Class DebyeHuckel represents a dilute liquid electrolyte phase which obeys the Debye Huckel formulation for nonideality. More...
#include <DebyeHuckel.h>
Public Member Functions | |
| DebyeHuckel () | |
| Default Constructor. More... | |
| DebyeHuckel (const DebyeHuckel &) | |
| DebyeHuckel & | operator= (const DebyeHuckel &) |
| virtual ThermoPhase * | duplMyselfAsThermoPhase () const |
| Duplication routine for objects which inherit from ThermoPhase. More... | |
| DebyeHuckel (const std::string &inputFile, const std::string &id="") | |
| Full constructor for creating the phase. More... | |
| DebyeHuckel (XML_Node &phaseRef, const std::string &id="") | |
| Full constructor for creating the phase. More... | |
| virtual bool | addSpecies (shared_ptr< Species > spec) |
| virtual void | initThermoXML (XML_Node &phaseNode, const std::string &id) |
| Import and initialize a ThermoPhase object using an XML tree. More... | |
| virtual double | A_Debye_TP (double temperature=-1.0, double pressure=-1.0) const |
| Return the Debye Huckel constant as a function of temperature and pressure (Units = sqrt(kg/gmol)) 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. 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... | |
| 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 | AionicRadius (int k=0) const |
| Reports the ionic radius of the kth species. More... | |
| int | formDH () const |
| Returns the form of the Debye-Huckel parameterization used. More... | |
| Array2D & | get_Beta_ij () |
| Returns a reference to M_Beta_ij. More... | |
Utilities | |
| virtual int | eosType () const |
| Equation of state type flag. More... | |
| 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 | 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... | |
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 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... | |
| 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... | |
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 | getPartialMolarCp (doublereal *cpbar) const |
| Return an array of partial molar heat capacities for the species in the mixture. More... | |
| virtual void | getPartialMolarVolumes (doublereal *vbar) const |
| Return an array of partial molar volumes for the species in the mixture. More... | |
 Public Member Functions inherited from MolalityVPSSTP | |
| MolalityVPSSTP () | |
| Default Constructor. More... | |
| MolalityVPSSTP (const MolalityVPSSTP &b) | |
| MolalityVPSSTP & | operator= (const MolalityVPSSTP &b) |
| 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 double | osmoticCoefficient () const |
| Calculate the osmotic coefficient. More... | |
| virtual void | initThermo () |
| Public Member Functions inherited from VPStandardStateTP | |
| VPStandardStateTP () | |
| Constructor. More... | |
| VPStandardStateTP (const VPStandardStateTP &b) | |
| VPStandardStateTP & | operator= (const VPStandardStateTP &b) |
| 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 | setVPSSMgr (VPSSMgr *vp_ptr) |
| set the VPSS Mgr More... | |
| VPSSMgr * | provideVPSSMgr () |
| Return a pointer to the VPSSMgr for this phase. More... | |
| void | createInstallPDSS (size_t k, const XML_Node &s, const XML_Node *phaseNode_ptr) |
| 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... | |
| ThermoPhase (const ThermoPhase &right) | |
| ThermoPhase & | operator= (const ThermoPhase &right) |
| doublereal | _RT () const |
| Return the Gas Constant multiplied by the current temperature. 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 | cv_mole () const |
| Molar heat capacity at constant volume. Units: J/kmol/K. 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... | |
| virtual void | setReferenceComposition (const doublereal *const x) |
| Sets the reference composition. More... | |
| virtual void | getReferenceComposition (doublereal *const x) const |
| Gets the reference composition. 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 | satPressure (doublereal t) |
| Return the saturation pressure given the temperature. 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... | |
| void | setSpeciesThermo (MultiSpeciesThermo *spthermo) |
| Install a species thermodynamic property manager. 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 | installSlavePhases (XML_Node *phaseNode) |
| Add in species from Slave phases. More... | |
| 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 &right) | |
| Phase & | operator= (const Phase &right) |
| 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... | |
| doublereal | size (size_t k) const |
| This routine returns the size of species k. More... | |
| 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 | |
| bool | m_useHelgesonFixedForm |
| If true, then the fixed for of Helgeson's activity for water is used instead of the rigorous form obtained from Gibbs-Duhem relation. More... | |
| int | m_form_A_Debye |
| Form of the constant outside the Debye-Huckel term called A. More... | |
Protected Attributes | |
| int | m_formDH |
| form of the Debye-Huckel parameterization used in the model. More... | |
| int | m_formGC |
| Format for the generalized concentration: More... | |
| vector_int | m_electrolyteSpeciesType |
| Vector containing the electrolyte species type. More... | |
| vector_fp | m_Aionic |
| a_k = Size of the ionic species in the DH formulation. units = meters More... | |
| double | m_IionicMolality |
| Current value of the ionic strength on the molality scale. More... | |
| double | m_maxIionicStrength |
| Maximum value of the ionic strength allowed in the calculation of the activity coefficients. More... | |
| double | m_IionicMolalityStoich |
| Stoichiometric ionic strength on the molality scale. More... | |
| double | m_A_Debye |
| Current value of the Debye Constant, A_Debye. More... | |
| double | m_B_Debye |
| Current value of the constant that appears in the denominator. More... | |
| vector_fp | m_B_Dot |
| Array of B_Dot values. More... | |
| PDSS_Water * | m_waterSS |
| Pointer to the Water standard state object. More... | |
| double | m_densWaterSS |
| Storage for the density of water's standard state. 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_speciesCharge_Stoich |
| Stoichiometric species charge -> This is for calculations of the ionic strength which ignore ion-ion pairing into neutral molecules. More... | |
| Array2D | m_Beta_ij |
| Array of 2D data used in the DHFORM_BETAIJ formulation Beta_ij.value(i,j) is the coefficient of the jth species for the specification of the chemical potential of the ith species. More... | |
| vector_fp | m_lnActCoeffMolal |
| Logarithm of the activity coefficients on the molality scale. More... | |
| vector_fp | m_dlnActCoeffMolaldT |
| Derivative of log act coeff wrt T. More... | |
| vector_fp | m_d2lnActCoeffMolaldT2 |
| 2nd Derivative of log act coeff wrt T More... | |
| vector_fp | m_dlnActCoeffMolaldP |
| Derivative of log act coeff wrt P. More... | |
| Protected Attributes inherited from MolalityVPSSTP | |
| size_t | m_indexSolvent |
| Index of the solvent. More... | |
| 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... | |
| doublereal | m_P0 |
| std::unique_ptr< VPSSMgr > | m_VPSS_ptr |
| Pointer to the VPSS manager that calculates all of the standard state info efficiently. More... | |
| std::vector< std::unique_ptr< PDSS > > | m_PDSS_storage |
| Storage for the PDSS objects for the species. 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. Length equal to number of elements. 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... | |
| vector_fp | xMol_Ref |
| Reference Mole Fraction Composition. 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_speciesSize |
| Vector of species sizes. 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... | |
Private Member Functions | |
| double | _osmoticCoeffHelgesonFixedForm () const |
| Formula for the osmotic coefficient that occurs in the GWB. More... | |
| double | _lnactivityWaterHelgesonFixedForm () const |
| Formula for the log of the water activity that occurs in the GWB. More... | |
| void | s_update_lnMolalityActCoeff () const |
| Calculate the log activity coefficients. More... | |
| void | s_update_dlnMolalityActCoeff_dT () const |
| Calculation of temperature derivative of activity coefficient. More... | |
| void | s_update_d2lnMolalityActCoeff_dT2 () const |
| Calculate the temperature 2nd derivative of the activity coefficient. More... | |
| void | s_update_dlnMolalityActCoeff_dP () const |
| Calculate the pressure derivative of the activity coefficient. More... | |
Static Private Member Functions | |
| static double | _nonpolarActCoeff (double IionicMolality) |
| Static function that implements the non-polar species salt-out modifications. More... | |
Mechanical Equation of State Properties | |
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. | |
| virtual void | setDensity (const doublereal rho) |
| Set the internally stored density (gm/m^3) of the phase. More... | |
| virtual void | setMolarDensity (const doublereal conc) |
| Set the internally stored molar density (kmol/m^3) of the phase. More... | |
| virtual 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... | |
| virtual 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... | |
| virtual void | applyphScale (doublereal *acMolality) const |
| Apply the current phScale to a set of activity Coefficients or activities. 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... | |
Detailed Description
Class DebyeHuckel represents a dilute liquid electrolyte phase which obeys the Debye Huckel formulation for nonideality.
The concentrations of the ionic species are assumed to obey the electroneutrality condition.
Specification of Species Standard State Properties
The standard states 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 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 \( P_0 \hat v\) 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.
\[ h^\triangle_k(T,P) = h^{\triangle,ref}_k(T) + \tilde v \left( P - P_{ref} \right) \]
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.
\[ u^\triangle_k(T,P) = h^{\triangle,ref}_k(T) - P_{ref} \tilde v \]
The standard state heat capacity and entropy are independent of pressure. The standard state Gibbs free energy is obtained from the enthalpy and entropy functions.
The vector Phase::m_speciesSize[] is used to hold the base values of species sizes. These are defined as the molar volumes of species at infinite dilution at 300 K and 1 atm of water. m_speciesSize are calculated during the initialization of the DebyeHuckel object and are then not touched.
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.
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-1).
In some instances, from some authors, a different formulation is used for the ionic strength in the equations below. The different formulation is due to the possibility of the existence of weak acids and how association wrt to the weak acid equilibrium relation affects the calculation of the activity coefficients via the assumed value of the ionic strength.
If we are to assume that the association reaction doesn't have an effect on the ionic strength, then we will want to consider the associated weak acid as in effect being fully dissociated, when we calculate an effective value for the ionic strength. We will call this calculated value, the stoichiometric ionic strength, \( I_s \), putting a subscript s to denote it from the more straightforward calculation of \( I \).
\[ I_s = \frac{1}{2} \sum_k{m_k^s z_k^2} \]
Here, \( m_k^s \) is the value of the molalities calculated assuming that all weak acid-base pairs are in their fully dissociated states. This calculation may be simplified by considering that the weakly associated acid may be made up of two charged species, k1 and k2, each with their own charges, obeying the following relationship:
\[ z_k = z_{k1} + z_{k2} \]
Then, we may only need to specify one charge value, say, \( z_{k1}\), the cation charge number, in order to get both numbers, since we have already specified \( z_k \) in the definition of original species. Then, the stoichiometric ionic strength may be calculated via the following formula.
\[ I_s = \frac{1}{2} \left(\sum_{k,ions}{m_k z_k^2}+ \sum_{k,weak_assoc}(m_k z_{k1}^2 + m_k z_{k2}^2) \right) \]
The specification of which species are weakly associated acids is made in the input file via the stoichIsMods XML block, where the charge for k1 is also specified. An example is given below:
Because we need the concept of a weakly associated acid in order to calculate \( I_s \) we need to catalog all species in the phase. This is done using the following categories:
cEST_solventSolvent species (neutral)cEST_chargedSpeciesCharged species (charged)cEST_weakAcidAssociatedSpecies which can break apart into charged species. It may or may not be charged. These may or may not be be included in the species solution vector.cEST_strongAcidAssociatedSpecies which always breaks apart into charged species. It may or may not be charged. Normally, these aren't included in the speciation vector.cEST_polarNeutralPolar neutral speciescEST_nonpolarNeutralNon polar neutral species
Polar and non-polar neutral species are differentiated, because some additions to the activity coefficient expressions distinguish between these two types of solutes. This is the so-called salt-out effect.
The type of species is specified in the electrolyteSpeciesType XML block. Note, this is not considered a part of the specification of the standard state for the species, at this time. Therefore, this information is put under the activityCoefficient XML block. An example is given below
Much of the species electrolyte type information is inferred from other information in the input file. For example, as species which is charged is given the "chargedSpecies" default category. A neutral solute species is put into the "nonpolarNeutral" category by default.
The specification of solute activity coefficients depends on the model assumed for the Debye-Huckel term. The model is set by the internal parameter m_formDH. We will now describe each category in its own section.
Debye-Huckel Dilute Limit
DHFORM_DILUTE_LIMIT = 0
This form assumes a dilute limit to DH, and is mainly for informational purposes:
\[ \ln(\gamma_k^\triangle) = - z_k^2 A_{Debye} \sqrt{I} \]
where \( I\) is the ionic strength
\[ I = \frac{1}{2} \sum_k{m_k z_k^2} \]
The activity for the solvent water, \( a_o \), is not independent and must be determined from the Gibbs-Duhem relation.
\[ \ln(a_o) = \frac{X_o - 1.0}{X_o} + \frac{ 2 A_{Debye} \tilde{M}_o}{3} (I)^{3/2} \]
Bdot Formulation
DHFORM_BDOT_AK = 1
This form assumes Bethke's format for the Debye Huckel activity coefficient:
\[ \ln(\gamma_k^\triangle) = -z_k^2 \frac{A_{Debye} \sqrt{I}}{ 1 + B_{Debye} a_k \sqrt{I}} + \log(10) B^{dot}_k I \]
Note, this particular form where \( a_k \) can differ in multielectrolyte solutions has problems with respect to a Gibbs-Duhem analysis. However, we include it here because there is a lot of data fit to it.
The activity for the solvent water, \( a_o \), is not independent and must be determined from the Gibbs-Duhem relation. Here, we use:
\[ \ln(a_o) = \frac{X_o - 1.0}{X_o} + \frac{ 2 A_{Debye} \tilde{M}_o}{3} (I)^{1/2} \left[ \sum_k{\frac{1}{2} m_k z_k^2 \sigma( B_{Debye} a_k \sqrt{I} ) } \right] - \frac{\log(10)}{2} \tilde{M}_o I \sum_k{ B^{dot}_k m_k} \]
where
\[ \sigma (y) = \frac{3}{y^3} \left[ (1+y) - 2 \ln(1 + y) - \frac{1}{1+y} \right] \]
Additionally, Helgeson's formulation for the water activity is offered as an alternative.
Bdot Formulation with Uniform Size Parameter in the Denominator
DHFORM_BDOT_AUNIFORM = 2
This form assumes Bethke's format for the Debye-Huckel activity coefficient
\[ \ln(\gamma_k^\triangle) = -z_k^2 \frac{A_{Debye} \sqrt{I}}{ 1 + B_{Debye} a \sqrt{I}} + \log(10) B^{dot}_k I \]
The value of a is determined at the beginning of the calculation, and not changed.
\[ \ln(a_o) = \frac{X_o - 1.0}{X_o} + \frac{ 2 A_{Debye} \tilde{M}_o}{3} (I)^{3/2} \sigma( B_{Debye} a \sqrt{I} ) - \frac{\log(10)}{2} \tilde{M}_o I \sum_k{ B^{dot}_k m_k} \]
Beta_IJ formulation
DHFORM_BETAIJ = 3
This form assumes a linear expansion in a virial coefficient form. It is used extensively in the book by Newmann, "Electrochemistry Systems", and is the beginning of more complex treatments for stronger electrolytes, fom Pitzer and from Harvey, Moller, and Weire.
\[ \ln(\gamma_k^\triangle) = -z_k^2 \frac{A_{Debye} \sqrt{I}}{ 1 + B_{Debye} a \sqrt{I}} + 2 \sum_j \beta_{j,k} m_j \]
In the current treatment the binary interaction coefficients, \( \beta_{j,k}\), are independent of temperature and pressure.
\[ \ln(a_o) = \frac{X_o - 1.0}{X_o} + \frac{ 2 A_{Debye} \tilde{M}_o}{3} (I)^{3/2} \sigma( B_{Debye} a \sqrt{I} ) - \tilde{M}_o \sum_j \sum_k \beta_{j,k} m_j m_k \]
In this formulation the ionic radius, \( a \), is a constant. This must be supplied to the model, in an ionicRadius XML block.
The \( \beta_{j,k} \) parameters are binary interaction parameters. They are supplied to the object in an DHBetaMatrix XML block. There are in principle \( N (N-1) /2 \) different, symmetric interaction parameters, where \( N \) are the number of solute species in the mechanism. An example is given below.
An example activityCoefficients XML block for this formulation is supplied below
Pitzer Beta_IJ formulation
DHFORM_PITZER_BETAIJ = 4
This form assumes an activity coefficient formulation consistent with a truncated form of Pitzer's formulation. Pitzer's formulation is equivalent to the formulations above in the dilute limit, where rigorous theory may be applied.
\[ \ln(\gamma_k^\triangle) = -z_k^2 \frac{A_{Debye}}{3} \frac{\sqrt{I}}{ 1 + B_{Debye} a \sqrt{I}} -2 z_k^2 \frac{A_{Debye}}{3} \frac{\ln(1 + B_{Debye} a \sqrt{I})}{ B_{Debye} a} + 2 \sum_j \beta_{j,k} m_j \]
\[ \ln(a_o) = \frac{X_o - 1.0}{X_o} + \frac{ 2 A_{Debye} \tilde{M}_o}{3} \frac{(I)^{3/2} }{1 + B_{Debye} a \sqrt{I} } - \tilde{M}_o \sum_j \sum_k \beta_{j,k} m_j m_k \]
Specification of the Debye Huckel Constants
In the equations above, the formulas for \( A_{Debye} \) and \( B_{Debye} \) are needed. The DebyeHuckel 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.
\[ A_{Debye} = \frac{F e B_{Debye}}{8 \pi \epsilon R T} {\left( C_o \tilde{M}_o \right)}^{1/2} \]
where
\[ B_{Debye} = \frac{F} {{(\frac{\epsilon R T}{2})}^{1/2}} \]
Therefore:
\[ A_{Debye} = \frac{1}{8 \pi} {\left(\frac{2 N_a \rho_o}{1000}\right)}^{1/2} {\left(\frac{N_a e^2}{\epsilon R T }\right)}^{3/2} \]
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 is given below.
Currently, \( B_{Debye} \) is a constant in the model, specified either by a default water value, or through the input file. This may have to be looked at, in the future.
Application within Kinetics Managers
For the time being, we have set the standard concentration for all species in this phase equal to the default concentration of the solvent at 298 K and 1 atm. This means that the kinetics operator essentially works on an activities basis, with units specified as if it were on a concentration basis.
For example, a bulk-phase binary reaction between liquid species j and k, producing a new liquid species l would have the following equation for its rate of progress variable, \( R^1 \), which has units of kmol m-3 s-1.
\[ R^1 = k^1 C_j^a C_k^a = k^1 (C_o a_j) (C_o a_k) \]
where
\[ C_j^a = C_o a_j \quad and \quad C_k^a = C_o a_k \]
\( C_j^a \) is the activity concentration of species j, and \( C_k^a \) is the activity concentration of species k. \( C_o \) is the concentration of water at 298 K and 1 atm. \( a_j \) is the activity of species j at the current temperature and pressure and concentration of the liquid phase. \(k^1 \) has units of m3 kmol-1 s-1.
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.
\[ R^{-1} = k^{-1} C_l^a = k^{-1} (C_o a_l) \]
where
\[ k^{-1} = k^1 K^{o,1} C_o \]
\(k^{-1} \) has units of s-1.
Note, this treatment may be modified in the future, as events dictate.
Instantiation of the Class
The constructor for this phase is NOT located in the default ThermoFactory for Cantera. However, a new DebyeHuckel 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.
Definition at line 563 of file DebyeHuckel.h.
Constructor & Destructor Documentation
◆ DebyeHuckel() [1/3]
| DebyeHuckel | ( | ) |
Default Constructor.
Definition at line 28 of file DebyeHuckel.cpp.
Referenced by DebyeHuckel::duplMyselfAsThermoPhase().
◆ DebyeHuckel() [2/3]
| DebyeHuckel | ( | const std::string & | inputFile, |
| const std::string & | id = "" |
||
| ) |
Full constructor for creating the phase.
- Parameters
-
inputFile File name containing the XML description of the phase id id attribute containing the name of the phase.
Definition at line 43 of file DebyeHuckel.cpp.
◆ DebyeHuckel() [3/3]
| DebyeHuckel | ( | XML_Node & | phaseRef, |
| const std::string & | id = "" |
||
| ) |
Full constructor for creating the phase.
- Parameters
-
phaseRef XML phase node containing the description of the phase id id attribute containing the name of the phase.
Definition at line 60 of file DebyeHuckel.cpp.
Member Function Documentation
◆ duplMyselfAsThermoPhase()
|
virtual |
Duplication routine for objects which inherit from ThermoPhase.
This virtual routine can be used to duplicate ThermoPhase objects inherited from ThermoPhase even if the application only has a pointer to ThermoPhase to work with.
These routines are basically wrappers around the derived copy constructor.
- Deprecated:
- To be removed after Cantera 2.3 for all classes derived from ThermoPhase.
Reimplemented from MolalityVPSSTP.
Definition at line 135 of file DebyeHuckel.cpp.
References DebyeHuckel::DebyeHuckel().
◆ eosType()
|
virtual |
Equation of state type flag.
The base class returns zero. Subclasses should define this to return a unique non-zero value. Constants defined for this purpose are listed in mix_defs.h.
- Deprecated:
- To be removed after Cantera 2.3. Use
type()instead.
Reimplemented from ThermoPhase.
Definition at line 140 of file DebyeHuckel.cpp.
References Cantera::cDebyeHuckel0, DebyeHuckel::m_formGC, and Cantera::warn_deprecated().
◆ 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.
Definition at line 592 of file DebyeHuckel.h.
◆ enthalpy_mole()
|
virtual |
Molar enthalpy. Units: J/kmol.
Reimplemented from ThermoPhase.
Definition at line 164 of file DebyeHuckel.cpp.
References DebyeHuckel::getPartialMolarEnthalpies(), DebyeHuckel::m_tmpV, and Phase::mean_X().
◆ entropy_mole()
|
virtual |
Molar entropy. 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
Reimplemented from ThermoPhase.
Definition at line 170 of file DebyeHuckel.cpp.
References DebyeHuckel::getPartialMolarEntropies(), DebyeHuckel::m_tmpV, and Phase::mean_X().
◆ gibbs_mole()
|
virtual |
Molar Gibbs function. Units: J/kmol.
Reimplemented from ThermoPhase.
Definition at line 176 of file DebyeHuckel.cpp.
References DebyeHuckel::getChemPotentials(), DebyeHuckel::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 182 of file DebyeHuckel.cpp.
References DebyeHuckel::getPartialMolarCp(), DebyeHuckel::m_tmpV, and Phase::mean_X().
◆ calcDensity()
|
protectedvirtual |
Calculate the density of the mixture using the partial molar volumes and mole fractions as input.
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 function is not a member of the ThermoPhase base class.
Reimplemented from VPStandardStateTP.
Definition at line 190 of file DebyeHuckel.cpp.
References PDSS_Water::density(), DebyeHuckel::getPartialMolarVolumes(), DebyeHuckel::m_densWaterSS, DebyeHuckel::m_tmpV, DebyeHuckel::m_waterSS, Phase::mean_X(), Phase::meanMolecularWeight(), and Phase::setDensity().
◆ setDensity()
|
virtual |
Set the internally stored density (gm/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
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.
This function will now throw an error condition if the input isn't exactly equal to the current density.
- Todo:
- 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 202 of file DebyeHuckel.cpp.
References Phase::density().
◆ setMolarDensity()
|
virtual |
Set the internally stored molar density (kmol/m^3) of the phase.
Overridden setMolarDensity() function is necessary because the density is not an independent variable.
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 211 of file DebyeHuckel.cpp.
References Phase::molarDensity().
◆ getActivityConcentrations()
|
virtual |
This method returns an array of generalized concentrations.
\( C^a_k\) are defined such that \( a_k = C^a_k / C^0_k, \) where \( C^0_k \) is a standard concentration defined below and \( a_k \) are activities used in the thermodynamic functions. These activity (or generalized) concentrations are used by kinetics manager classes to compute the forward and reverse rates of elementary reactions. Note that they may or may not have units of concentration — they might be partial pressures, mole fractions, or surface coverages, for example.
- Parameters
-
c Output array of generalized concentrations. The units depend upon the implementation of the reaction rate expressions within the phase.
Reimplemented from MolalityVPSSTP.
Definition at line 222 of file DebyeHuckel.cpp.
◆ 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 in kinetics calculations.
For the time being, we will use the concentration of pure solvent for the the standard concentration of all species. This has the effect of making reaction rates based on the molality of species proportional to the molality of the species.
- 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
Reimplemented from MolalityVPSSTP.
Definition at line 231 of file DebyeHuckel.cpp.
References MolalityVPSSTP::m_indexSolvent, and Phase::m_speciesSize.
◆ getActivities()
|
virtual |
Get the array of non-dimensional activities at the current solution temperature, pressure, and solution concentration.
(note solvent activity coefficient is on molar scale).
- Parameters
-
ac Output vector of activities. Length: m_kk.
Reimplemented from MolalityVPSSTP.
Definition at line 237 of file DebyeHuckel.cpp.
References VPStandardStateTP::_updateStandardStateThermo(), MolalityVPSSTP::m_indexSolvent, Phase::m_kk, DebyeHuckel::m_lnActCoeffMolal, MolalityVPSSTP::m_molalities, Phase::moleFraction(), and DebyeHuckel::s_update_lnMolalityActCoeff().
◆ getMolalityActivityCoefficients()
|
virtual |
Get the array of non-dimensional molality-based activity coefficients at the current solution temperature, pressure, and solution concentration.
note solvent is on molar scale. The solvent molar based activity coefficient is returned.
Note, most of the work is done in an internal private routine
- Parameters
-
acMolality Vector of Molality-based activity coefficients Length: m_kk
Reimplemented from MolalityVPSSTP.
Definition at line 254 of file DebyeHuckel.cpp.
References VPStandardStateTP::_updateStandardStateThermo(), DebyeHuckel::A_Debye_TP(), Phase::m_kk, DebyeHuckel::m_lnActCoeffMolal, and DebyeHuckel::s_update_lnMolalityActCoeff().
◆ 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 267 of file DebyeHuckel.cpp.
References VPStandardStateTP::getStandardChemPotentials(), MolalityVPSSTP::m_indexSolvent, Phase::m_kk, DebyeHuckel::m_lnActCoeffMolal, MolalityVPSSTP::m_molalities, Phase::moleFraction(), ThermoPhase::RT(), DebyeHuckel::s_update_lnMolalityActCoeff(), and Cantera::SmallNumber.
Referenced by DebyeHuckel::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
\[ \bar h_o(T,P) = h^{o}_o(T,P) - R T^2 \frac{d \ln(a_o}{dT} \]
The temperature dependence of the activity coefficients currently only occurs through the temperature dependence of the Debye constant.
- Parameters
-
hbar Output vector of species partial molar enthalpies. Length: m_kk. units are J/kmol.
Reimplemented from ThermoPhase.
Definition at line 290 of file DebyeHuckel.cpp.
References DebyeHuckel::dA_DebyedT_TP(), VPStandardStateTP::getEnthalpy_RT(), DebyeHuckel::m_dlnActCoeffMolaldT, Phase::m_kk, ThermoPhase::RT(), DebyeHuckel::s_update_dlnMolalityActCoeff_dT(), DebyeHuckel::s_update_lnMolalityActCoeff(), and Phase::temperature().
Referenced by DebyeHuckel::enthalpy_mole().
◆ getPartialMolarEntropies()
|
virtual |
Returns an array of partial molar entropies of the species in the solution.
Units: J/kmol/K.
Maxwell's equations provide an insight in how to calculate this (p.215 Smith and Van Ness)
\[ \frac{d\mu_i}{dT} = -\bar{s}_i \]
For this phase, the partial molar entropies are equal to the SS species entropies plus the ideal solution contribution:
\[ \bar s_k(T,P) = \hat s^0_k(T) - R log(M0 * molality[k]) \]
\[ \bar s_{solvent}(T,P) = \hat s^0_{solvent}(T) - R ((xmolSolvent - 1.0) / xmolSolvent) \]
The reference-state pure-species entropies, \( \hat s^0_k(T) \), at the reference pressure, \( P_{ref} \), are computed by the species thermodynamic property manager. They are polynomial functions of temperature.
- See also
- MultiSpeciesThermo
- Parameters
-
sbar Output vector of species partial molar entropies. Length = m_kk. units are J/kmol/K.
Reimplemented from ThermoPhase.
Definition at line 315 of file DebyeHuckel.cpp.
References DebyeHuckel::dA_DebyedT_TP(), Cantera::GasConstant, VPStandardStateTP::getEntropy_R(), DebyeHuckel::m_dlnActCoeffMolaldT, MolalityVPSSTP::m_indexSolvent, Phase::m_kk, DebyeHuckel::m_lnActCoeffMolal, MolalityVPSSTP::m_molalities, Phase::moleFraction(), ThermoPhase::RT(), DebyeHuckel::s_update_dlnMolalityActCoeff_dT(), DebyeHuckel::s_update_lnMolalityActCoeff(), and Cantera::SmallNumber.
Referenced by DebyeHuckel::entropy_mole().
◆ getPartialMolarCp()
|
virtual |
Return an array of partial molar heat capacities for the species in the mixture.
Units: J/kmol/K
- 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 367 of file DebyeHuckel.cpp.
References DebyeHuckel::dA_DebyedT_TP(), Cantera::GasConstant, VPStandardStateTP::getCp_R(), DebyeHuckel::m_d2lnActCoeffMolaldT2, DebyeHuckel::m_dlnActCoeffMolaldT, Phase::m_kk, ThermoPhase::RT(), DebyeHuckel::s_update_d2lnMolalityActCoeff_dT2(), DebyeHuckel::s_update_dlnMolalityActCoeff_dT(), DebyeHuckel::s_update_lnMolalityActCoeff(), and Phase::temperature().
Referenced by DebyeHuckel::cp_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 normally equal to the constant species molar volumes, except when the activity coefficients depend on pressure.
The general relation is
vbar_i = d(chemPot_i)/dP at const T, n
= V0_i + d(Gex)/dP)_T,M
= V0_i + RT d(lnActCoeffi)dP _T,M
- Parameters
-
vbar Output vector of species partial molar volumes. Length = m_kk. units are m^3/kmol.
Reimplemented from ThermoPhase.
Definition at line 355 of file DebyeHuckel.cpp.
References VPStandardStateTP::getStandardVolumes(), DebyeHuckel::m_dlnActCoeffMolaldP, Phase::m_kk, ThermoPhase::RT(), DebyeHuckel::s_update_dlnMolalityActCoeff_dP(), and DebyeHuckel::s_update_lnMolalityActCoeff().
Referenced by DebyeHuckel::calcDensity().
◆ addSpecies()
|
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 917 of file DebyeHuckel.cpp.
References MolalityVPSSTP::addSpecies(), DebyeHuckel::m_Aionic, DebyeHuckel::m_B_Dot, DebyeHuckel::m_d2lnActCoeffMolaldT2, DebyeHuckel::m_dlnActCoeffMolaldP, DebyeHuckel::m_dlnActCoeffMolaldT, DebyeHuckel::m_electrolyteSpeciesType, DebyeHuckel::m_lnActCoeffMolal, Phase::m_speciesSize, and DebyeHuckel::m_tmpV.
◆ initThermoXML()
|
virtual |
Import and initialize a ThermoPhase object using an XML tree.
Here we read extra information about the XML description of a phase. Regular information about elements and species and their reference state thermodynamic information have already been read at this point. For example, we do not need to call this function for ideal gas equations of state. This function is called from importPhase() after the elements and the species are initialized with default ideal solution level data.
The default implementation in ThermoPhase calls the virtual function initThermo() and then sets the "state" of the phase by looking for an XML element named "state", and then interpreting its contents by calling the virtual function setStateFromXML().
- 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 VPStandardStateTP.
Definition at line 420 of file DebyeHuckel.cpp.
References XML_Node::child(), XML_Node::hasChild(), XML_Node::id(), and DebyeHuckel::m_formDH.
◆ A_Debye_TP()
|
virtual |
Return the Debye Huckel constant as a function of temperature and pressure (Units = sqrt(kg/gmol))
The default is to assume that it is 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.
\[ A_{Debye} = \frac{F e B_{Debye}}{8 \pi \epsilon R T} {\left( C_o \tilde{M}_o \right)}^{1/2} \]
where
\[ B_{Debye} = \frac{F} {{(\frac{\epsilon R T}{2})}^{1/2}} \]
Therefore:
\[ A_{Debye} = \frac{1}{8 \pi} {\left(\frac{2 N_a \rho_o}{1000}\right)}^{1/2} {\left(\frac{N_a e^2}{\epsilon R T }\right)}^{3/2} \]
where
- Units = sqrt(kg/gmol)
- \( N_a \) 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
- Parameters
-
temperature Temperature in kelvin. Defaults to -1, in which case the temperature of the phase is assumed. pressure Pressure (Pa). Defaults to -1, in which case the pressure of the phase is assumed.
Definition at line 810 of file DebyeHuckel.cpp.
Referenced by DebyeHuckel::getMolalityActivityCoefficients(), and DebyeHuckel::s_update_lnMolalityActCoeff().
◆ dA_DebyedT_TP()
|
virtual |
Value of the derivative of the Debye Huckel constant with respect to temperature.
This is a function of temperature and pressure. See A_Debye_TP() for a definition of \( A_{Debye} \).
Units = sqrt(kg/gmol) K-1
- Parameters
-
temperature Temperature in kelvin. Defaults to -1, in which case the temperature of the phase is assumed. pressure Pressure (Pa). Defaults to -1, in which case the pressure of the phase is assumed.
Definition at line 836 of file DebyeHuckel.cpp.
Referenced by DebyeHuckel::getPartialMolarCp(), DebyeHuckel::getPartialMolarEnthalpies(), DebyeHuckel::getPartialMolarEntropies(), DebyeHuckel::s_update_d2lnMolalityActCoeff_dT2(), and DebyeHuckel::s_update_dlnMolalityActCoeff_dT().
◆ 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.
This is a function of temperature and pressure. See A_Debye_TP() for a definition of \( A_{Debye} \).
Units = sqrt(kg/gmol) K-2
- Parameters
-
temperature Temperature in kelvin. Defaults to -1, in which case the temperature of the phase is assumed. pressure Pressure (Pa). Defaults to -1, in which case the pressure of the phase is assumed.
Definition at line 860 of file DebyeHuckel.cpp.
Referenced by DebyeHuckel::s_update_d2lnMolalityActCoeff_dT2().
◆ dA_DebyedP_TP()
|
virtual |
Value of the derivative of the Debye Huckel constant with respect to pressure, as a function of temperature and pressure.
This is a function of temperature and pressure. See A_Debye_TP() for a definition of \( A_{Debye} \).
Units = sqrt(kg/gmol) Pa-1
- Parameters
-
temperature Temperature in kelvin. Defaults to -1, in which case the temperature of the phase is assumed. pressure Pressure (Pa). Defaults to -1, in which case the pressure of the phase is assumed.
Definition at line 884 of file DebyeHuckel.cpp.
Referenced by DebyeHuckel::s_update_dlnMolalityActCoeff_dP().
◆ AionicRadius()
| double AionicRadius | ( | int | k = 0 | ) | const |
Reports the ionic radius of the kth species.
- Parameters
-
k species index.
Definition at line 910 of file DebyeHuckel.cpp.
References DebyeHuckel::m_Aionic.
◆ formDH()
|
inline |
Returns the form of the Debye-Huckel parameterization used.
Definition at line 924 of file DebyeHuckel.h.
References DebyeHuckel::m_formDH.
◆ get_Beta_ij()
|
inline |
Returns a reference to M_Beta_ij.
Definition at line 929 of file DebyeHuckel.h.
References DebyeHuckel::m_Beta_ij.
◆ _nonpolarActCoeff()
|
staticprivate |
Static function that implements the non-polar species salt-out modifications.
Returns the calculated activity coefficients.
- Parameters
-
IionicMolality Value of the ionic molality (sqrt(gmol/kg))
Definition at line 934 of file DebyeHuckel.cpp.
◆ _osmoticCoeffHelgesonFixedForm()
|
private |
Formula for the osmotic coefficient that occurs in the GWB.
It is originally from Helgeson for a variable NaCl brine. It's to be used with extreme caution.
Definition at line 948 of file DebyeHuckel.cpp.
References DebyeHuckel::m_A_Debye, and DebyeHuckel::m_IionicMolalityStoich.
Referenced by DebyeHuckel::_lnactivityWaterHelgesonFixedForm().
◆ _lnactivityWaterHelgesonFixedForm()
|
private |
Formula for the log of the water activity that occurs in the GWB.
It is originally from Helgeson for a variable NaCl brine. It's to be used with extreme caution.
Definition at line 967 of file DebyeHuckel.cpp.
References DebyeHuckel::_osmoticCoeffHelgesonFixedForm(), MolalityVPSSTP::calcMolalities(), MolalityVPSSTP::m_indexSolvent, Phase::m_kk, DebyeHuckel::m_maxIionicStrength, MolalityVPSSTP::m_Mnaught, and MolalityVPSSTP::m_molalities.
◆ s_update_lnMolalityActCoeff()
|
private |
Calculate the log activity coefficients.
This function updates the internally stored natural logarithm of the molality activity coefficients. This is the main routine for implementing the activity coefficient formulation.
Definition at line 984 of file DebyeHuckel.cpp.
References DebyeHuckel::A_Debye_TP(), MolalityVPSSTP::calcMolalities(), DebyeHuckel::m_A_Debye, DebyeHuckel::m_IionicMolality, DebyeHuckel::m_IionicMolalityStoich, MolalityVPSSTP::m_indexSolvent, Phase::m_kk, DebyeHuckel::m_maxIionicStrength, MolalityVPSSTP::m_molalities, Phase::m_speciesCharge, DebyeHuckel::m_speciesCharge_Stoich, and Phase::moleFraction().
Referenced by DebyeHuckel::getActivities(), DebyeHuckel::getChemPotentials(), DebyeHuckel::getMolalityActivityCoefficients(), DebyeHuckel::getPartialMolarCp(), DebyeHuckel::getPartialMolarEnthalpies(), DebyeHuckel::getPartialMolarEntropies(), and DebyeHuckel::getPartialMolarVolumes().
◆ s_update_dlnMolalityActCoeff_dT()
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private |
Calculation of temperature derivative of activity coefficient.
Using internally stored values, this function calculates the temperature derivative of the logarithm of the activity coefficient for all species in the mechanism.
We assume that the activity coefficients are current in this routine. The solvent activity coefficient is on the molality scale. Its derivative is too.
Definition at line 1212 of file DebyeHuckel.cpp.
References DebyeHuckel::dA_DebyedT_TP(), DebyeHuckel::m_dlnActCoeffMolaldT, MolalityVPSSTP::m_indexSolvent, Phase::m_kk, and Phase::moleFraction().
Referenced by DebyeHuckel::getPartialMolarCp(), DebyeHuckel::getPartialMolarEnthalpies(), and DebyeHuckel::getPartialMolarEntropies().
◆ s_update_d2lnMolalityActCoeff_dT2()
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private |
Calculate the temperature 2nd derivative of the activity coefficient.
Using internally stored values, this function calculates the temperature 2nd derivative of the logarithm of the activity coefficient for all species in the mechanism.
We assume that the activity coefficients are current in this routine. Solvent activity coefficient is on the molality scale. Its derivatives are too.
Definition at line 1331 of file DebyeHuckel.cpp.
References DebyeHuckel::d2A_DebyedT2_TP(), DebyeHuckel::dA_DebyedT_TP(), DebyeHuckel::m_d2lnActCoeffMolaldT2, MolalityVPSSTP::m_indexSolvent, Phase::m_kk, and Phase::moleFraction().
Referenced by DebyeHuckel::getPartialMolarCp().
◆ s_update_dlnMolalityActCoeff_dP()
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private |
Calculate the pressure derivative of the activity coefficient.
Using internally stored values, this function calculates the pressure derivative of the logarithm of the activity coefficient for all species in the mechanism.
We assume that the activity coefficients, molalities, and A_Debye are current. Solvent activity coefficient is on the molality scale. Its derivatives are too.
Definition at line 1446 of file DebyeHuckel.cpp.
References DebyeHuckel::dA_DebyedP_TP(), DebyeHuckel::m_dlnActCoeffMolaldP, MolalityVPSSTP::m_indexSolvent, Phase::m_kk, and Phase::moleFraction().
Referenced by DebyeHuckel::getPartialMolarVolumes().
Member Data Documentation
◆ m_formDH
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protected |
form of the Debye-Huckel parameterization used in the model.
The options are described at the top of this document, and in the general documentation. The list is repeated here:
DHFORM_DILUTE_LIMIT = 0 (default) DHFORM_BDOT_AK = 1 DHFORM_BDOT_AUNIFORM = 2 DHFORM_BETAIJ = 3 DHFORM_PITZER_BETAIJ = 4
Definition at line 971 of file DebyeHuckel.h.
Referenced by DebyeHuckel::formDH(), and DebyeHuckel::initThermoXML().
◆ m_formGC
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protected |
Format for the generalized concentration:
0 = unity 1 = molar_volume 2 = solvent_volume (default)
The generalized concentrations can have three different forms depending on the value of the member attribute m_formGC, which is supplied in the constructor.
| m_formGC | GeneralizedConc | StandardConc |
|---|---|---|
| 0 | X_k | 1.0 |
| 1 | X_k / V_k | 1.0 / V_k |
| 2 | X_k / V_N | 1.0 / V_N |
The value and form of the generalized concentration will affect reaction rate constants involving species in this phase.
(HKM Note: Using option #1 may lead to spurious results and has been included only with warnings. The reason is that it molar volumes of electrolytes may often be negative. The molar volume of H+ is defined to be zero too. Either options 0 or 2 are the appropriate choice. Option 0 leads to bulk reaction rate constants which have units of s-1. Option 2 leads to bulk reaction rate constants for bimolecular rxns which have units of m-3 kmol-1 s-1.)
Definition at line 1001 of file DebyeHuckel.h.
Referenced by DebyeHuckel::eosType().
◆ m_electrolyteSpeciesType
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protected |
Vector containing the electrolyte species type.
The possible types are:
- solvent
- Charged Species
- weakAcidAssociated
- strongAcidAssociated
- polarNeutral
- nonpolarNeutral
Definition at line 1014 of file DebyeHuckel.h.
Referenced by DebyeHuckel::addSpecies().
◆ m_Aionic
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protected |
a_k = Size of the ionic species in the DH formulation. units = meters
Definition at line 1017 of file DebyeHuckel.h.
Referenced by DebyeHuckel::addSpecies(), and DebyeHuckel::AionicRadius().
◆ m_IionicMolality
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mutableprotected |
Current value of the ionic strength on the molality scale.
Definition at line 1020 of file DebyeHuckel.h.
Referenced by DebyeHuckel::s_update_lnMolalityActCoeff().
◆ m_maxIionicStrength
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protected |
Maximum value of the ionic strength allowed in the calculation of the activity coefficients.
Definition at line 1024 of file DebyeHuckel.h.
Referenced by DebyeHuckel::_lnactivityWaterHelgesonFixedForm(), and DebyeHuckel::s_update_lnMolalityActCoeff().
◆ m_useHelgesonFixedForm
| bool m_useHelgesonFixedForm |
If true, then the fixed for of Helgeson's activity for water is used instead of the rigorous form obtained from Gibbs-Duhem relation.
This should be used with caution, and is really only included as a validation exercise.
Definition at line 1031 of file DebyeHuckel.h.
◆ m_IionicMolalityStoich
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mutableprotected |
Stoichiometric ionic strength on the molality scale.
Definition at line 1034 of file DebyeHuckel.h.
Referenced by DebyeHuckel::_osmoticCoeffHelgesonFixedForm(), and DebyeHuckel::s_update_lnMolalityActCoeff().
◆ 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,
Definition at line 1053 of file DebyeHuckel.h.
◆ m_A_Debye
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mutableprotected |
Current value of the Debye Constant, 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 and pressure.
A_Debye = (F e B_Debye) / (8 Pi epsilon R T)
Units = sqrt(kg/gmol)
Nominal value(298K, atm) = 1.172576 sqrt(kg/gmol) based on: epsilon/epsilon_0 = 78.54 (water at 25C) T = 298.15 K B_Debye = 3.28640E9 sqrt(kg/gmol)/m
note in Pitzer's nomenclature, A_phi = A_Debye/3.0
Definition at line 1075 of file DebyeHuckel.h.
Referenced by DebyeHuckel::_osmoticCoeffHelgesonFixedForm(), and DebyeHuckel::s_update_lnMolalityActCoeff().
◆ m_B_Debye
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protected |
Current value of the constant that appears in the denominator.
B_Debye -> this expression appears on the bottom of the ln actCoeff term in the general Debye-Huckel expression It depends on temperature
B_Bebye = F / sqrt( epsilon R T / 2 )
Units = sqrt(kg/gmol) / m
Nominal value = 3.28640E9 sqrt(kg/gmol) / m based on: epsilon/epsilon_0 = 78.54 (water at 25C) T = 298.15 K
Definition at line 1093 of file DebyeHuckel.h.
◆ m_B_Dot
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protected |
Array of B_Dot values.
This expression is an extension of the Debye-Huckel expression used in some formulations to extend DH to higher molalities. B_dot is specific to the major ionic pair.
Definition at line 1101 of file DebyeHuckel.h.
Referenced by DebyeHuckel::addSpecies().
◆ m_waterSS
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protected |
Pointer to the Water standard state object.
derived from the equation of state for water.
Definition at line 1107 of file DebyeHuckel.h.
Referenced by DebyeHuckel::calcDensity().
◆ m_densWaterSS
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protected |
Storage for the density of water's standard state.
Density depends on temperature and pressure.
Definition at line 1113 of file DebyeHuckel.h.
Referenced by DebyeHuckel::calcDensity().
◆ m_waterProps
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protected |
Pointer to the water property calculator.
Definition at line 1116 of file DebyeHuckel.h.
◆ m_tmpV
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mutableprotected |
vector of size m_kk, used as a temporary holding area.
Definition at line 1119 of file DebyeHuckel.h.
Referenced by DebyeHuckel::addSpecies(), DebyeHuckel::calcDensity(), DebyeHuckel::cp_mole(), DebyeHuckel::enthalpy_mole(), DebyeHuckel::entropy_mole(), and DebyeHuckel::gibbs_mole().
◆ m_speciesCharge_Stoich
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protected |
Stoichiometric species charge -> This is for calculations of the ionic strength which ignore ion-ion pairing into neutral molecules.
The Stoichiometric species charge is the charge of one of the ion that would occur if the species broke into two charged ion pairs. NaCl -> m_speciesCharge_Stoich = -1; HSO4- -> H+ + SO42- = -2 -> The other charge is calculated. For species that aren't ion pairs, it's equal to the m_speciesCharge[] value.
Definition at line 1133 of file DebyeHuckel.h.
Referenced by DebyeHuckel::s_update_lnMolalityActCoeff().
◆ m_Beta_ij
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protected |
Array of 2D data used in the DHFORM_BETAIJ formulation Beta_ij.value(i,j) is the coefficient of the jth species for the specification of the chemical potential of the ith species.
Definition at line 1141 of file DebyeHuckel.h.
Referenced by DebyeHuckel::get_Beta_ij().
◆ m_lnActCoeffMolal
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mutableprotected |
Logarithm of the activity coefficients on the molality scale.
mutable because we change this if the composition or temperature or pressure changes.
Definition at line 1148 of file DebyeHuckel.h.
Referenced by DebyeHuckel::addSpecies(), DebyeHuckel::getActivities(), DebyeHuckel::getChemPotentials(), DebyeHuckel::getMolalityActivityCoefficients(), and DebyeHuckel::getPartialMolarEntropies().
◆ m_dlnActCoeffMolaldT
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mutableprotected |
Derivative of log act coeff wrt T.
Definition at line 1151 of file DebyeHuckel.h.
Referenced by DebyeHuckel::addSpecies(), DebyeHuckel::getPartialMolarCp(), DebyeHuckel::getPartialMolarEnthalpies(), DebyeHuckel::getPartialMolarEntropies(), and DebyeHuckel::s_update_dlnMolalityActCoeff_dT().
◆ m_d2lnActCoeffMolaldT2
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mutableprotected |
2nd Derivative of log act coeff wrt T
Definition at line 1154 of file DebyeHuckel.h.
Referenced by DebyeHuckel::addSpecies(), DebyeHuckel::getPartialMolarCp(), and DebyeHuckel::s_update_d2lnMolalityActCoeff_dT2().
◆ m_dlnActCoeffMolaldP
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mutableprotected |
Derivative of log act coeff wrt P.
Definition at line 1157 of file DebyeHuckel.h.
Referenced by DebyeHuckel::addSpecies(), DebyeHuckel::getPartialMolarVolumes(), and DebyeHuckel::s_update_dlnMolalityActCoeff_dP().
The documentation for this class was generated from the following files:
