of the ionic strength on the molality scale Associated Salts, if present in the mechanism, don't contribute to the value of the ionic strength in this version of the Ionic strength.
Definition at line 1722 of file HMWSoln.h.
Referenced by HMWSoln::s_NBS_CLM_d2lnMolalityActCoeff_dT2(), HMWSoln::s_NBS_CLM_dlnMolalityActCoeff_dP(), HMWSoln::s_NBS_CLM_dlnMolalityActCoeff_dT(), HMWSoln::s_NBS_CLM_lnMolalityActCoeff(), HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
◆ m_maxIionicStrength
|
private |
Maximum value of the ionic strength allowed in the calculation of the activity coefficients.
Definition at line 1726 of file HMWSoln.h.
Referenced by HMWSoln::calcMolalitiesCropped().
◆ m_TempPitzerRef
|
private |
◆ m_form_A_Debye
| int m_form_A_Debye |
Form of the constant outside the Debye-Huckel term called A.
It's normally a function of temperature and pressure. However, it can be set from the input file in order to aid in numerical comparisons. Acceptable forms:
A_DEBYE_CONST 0 A_DEBYE_WATER 1
The A_DEBYE_WATER form may be used for water solvents with needs to cover varying temperatures and pressures. Note, the dielectric constant of water is a relatively strong function of T, and its variability must be accounted for,
◆ m_A_Debye
|
mutableprivate |
A_Debye: this expression appears on the top of the ln actCoeff term in the general Debye-Huckel expression It depends on temperature.
And, therefore, most be recalculated whenever T or P changes. This variable is a local copy of the calculation.
A_Debye = (F e B_Debye) / (8 Pi epsilon R T)
where B_Debye = F / sqrt(epsilon R T/2)
(dw/1000)^(1/2)
A_Debye = (1/ (8 Pi)) (2 Na * dw/1000)^(1/2) (e * e / (epsilon * kb * T))^(3/2)
Units = sqrt(kg/gmol)
Nominal value = 1.172576 sqrt(kg/gmol) based on: epsilon/epsilon_0 = 78.54 (water at 25C) epsilon_0 = 8.854187817E-12 C2 N-1 m-2 e = 1.60217653 E-19 C F = 9.6485309E7 C kmol-1 R = 8.314472E3 kg m2 s-2 kmol-1 K-1 T = 298.15 K B_Debye = 3.28640E9 sqrt(kg/gmol)/m dw = C_0 * M_0 (density of water) (kg/m3) = 1.0E3 at 25C
◆ m_waterSS
|
private |
Water standard state calculator.
derived from the equation of state for water.
Definition at line 1784 of file HMWSoln.h.
Referenced by HMWSoln::initThermo(), and HMWSoln::satPressure().
◆ m_waterProps
|
private |
Pointer to the water property calculator.
Definition at line 1787 of file HMWSoln.h.
Referenced by HMWSoln::initThermo().
◆ m_tmpV
|
mutableprivate |
vector of size m_kk, used as a temporary holding area.
Definition at line 1790 of file HMWSoln.h.
Referenced by HMWSoln::calcDensity(), HMWSoln::cp_mole(), HMWSoln::enthalpy_mole(), HMWSoln::entropy_mole(), HMWSoln::gibbs_mole(), HMWSoln::initLengths(), HMWSoln::printCoeffs(), HMWSoln::relative_enthalpy(), HMWSoln::relative_molal_enthalpy(), and HMWSoln::standardConcentration().
◆ m_Beta0MX_ij
|
mutableprivate |
Array of 2D data used in the Pitzer/HMW formulation.
Beta0_ij[i][j] is the value of the Beta0 coefficient for the ij salt. It will be nonzero iff i and j are both charged and have opposite sign. The array is also symmetric. counterIJ where counterIJ = m_counterIJ[i][j] is used to access this array.
Definition at line 1799 of file HMWSoln.h.
Referenced by HMWSoln::printCoeffs().
◆ m_Beta0MX_ij_L
|
mutableprivate |
◆ m_Beta0MX_ij_LL
|
mutableprivate |
◆ m_Beta0MX_ij_P
|
mutableprivate |
◆ m_Beta0MX_ij_coeff
|
mutableprivate |
◆ m_Beta1MX_ij
|
mutableprivate |
Array of 2D data used in the Pitzer/HMW formulation.
Beta1_ij[i][j] is the value of the Beta1 coefficient for the ij salt. It will be nonzero iff i and j are both charged and have opposite sign. The array is also symmetric. counterIJ where counterIJ = m_counterIJ[i][j] is used to access this array.
Definition at line 1823 of file HMWSoln.h.
Referenced by HMWSoln::printCoeffs().
◆ m_Beta1MX_ij_L
|
mutableprivate |
◆ m_Beta1MX_ij_LL
|
mutableprivate |
◆ m_Beta1MX_ij_P
|
mutableprivate |
◆ m_Beta1MX_ij_coeff
|
mutableprivate |
◆ m_Beta2MX_ij
|
mutableprivate |
Array of 2D data used in the Pitzer/HMW formulation.
Beta2_ij[i][j] is the value of the Beta2 coefficient for the ij salt. It will be nonzero iff i and j are both charged and have opposite sign, and i and j both have charges of 2 or more. The array is also symmetric. counterIJ where counterIJ = m_counterIJ[i][j] is used to access this array.
Definition at line 1847 of file HMWSoln.h.
Referenced by HMWSoln::printCoeffs().
◆ m_Beta2MX_ij_L
|
mutableprivate |
◆ m_Beta2MX_ij_LL
|
mutableprivate |
◆ m_Beta2MX_ij_P
|
mutableprivate |
◆ m_Beta2MX_ij_coeff
|
mutableprivate |
Array of coefficients for Beta2, a variable in Pitzer's papers.
column index is counterIJ. m_Beta2MX_ij_coeff.ptrColumn(counterIJ) is a double* containing the vector of coefficients for the counterIJ interaction. This was added for the YMP database version of the code since it contains temperature-dependent parameters for some 2-2 electrolytes.
◆ m_Alpha2MX_ij
|
private |
Array of 2D data used in the Pitzer/HMW formulation.
Alpha2MX_ij[i][j] is the value of the alpha2 coefficient for the ij interaction. It will be nonzero iff i and j are both charged and have opposite sign, and i and j both have charges of 2 or more, usually. It is symmetric wrt i, j. counterIJ, where counterIJ = m_counterIJ[i][j], is used to access this array.
◆ m_CphiMX_ij
|
mutableprivate |
Array of 2D data used in the Pitzer/HMW formulation.
CphiMX_ij[i][j] is the value of the Cphi coefficient for the ij interaction. It will be nonzero iff i and j are both charged and have opposite sign, and i and j both have charges of 2 or more. The array is also symmetric. counterIJ where counterIJ = m_counterIJ[i][j] is used to access this array.
Definition at line 1888 of file HMWSoln.h.
Referenced by HMWSoln::printCoeffs().
◆ m_CphiMX_ij_L
|
mutableprivate |
◆ m_CphiMX_ij_LL
|
mutableprivate |
◆ m_CphiMX_ij_P
|
mutableprivate |
◆ m_CphiMX_ij_coeff
|
mutableprivate |
◆ m_Theta_ij
|
mutableprivate |
Array of 2D data for Theta_ij[i][j] in the Pitzer/HMW formulation.
Array of 2D data used in the Pitzer/HMW formulation. Theta_ij[i][j] is the value of the theta coefficient for the ij interaction. It will be nonzero for charged ions with the same sign. It is symmetric. counterIJ where counterIJ = m_counterIJ[i][j] is used to access this array.
HKM Recent Pitzer papers have used a functional form for Theta_ij, which depends on the ionic strength.
Definition at line 1918 of file HMWSoln.h.
Referenced by HMWSoln::printCoeffs().
◆ m_Theta_ij_L
|
mutableprivate |
◆ m_Theta_ij_LL
|
mutableprivate |
◆ m_Theta_ij_P
|
mutableprivate |
◆ m_Theta_ij_coeff
|
private |
Array of coefficients for Theta_ij[i][j] in the Pitzer/HMW formulation.
Theta_ij[i][j] is the value of the theta coefficient for the ij interaction. It will be nonzero for charged ions with the same sign. It is symmetric. Column index is counterIJ. counterIJ where counterIJ = m_counterIJ[i][j] is used to access this array.
m_Theta_ij_coeff.ptrColumn(counterIJ) is a double* containing the vector of coefficients for the counterIJ interaction.
◆ m_Psi_ijk
|
mutableprivate |
Array of 3D data used in the Pitzer/HMW formulation.
Psi_ijk[n] is the value of the psi coefficient for the ijk interaction where
n = k + j * m_kk + i * m_kk * m_kk;
It is potentially nonzero everywhere. The first two coordinates are symmetric wrt cations, and the last two coordinates are symmetric wrt anions.
Definition at line 1952 of file HMWSoln.h.
Referenced by HMWSoln::printCoeffs().
◆ m_Psi_ijk_L
|
mutableprivate |
◆ m_Psi_ijk_LL
|
mutableprivate |
◆ m_Psi_ijk_P
|
mutableprivate |
◆ m_Psi_ijk_coeff
|
private |
Array of coefficients for Psi_ijk[n] in the Pitzer/HMW formulation.
Psi_ijk[n] is the value of the psi coefficient for the ijk interaction where
n = k + j * m_kk + i * m_kk * m_kk;
It is potentially nonzero everywhere. The first two coordinates are symmetric wrt cations, and the last two coordinates are symmetric wrt anions.
m_Psi_ijk_coeff.ptrColumn(n) is a double* containing the vector of coefficients for the n interaction.
◆ m_Lambda_nj
|
mutableprivate |
Lambda coefficient for the ij interaction.
Array of 2D data used in the Pitzer/HMW formulation. Lambda_nj[n][j] represents the lambda coefficient for the ij interaction. This is a general interaction representing neutral species. The neutral species occupy the first index, i.e., n. The charged species occupy the j coordinate. neutral, neutral interactions are also included here.
◆ m_Lambda_nj_L
|
mutableprivate |
◆ m_Lambda_nj_LL
|
mutableprivate |
◆ m_Lambda_nj_P
|
mutableprivate |
◆ m_Lambda_nj_coeff
|
private |
Array of coefficients for Lambda_nj[i][j] in the Pitzer/HMW formulation.
Array of 2D data used in the Pitzer/HMW formulation. Lambda_ij[i][j] represents the lambda coefficient for the ij interaction. This is a general interaction representing neutral species. The neutral species occupy the first index, i.e., i. The charged species occupy the j coordinate. Neutral, neutral interactions are also included here.
n = j + m_kk * i
m_Lambda_ij_coeff.ptrColumn(n) is a double* containing the vector of coefficients for the (i,j) interaction.
◆ m_Mu_nnn
|
mutableprivate |
Mu coefficient for the self-ternary neutral coefficient.
Array of 2D data used in the Pitzer/HMW formulation. Mu_nnn[i] represents the Mu coefficient for the nnn interaction. This is a general interaction representing neutral species interacting with itself.
◆ m_Mu_nnn_L
|
mutableprivate |
Mu coefficient temperature derivative for the self-ternary neutral coefficient.
Array of 2D data used in the Pitzer/HMW formulation. Mu_nnn_L[i] represents the Mu coefficient temperature derivative for the nnn interaction. This is a general interaction representing neutral species interacting with itself.
◆ m_Mu_nnn_LL
|
mutableprivate |
Mu coefficient 2nd temperature derivative for the self-ternary neutral coefficient.
Array of 2D data used in the Pitzer/HMW formulation. Mu_nnn_L[i] represents the Mu coefficient 2nd temperature derivative for the nnn interaction. This is a general interaction representing neutral species interacting with itself.
◆ m_Mu_nnn_P
|
mutableprivate |
Mu coefficient pressure derivative for the self-ternary neutral coefficient.
Array of 2D data used in the Pitzer/HMW formulation. Mu_nnn_L[i] represents the Mu coefficient pressure derivative for the nnn interaction. This is a general interaction representing neutral species interacting with itself.
◆ m_Mu_nnn_coeff
|
private |
◆ m_lnActCoeffMolal_Scaled
|
mutableprivate |
Logarithm of the activity coefficients on the molality scale.
mutable because we change this if the composition or temperature or pressure changes. Index is the species index
Definition at line 2062 of file HMWSoln.h.
Referenced by HMWSoln::getActivities(), HMWSoln::getChemPotentials(), HMWSoln::getPartialMolarEntropies(), and HMWSoln::s_updateScaling_pHScaling().
◆ m_lnActCoeffMolal_Unscaled
|
mutableprivate |
Logarithm of the activity coefficients on the molality scale.
mutable because we change this if the composition or temperature or pressure changes. Index is the species index
Definition at line 2069 of file HMWSoln.h.
Referenced by HMWSoln::applyphScale(), HMWSoln::getUnscaledMolalityActivityCoefficients(), and HMWSoln::s_updateScaling_pHScaling().
◆ m_dlnActCoeffMolaldT_Scaled
|
mutableprivate |
Derivative of the Logarithm of the activity coefficients on the molality scale wrt T.
Index is the species index
Definition at line 2073 of file HMWSoln.h.
Referenced by HMWSoln::getPartialMolarCp(), HMWSoln::getPartialMolarEnthalpies(), HMWSoln::getPartialMolarEntropies(), and HMWSoln::s_updateScaling_pHScaling_dT().
◆ m_dlnActCoeffMolaldT_Unscaled
|
mutableprivate |
Derivative of the Logarithm of the activity coefficients on the molality scale wrt T.
Index is the species index
Definition at line 2077 of file HMWSoln.h.
Referenced by HMWSoln::s_update_dlnMolalityActCoeff_dT(), and HMWSoln::s_updateScaling_pHScaling_dT().
◆ m_d2lnActCoeffMolaldT2_Scaled
|
mutableprivate |
Derivative of the Logarithm of the activity coefficients on the molality scale wrt TT.
Index is the species index.
Definition at line 2081 of file HMWSoln.h.
Referenced by HMWSoln::getPartialMolarCp(), and HMWSoln::s_updateScaling_pHScaling_dT2().
◆ m_d2lnActCoeffMolaldT2_Unscaled
|
mutableprivate |
Derivative of the Logarithm of the activity coefficients on the molality scale wrt TT.
Index is the species index
Definition at line 2085 of file HMWSoln.h.
Referenced by HMWSoln::s_update_d2lnMolalityActCoeff_dT2(), and HMWSoln::s_updateScaling_pHScaling_dT2().
◆ m_dlnActCoeffMolaldP_Scaled
|
mutableprivate |
Derivative of the Logarithm of the activity coefficients on the molality scale wrt P.
Index is the species index
Definition at line 2089 of file HMWSoln.h.
Referenced by HMWSoln::getPartialMolarVolumes(), and HMWSoln::s_updateScaling_pHScaling_dP().
◆ m_dlnActCoeffMolaldP_Unscaled
|
mutableprivate |
Derivative of the Logarithm of the activity coefficients on the molality scale wrt P.
Index is the species index
Definition at line 2093 of file HMWSoln.h.
Referenced by HMWSoln::s_update_dlnMolalityActCoeff_dP(), and HMWSoln::s_updateScaling_pHScaling_dP().
◆ m_molalitiesCropped
|
mutableprivate |
Cropped and modified values of the molalities used in activity coefficient calculations.
Definition at line 2099 of file HMWSoln.h.
Referenced by HMWSoln::calcMolalitiesCropped(), HMWSoln::initLengths(), HMWSoln::printCoeffs(), HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
◆ m_molalitiesAreCropped
|
mutableprivate |
Boolean indicating whether the molalities are cropped or are modified.
Definition at line 2102 of file HMWSoln.h.
Referenced by HMWSoln::calcMolalitiesCropped().
◆ m_CounterIJ
|
mutableprivate |
a counter variable for keeping track of symmetric binary interactions amongst the solute species.
n = m_kk*i + j m_CounterIJ[n] = counterIJ
Definition at line 2110 of file HMWSoln.h.
Referenced by HMWSoln::counterIJ_setup(), HMWSoln::printCoeffs(), HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
◆ elambda
|
mutableprivate |
This is elambda, MEC.
Definition at line 2113 of file HMWSoln.h.
Referenced by HMWSoln::calc_thetas(), and HMWSoln::initThermo().
◆ elambda1
|
mutableprivate |
This is elambda1, MEC.
Definition at line 2116 of file HMWSoln.h.
Referenced by HMWSoln::calc_thetas(), and HMWSoln::initThermo().
◆ m_gfunc_IJ
|
mutableprivate |
◆ m_g2func_IJ
|
mutableprivate |
◆ m_hfunc_IJ
|
mutableprivate |
◆ m_h2func_IJ
|
mutableprivate |
◆ m_BMX_IJ
|
mutableprivate |
◆ m_BMX_IJ_L
|
mutableprivate |
◆ m_BMX_IJ_LL
|
mutableprivate |
◆ m_BMX_IJ_P
|
mutableprivate |
◆ m_BprimeMX_IJ
|
mutableprivate |
◆ m_BprimeMX_IJ_L
|
mutableprivate |
◆ m_BprimeMX_IJ_LL
|
mutableprivate |
◆ m_BprimeMX_IJ_P
|
mutableprivate |
◆ m_BphiMX_IJ
|
mutableprivate |
◆ m_BphiMX_IJ_L
|
mutableprivate |
◆ m_BphiMX_IJ_LL
|
mutableprivate |
◆ m_BphiMX_IJ_P
|
mutableprivate |
◆ m_Phi_IJ
|
mutableprivate |
◆ m_Phi_IJ_L
|
mutableprivate |
◆ m_Phi_IJ_LL
|
mutableprivate |
◆ m_Phi_IJ_P
|
mutableprivate |
◆ m_Phiprime_IJ
|
mutableprivate |
◆ m_PhiPhi_IJ
|
mutableprivate |
◆ m_PhiPhi_IJ_L
|
mutableprivate |
◆ m_PhiPhi_IJ_LL
|
mutableprivate |
◆ m_PhiPhi_IJ_P
|
mutableprivate |
◆ m_CMX_IJ
|
mutableprivate |
◆ m_CMX_IJ_L
|
mutableprivate |
◆ m_CMX_IJ_LL
|
mutableprivate |
◆ m_CMX_IJ_P
|
mutableprivate |
◆ m_gamma_tmp
|
mutableprivate |
Intermediate storage of the activity coefficient itself.
Vector index is the species index
Definition at line 2222 of file HMWSoln.h.
Referenced by HMWSoln::relative_enthalpy(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
◆ IMS_lnActCoeffMolal_
|
mutableprivate |
Logarithm of the molal activity coefficients.
Normally these are all one. However, stability schemes will change that
Definition at line 2226 of file HMWSoln.h.
Referenced by HMWSoln::s_updateIMS_lnMolalityActCoeff().
◆ IMS_X_o_cutoff_
|
private |
value of the solute mole fraction that centers the cutoff polynomials for the cutoff =1 process;
Definition at line 2230 of file HMWSoln.h.
Referenced by HMWSoln::calcIMSCutoffParams_(), and HMWSoln::s_updateIMS_lnMolalityActCoeff().
◆ IMS_cCut_
|
private |
Parameter in the polyExp cutoff treatment having to do with rate of exp decay.
Definition at line 2233 of file HMWSoln.h.
Referenced by HMWSoln::calcIMSCutoffParams_(), and HMWSoln::s_updateIMS_lnMolalityActCoeff().
◆ IMS_slopegCut_
|
private |
◆ MC_X_o_cutoff_
|
private |
value of the solvent mole fraction that centers the cutoff polynomials for the cutoff =1 process;
Definition at line 2256 of file HMWSoln.h.
Referenced by HMWSoln::calcMCCutoffParams_().
◆ CROP_speciesCropped_
|
mutableprivate |
This is a boolean-type vector indicating whether a species's activity coefficient is in the cropped regime.
- 0 = Not in cropped regime
- 1 = In a transition regime where it is altered but there still may be a temperature or pressure dependence
- 2 = In a cropped regime where there is no temperature or pressure dependence
Definition at line 2279 of file HMWSoln.h.
Referenced by HMWSoln::s_update_d2lnMolalityActCoeff_dT2(), HMWSoln::s_update_dlnMolalityActCoeff_dP(), and HMWSoln::s_update_dlnMolalityActCoeff_dT().
The documentation for this class was generated from the following files:
