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... | |
| HMWSoln (const HMWSoln &right) | |
| Copy Constructor. More... | |
| HMWSoln & | operator= (const HMWSoln &right) |
| Assignment operator. More... | |
| HMWSoln (int testProb) | |
| This is a special constructor, used to replicate test problems during the initial verification of the object. More... | |
| virtual | ~HMWSoln () |
| Destructor. More... | |
| ThermoPhase * | duplMyselfAsThermoPhase () const |
| Duplicator from the ThermoPhase parent class. More... | |
| void | constructPhaseFile (std::string inputFile, std::string id) |
| Import, construct, and initialize a HMWSoln phase specification from an XML tree into the current object. More... | |
| void | constructPhaseXML (XML_Node &phaseNode, std::string id) |
| Import and initialize a HMWSoln phase specification in an XML tree into the current object. 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 | initThermo () |
| Internal initialization required after all species have been added. More... | |
| 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... | |
| double | AionicRadius (int k=0) const |
| Reports the ionic radius of the kth species. More... | |
| int | formPitzer () const |
| formPitzer(): 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... | |
| int | debugPrinting () |
| Return int specifying the amount of debug printing. More... | |
Utilities | |
| virtual int | eosType () const |
| Equation of state type flag. 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 | intEnergy_mole () const |
| Molar internal energy. 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... | |
| 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 doublereal | logStandardConc (size_t k=0) const |
| Returns the natural logarithm of the standard concentration of the kth species. More... | |
| virtual void | getUnitsStandardConc (double *uA, int k=0, int sizeUA=6) const |
| Returns the units of the standard and generalized concentrations. 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... | |
Chemical Equilibrium | |
| virtual void | setToEquilState (const doublereal *lambda_RT) |
| This method is used by the ChemEquil equilibrium solver. More... | |
Critical state properties. | |
These methods are only implemented by some subclasses. | |
| virtual doublereal | critTemperature () const |
| Critical temperature (K). More... | |
| virtual doublereal | critPressure () const |
| Critical pressure (Pa). More... | |
| virtual doublereal | critDensity () const |
| Critical density (kg/m3). More... | |
Saturation properties. | |
These methods are only implemented by subclasses that implement full liquid-vapor equations of state. | |
| virtual doublereal | satTemperature (doublereal p) const |
| Return the saturation temperature given the pressure. More... | |
| virtual doublereal | satPressure (doublereal T) |
| Get the saturation pressure for a given 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... | |
 Public Member Functions inherited from MolalityVPSSTP | |
| MolalityVPSSTP () | |
| Default Constructor. More... | |
| MolalityVPSSTP (const MolalityVPSSTP &b) | |
| Copy constructor. More... | |
| MolalityVPSSTP & | operator= (const MolalityVPSSTP &b) |
| Assignment operator. 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, 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) 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 (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 |
| This method returns the activity convention. More... | |
| 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... | |
| void | getElectrochemPotentials (doublereal *mu) const |
| Get the species electrochemical potentials. More... | |
| void | initThermoXML (XML_Node &phaseNode, const std::string &id) |
| Import and initialize a ThermoPhase object. More... | |
| Public Member Functions inherited from VPStandardStateTP | |
| VPStandardStateTP () | |
| Constructor. More... | |
| VPStandardStateTP (const VPStandardStateTP &b) | |
| Copy Constructor. More... | |
| VPStandardStateTP & | operator= (const VPStandardStateTP &b) |
| Assignment operator. More... | |
| virtual | ~VPStandardStateTP () |
| Destructor. 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 concentration-like derivatives of the log activity coefficients. More... | |
| 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. 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 Enthalpy 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 at their standard states of solution at the current T and P of the solution. More... | |
| void | getPureGibbs (doublereal *gpure) const |
| Get the standard state Gibbs functions for each species at the current T and P. More... | |
| virtual void | getIntEnergy_RT (doublereal *urt) const |
| Returns the vector of nondimensional internal Energies of the standard state at the current temperature and pressure of the solution for each species. More... | |
| virtual void | getCp_R (doublereal *cpr) const |
| Get the nondimensional Heat Capacities at constant pressure for the standard state of the species at the current T and P. More... | |
| virtual void | getStandardVolumes (doublereal *vol) const |
| Get the molar volumes of each species in their standard states at the current T and P of the solution. More... | |
| virtual const vector_fp & | getStandardVolumes () const |
| 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... | |
| virtual void | getEnthalpy_RT_ref (doublereal *hrt) const |
| Returns the vector of nondimensional enthalpies of the reference state at the current temperature of the solution and the reference pressure for the species. More... | |
| 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 |
| virtual void | getEntropy_R_ref (doublereal *er) const |
| virtual void | getCp_R_ref (doublereal *cprt) const |
| 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... | |
| 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 |
| Public Member Functions inherited from ThermoPhase | |
| ThermoPhase () | |
| Constructor. More... | |
| virtual | ~ThermoPhase () |
| Destructor. Deletes the species thermo manager. More... | |
| ThermoPhase (const ThermoPhase &right) | |
| Copy Constructor for the ThermoPhase object. More... | |
| ThermoPhase & | operator= (const ThermoPhase &right) |
| Assignment operator. 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 int k) const |
| Report the 298 K Heat of Formation of the standard state of one species (J kmol-1) More... | |
| virtual void | modifyOneHf298SS (const int 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 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 | cv_vib (int, double) const |
| 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 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 | getdPartialMolarVolumes_dT (doublereal *d_vbar_dT) const |
| Return an array of derivatives of partial molar volumes wrt temperature for the species in the mixture. More... | |
| virtual void | getdPartialMolarVolumes_dP (doublereal *d_vbar_dP) const |
| Return an array of derivatives of partial molar volumes wrt pressure for the species in the mixture. More... | |
| virtual void | getdStandardVolumes_dT (doublereal *d_vol_dT) const |
| Get the derivative of the molar volumes of the species standard states wrt temperature at the current T and P of the solution. More... | |
| virtual void | getdStandardVolumes_dP (doublereal *d_vol_dP) const |
| Get the derivative molar volumes of the species standard states wrt pressure at the current T and P of the solution. 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. More... | |
| doublereal | intEnergy_mass () const |
| Specific internal energy. More... | |
| doublereal | entropy_mass () const |
| Specific entropy. More... | |
| doublereal | gibbs_mass () const |
| Specific Gibbs function. More... | |
| doublereal | cp_mass () const |
| Specific heat at constant pressure. More... | |
| doublereal | cv_mass () const |
| Specific heat at constant volume. 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... | |
| 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 (SpeciesThermo *spthermo) |
| Install a species thermodynamic property manager. More... | |
| virtual SpeciesThermo & | 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 (Cantera::XML_Node *phaseNode) |
| Add in species from Slave phases. 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... | |
| 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, 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, 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 (doublereal h, doublereal p, doublereal tol=1.e-4) |
| Set the internally stored specific enthalpy (J/kg) and pressure (Pa) of the phase. More... | |
| virtual void | setState_UV (doublereal u, doublereal v, doublereal tol=1.e-4) |
| Set the specific internal energy (J/kg) and specific volume (m^3/kg). More... | |
| virtual void | setState_SP (doublereal s, doublereal p, doublereal tol=1.e-4) |
| Set the specific entropy (J/kg/K) and pressure (Pa). More... | |
| virtual void | setState_SV (doublereal s, doublereal v, doublereal tol=1.e-4) |
| Set the specific entropy (J/kg/K) and specific volume (m^3/kg). More... | |
| Public Member Functions inherited from Phase | |
| Phase () | |
| Default constructor. More... | |
| virtual | ~Phase () |
| Destructor. More... | |
| Phase (const Phase &right) | |
| Copy Constructor. More... | |
| Phase & | operator= (const Phase &right) |
| Assignment operator. More... | |
| XML_Node & | xml () |
| Returns a reference to the XML_Node stored for the phase. More... | |
| void | saveState (vector_fp &state) const |
| Save the current internal state of the phase Write to vector 'state' the current internal state. 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 void | freezeSpecies () |
| Call when finished adding species. More... | |
| bool | speciesFrozen () |
| True if freezeSpecies has been called. More... | |
| virtual bool | ready () const |
| 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 Throws an exception if m is greater than nElements()-1. More... | |
| void | checkElementArraySize (size_t mm) const |
| Check that an array size is at least nElements() Throws an exception if mm is less than 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 Throws an exception if k is greater than nSpecies()-1. More... | |
| void | checkSpeciesArraySize (size_t kk) const |
| Check that an array size is at least nSpecies() Throws an exception if kk is less than nSpecies(). More... | |
| void | setMoleFractionsByName (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 (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, 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, 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... | |
| void | getMoleFractionsByName (compositionMap &x) 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... | |
| 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 There is no restriction on the sum of the mole fraction vector. 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... | |
| const doublereal * | moleFractdivMMW () const |
| Returns a const pointer to the start of the moleFraction/MW array. More... | |
| doublereal | temperature () const |
| Temperature (K). 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_Y (const doublereal *const Q) const |
| Evaluate the mass-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... | |
| doublereal | sum_xlogQ (doublereal *const Q) const |
| Evaluate \( \sum_k X_k \log Q_k \). More... | |
| void | addElement (const std::string &symbol, doublereal weight=-12345.0) |
| Add an element. More... | |
| void | addElement (const XML_Node &e) |
| Add an element from an XML specification. More... | |
| void | addUniqueElement (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, checking for uniqueness The uniqueness is checked by comparing the string symbol. More... | |
| void | addUniqueElement (const XML_Node &e) |
| Add an element, checking for uniqueness The uniqueness is checked by comparing the string symbol. More... | |
| void | addElementsFromXML (const XML_Node &phase) |
| Add all elements referenced in an XML_Node tree. More... | |
| void | freezeElements () |
| Prohibit addition of more elements, and prepare to add species. More... | |
| bool | elementsFrozen () |
| True if freezeElements has been called. More... | |
| size_t | addUniqueElementAfterFreeze (const std::string &symbol, doublereal weight, int atomicNumber, doublereal entropy298=ENTROPY298_UNKNOWN, int elem_type=CT_ELEM_TYPE_ABSPOS) |
| Add an element after elements have been frozen, checking for uniqueness The uniqueness is checked by comparing the string symbol. More... | |
| void | addSpecies (const std::string &name, const doublereal *comp, doublereal charge=0.0, doublereal size=1.0) |
| void | addUniqueSpecies (const std::string &name, const doublereal *comp, doublereal charge=0.0, doublereal size=1.0) |
| Add a species to the phase, checking for uniqueness of the name This routine checks for uniqueness of the string name. More... | |
Public Attributes | |
| int | m_form_A_Debye |
| Form of the constant outside the Debye-Huckel term called A. More... | |
| int | m_debugCalc |
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... | |
| doublereal | err (const std::string &msg) const |
| Local error routine. 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 | readXMLThetaAnion (XML_Node &BinSalt) |
| Process an XML node called "thetaAnion". More... | |
| void | readXMLThetaCation (XML_Node &BinSalt) |
| Process an XML node called "thetaCation". More... | |
| void | readXMLPsiCommonAnion (XML_Node &BinSalt) |
| Process an XML node called "psiCommonAnion". More... | |
| void | readXMLPsiCommonCation (XML_Node &BinSalt) |
| Process an XML node called "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 | readXMLCroppingCoefficients (const XML_Node &acNode) |
| Process an XML node called "croppingCoefficients" for the cropping coefficients values. More... | |
| void | calcIMSCutoffParams_ () |
| Precalculate the IMS Cutoff parameters for typeCutoff = 2. More... | |
| void | calcMCCutoffParams_ () |
| Calculate molality cut-off parameters. More... | |
Static Private Member Functions | |
| static int | interp_est (const std::string &estString) |
| Utility function to assign an integer value from a string for the ElectrolyteSpeciesType field. More... | |
Private Attributes | |
| int | m_formPitzer |
| This is the form of the Pitzer parameterization used in this model. More... | |
| int | m_formPitzerTemp |
| This is the form of the temperature dependence of Pitzer 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 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_IionicMolalityStoich |
| Stoichiometric ionic strength on the molality scale. 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... | |
| double | m_densWaterSS |
| density of standard-state water More... | |
| WaterProps * | m_waterProps |
| Pointer to the water property calculator. More... | |
| vector_fp | m_pp |
| Temporary array used in equilibrium calculations. 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... | |
| 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. More... | |
| vector_fp | m_Beta0MX_ij_LL |
| Derivative of Beta0_ij[i][j] wrt TT. More... | |
| vector_fp | m_Beta0MX_ij_P |
| Derivative of Beta0_ij[i][j] wrt P. More... | |
| Array2D | m_Beta0MX_ij_coeff |
| Array of coefficients for Beta0, a variable in Pitzer's papers. More... | |
| vector_fp | m_Beta1MX_ij |
| vector_fp | m_Beta1MX_ij_L |
| Derivative of Beta1_ij[i][j] wrt T. More... | |
| vector_fp | m_Beta1MX_ij_LL |
| Derivative of Beta1_ij[i][j] wrt TT. More... | |
| vector_fp | m_Beta1MX_ij_P |
| Derivative of Beta1_ij[i][j] wrt P. 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. More... | |
| vector_fp | m_Beta2MX_ij_LL |
| Derivative of Beta2_ij[i][j] wrt TT. More... | |
| vector_fp | m_Beta2MX_ij_P |
| Derivative of Beta2_ij[i][j] wrt P. More... | |
| Array2D | m_Beta2MX_ij_coeff |
| Array of coefficients for Beta2, a variable in Pitzer's papers. More... | |
| vector_fp | m_Alpha1MX_ij |
| Array of 2D data used in the Pitzer/HMW formulation. More... | |
| 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. More... | |
| vector_fp | m_CphiMX_ij_LL |
| Derivative of Cphi_ij[i][j] wrt TT. More... | |
| vector_fp | m_CphiMX_ij_P |
| Derivative of Cphi_ij[i][j] wrt P. 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. More... | |
| vector_fp | m_Theta_ij_LL |
| Derivative of Theta_ij[i][j] wrt TT. More... | |
| vector_fp | m_Theta_ij_P |
| Derivative of Theta_ij[i][j] wrt P. 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. 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 This is the basic cation - anion interaction. More... | |
| vector_fp | m_BMX_IJ_L |
| Derivative of BMX_IJ wrt T. More... | |
| vector_fp | m_BMX_IJ_LL |
| Derivative of BMX_IJ wrt TT. More... | |
| vector_fp | m_BMX_IJ_P |
| Derivative of BMX_IJ wrt P. 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. More... | |
| vector_fp | m_BprimeMX_IJ_LL |
| Derivative of BprimeMX wrt TT. More... | |
| vector_fp | m_BprimeMX_IJ_P |
| Derivative of BprimeMX wrt P. 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. More... | |
| vector_fp | m_BphiMX_IJ_LL |
| Derivative of BphiMX_IJ wrt TT. More... | |
| vector_fp | m_BphiMX_IJ_P |
| Derivative of BphiMX_IJ wrt P. 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. More... | |
| vector_fp | m_Phi_IJ_LL |
| Derivative of m_Phi_IJ wrt TT. More... | |
| vector_fp | m_Phi_IJ_P |
| Derivative of m_Phi_IJ wrt P. 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. More... | |
| vector_fp | m_PhiPhi_IJ_LL |
| Derivative of m_PhiPhi_IJ wrt TT. More... | |
| vector_fp | m_PhiPhi_IJ_P |
| Derivative of m_PhiPhi_IJ wrt P. 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. More... | |
| vector_fp | m_CMX_IJ_LL |
| Derivative of m_CMX_IJ wrt TT. More... | |
| vector_fp | m_CMX_IJ_P |
| Derivative of m_CMX_IJ wrt P. 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... | |
| int | IMS_typeCutoff_ |
| IMS Cutoff type. 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_gamma_o_min_ |
| gamma_o value for the cutoff process at the zero solvent point More... | |
| doublereal | IMS_gamma_k_min_ |
| gamma_k minimum for the cutoff process at the zero solvent point More... | |
| doublereal | IMS_cCut_ |
| Parameter in the polyExp cutoff treatment having to do with rate of exp decay. More... | |
| doublereal | IMS_slopefCut_ |
| Parameter in the polyExp cutoff treatment. 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 | MC_X_o_min_ |
| gamma_o value for the cutoff process at the zero solvent point More... | |
| doublereal | MC_slopepCut_ |
| Parameter in the Molality Exp cutoff treatment. More... | |
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 |
| std::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 doublereal | pressure () const |
| Pressure. More... | |
| virtual void | setPressure (doublereal p) |
| Set the internally stored pressure (Pa) at constant temperature and composition. More... | |
| virtual doublereal | density () const |
| Returns the current value of the density. More... | |
| void | setDensity (const doublereal rho) |
| Set the internally stored density (kg/m^3) of the phase. More... | |
| void | setMolarDensity (const doublereal conc) |
| Set the internally stored molar density (kmol/m^3) for the phase. More... | |
| virtual void | setTemperature (const doublereal temp) |
| Set the temperature (K) More... | |
| virtual void | setState_TP (doublereal t, doublereal p) |
| Set the temperature (K) and pressure (Pa) More... | |
| virtual doublereal | isothermalCompressibility () const |
| The isothermal compressibility. More... | |
| virtual doublereal | thermalExpansionCoeff () const |
| The thermal expansion coefficient. 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... | |
| const vector_fp & | Gibbs_RT_ref () const |
| Protected Member Functions inherited from Phase | |
| void | init (const vector_fp &mw) |
| void | setMolecularWeight (const int k, const double mw) |
| Set the molecular weight of a single species to a given value. 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 |
| VPSSMgr * | m_VPSS_ptr |
| Pointer to the VPSS manager that calculates all of the standard state info efficiently. More... | |
| std::vector< PDSS * > | m_PDSS_storage |
| Storage for the PDSS objects for the species. More... | |
| Protected Attributes inherited from ThermoPhase | |
| SpeciesThermo * | 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. 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... | |
| std::vector< doublereal > | xMol_Ref |
| Reference Mole Fraction Composition. More... | |
| Protected Attributes inherited from Phase | |
| 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... | |
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 \form#175 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 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 HMWSoln 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. 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.
<H3> Ionic Strength </H3> Most of the parameterizations within the model use the ionic strength as a key variable. The ionic strength, \form#185 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 calculated
\( I_s \) we need to catalog all species in the phase. This is done using the following categories:
- cEST_solvent : Solvent species (neutral)
- cEST_chargedSpecies Charged species (charged)
- cEST_weakAcidAssociated Species 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_strongAcidAssociated Species which always breaks apart into charged species. It may or may not be charged. Normally, these aren't included in the speciation vector.
- cEST_polarNeutral Polar neutral species
- cEST_nonpolarNeutral Non 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. <H3> Specification of the Excess Gibbs Free Energy </H3> Pitzer's formulation may best be represented as a specification of the excess gibbs free energy, \form#270, 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.
<H3> Multicomponent Activity Coefficients for Solutes </H3> 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
\[ \ln(\gamma_N^\triangle) = 2 \left( \sum_i m_i \lambda_{iN}\right) \]
<H3> Activity of the Water Solvent </H3> The activity for the solvent water, \form#197, 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, \form#82.
\[ \phi - 1 = - \left( \frac{d\left(\frac{G^{ex}}{RT} \right)}{d(\tilde{M}_o n_o)} \right) \frac{1}{\sum_{i \ne 0} m_i} \]
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.
\[ \Phi^{\phi}_{c{c'}} = {\Phi}_{c{c'}} + I \frac{d{\Phi}_{c{c'}}}{dI} \]
\[ \Phi^{\phi}_{a{a'}} = \Phi_{a{a'}} + I \frac{d\Phi_{a{a'}}}{dI} \]
<H3> Temperature and Pressure Dependence of the Pitzer Parameters </H3> 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 \( \Psi_{ca{a'}} \).
<H3> Like-Charged Binary Ion Parameters and the Mixing Parameters </H3> The previous section contained the functions, \form#274,
\( \Phi_{a{a'}} \) 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.
<H3> Ternary Pitzer Parameters </H3> The \form#286 and \form#342 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 <TT> psiCommonCation </TT> and <TT> psiCommonAnion </TT>. The species id's are specified in attribute fields in the XML element. The fields <TT>cation</TT>, <TT> anion1</TT>, and <TT> anion2</TT> are used for <TT>psiCommonCation</TT>. The fields <TT> anion</TT>, <TT>cation1</TT> and <TT>cation2</TT> are used for <TT> psiCommonAnion</TT>. An example block is given below. The <TT> Theta </TT> field below is a duplicate of the <TT> thetaAnion </TT> 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
<activityCoefficients model="Pitzer" TempModel="complex1">
<!-- Pitzer Coefficients
These coefficients are from Pitzer's main
paper, in his book.
-->
<A_Debye model="water" />
<ionicRadius default="3.042843" units="Angstroms">
</ionicRadius>
<binarySaltParameters cation="Na+" anion="Cl-">
<beta0> 0.0765, 0.008946, -3.3158E-6,
-777.03, -4.4706
</beta0>
<beta1> 0.2664, 6.1608E-5, 1.0715E-6, 0.0, 0.0 </beta1>
<beta2> 0.0, 0.0, 0.0, 0.0, 0.0 </beta2>
<Cphi> 0.00127, -4.655E-5, 0.0,
33.317, 0.09421
</Cphi>
<Alpha1> 2.0 </Alpha1>
</binarySaltParameters>
<binarySaltParameters cation="H+" anion="Cl-">
<beta0> 0.1775, 0.0, 0.0, 0.0, 0.0 </beta0>
<beta1> 0.2945, 0.0, 0.0, 0.0, 0.0 </beta1>
<beta2> 0.0, 0.0, 0.0, 0.0, 0.0 </beta2>
<Cphi> 0.0008, 0.0, 0.0, 0.0, 0.0 </Cphi>
<Alpha1> 2.0 </Alpha1>
</binarySaltParameters>
<binarySaltParameters cation="Na+" anion="OH-">
<beta0> 0.0864, 0.0, 0.0, 0.0, 0.0 </beta0>
<beta1> 0.253, 0.0, 0.0 0.0, 0.0 </beta1>
<beta2> 0.0 0.0, 0.0, 0.0, 0.0 </beta2>
<Cphi> 0.0044, 0.0, 0.0, 0.0, 0.0 </Cphi>
<Alpha1> 2.0 </Alpha1>
</binarySaltParameters>
<thetaAnion anion1="Cl-" anion2="OH-">
<Theta> -0.05, 0.0, 0.0, 0.0, 0.0 </Theta>
</thetaAnion>
<psiCommonCation cation="Na+" anion1="Cl-" anion2="OH-">
<Theta> -0.05, 0.0, 0.0, 0.0, 0.0 </Theta>
<Psi> -0.006 </Psi>
</psiCommonCation>
<thetaCation cation1="Na+" cation2="H+">
<Theta> 0.036, 0.0, 0.0, 0.0, 0.0 </Theta>
</thetaCation>
<psiCommonAnion anion="Cl-" cation1="Na+" cation2="H+">
<Theta> 0.036, 0.0, 0.0, 0.0, 0.0 </Theta>
<Psi> -0.004 </Psi>
</psiCommonAnion>
</activityCoefficients>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-1
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 m3 kmol-1 s-1.
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 s-1.
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.
<phase id="NaCl_electrolyte" dim="3">
<speciesArray datasrc="#species_waterSolution">
H2O(L) Na+ Cl- H+ OH-
</speciesArray>
<state>
<temperature units="K"> 300 </temperature>
<pressure units="Pa">101325.0</pressure>
<soluteMolalities>
Na+:3.0
Cl-:3.0
H+:1.0499E-8
OH-:1.3765E-6
</soluteMolalities>
</state>
<!-- thermo model identifies the inherited class
from ThermoPhase that will handle the thermodynamics.
-->
<thermo model="HMW">
<standardConc model="solvent_volume" />
<activityCoefficients model="Pitzer" TempModel="complex1">
<!-- Pitzer Coefficients
These coefficients are from Pitzer's main
paper, in his book.
-->
<A_Debye model="water" />
<ionicRadius default="3.042843" units="Angstroms">
</ionicRadius>
<binarySaltParameters cation="Na+" anion="Cl-">
<beta0> 0.0765, 0.008946, -3.3158E-6,
-777.03, -4.4706
</beta0>
<beta1> 0.2664, 6.1608E-5, 1.0715E-6 </beta1>
<beta2> 0.0 </beta2>
<Cphi> 0.00127, -4.655E-5, 0.0,
33.317, 0.09421
</Cphi>
<Alpha1> 2.0 </Alpha1>
</binarySaltParameters>
<binarySaltParameters cation="H+" anion="Cl-">
<beta0> 0.1775, 0.0, 0.0, 0.0, 0.0</beta0>
<beta1> 0.2945, 0.0, 0.0 </beta1>
<beta2> 0.0 </beta2>
<Cphi> 0.0008, 0.0, 0.0, 0.0, 0.0 </Cphi>
<Alpha1> 2.0 </Alpha1>
</binarySaltParameters>
<binarySaltParameters cation="Na+" anion="OH-">
<beta0> 0.0864, 0.0, 0.0, 0.0, 0.0 </beta0>
<beta1> 0.253, 0.0, 0.0 </beta1>
<beta2> 0.0 </beta2>
<Cphi> 0.0044, 0.0, 0.0, 0.0, 0.0 </Cphi>
<Alpha1> 2.0 </Alpha1>
</binarySaltParameters>
<thetaAnion anion1="Cl-" anion2="OH-">
<Theta> -0.05 </Theta>
</thetaAnion>
<psiCommonCation cation="Na+" anion1="Cl-" anion2="OH-">
<Theta> -0.05 </Theta>
<Psi> -0.006 </Psi>
</psiCommonCation>
<thetaCation cation1="Na+" cation2="H+">
<Theta> 0.036 </Theta>
</thetaCation>
<psiCommonAnion anion="Cl-" cation1="Na+" cation2="H+">
<Theta> 0.036 </Theta>
<Psi> -0.004 </Psi>
</psiCommonAnion>
</activityCoefficients>
<solvent> H2O(L) </solvent>
</thermo>
<elementArray datasrc="elements.xml"> O H Na Cl </elementArray>
<kinetics model="none" >
</kinetics>
</phase>
Constructor & Destructor Documentation
| HMWSoln | ( | ) |
Default Constructor.
Definition at line 31 of file HMWSoln.cpp.
References HMWSoln::elambda, and HMWSoln::elambda1.
Referenced by HMWSoln::duplMyselfAsThermoPhase().
| 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 81 of file HMWSoln.cpp.
References HMWSoln::elambda, HMWSoln::elambda1, and ThermoPhase::initThermoFile().
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 132 of file HMWSoln.cpp.
References HMWSoln::elambda, HMWSoln::elambda1, Cantera::findXMLPhase(), and Cantera::importPhase().
Copy Constructor.
Copy constructor for the object. Constructed object will be a clone of this object, but will also own all of its data. This is a wrapper around the assignment operator
- Parameters
-
right Object to be copied.
Definition at line 183 of file HMWSoln.cpp.
| HMWSoln | ( | int | testProb | ) |
This is a special constructor, used to replicate test problems during the initial verification of the object.
test problems: 1 = NaCl problem - 5 species - the thermo is read in from an XML file
speci molality charge Cl- 6.0954 6.0997E+00 -1 H+ 1.0000E-08 2.1628E-09 1 Na+ 6.0954E+00 6.0997E+00 1 OH- 7.5982E-07 1.3977E-06 -1 HMW_params____beta0MX__beta1MX__beta2MX__CphiMX_____alphaMX__thetaij 10 1 2 0.1775 0.2945 0.0 0.00080 2.0 0.0 1 3 0.0765 0.2664 0.0 0.00127 2.0 0.0 1 4 0.0 0.0 0.0 0.0 0.0 -0.050 2 3 0.0 0.0 0.0 0.0 0.0 0.036 2 4 0.0 0.0 0.0 0.0 0.0 0.0 3 4 0.0864 0.253 0.0 0.0044 2.0 0.0 Triplet_interaction_parameters_psiaa'_or_psicc' 2 1 2 3 -0.004 1 3 4 -0.006
- Parameters
-
testProb Hard -coded test problem to instantiate. Current valid values are 1.
- Deprecated:
- To be refactored into a standalone test
Definition at line 395 of file HMWSoln.cpp.
References ThermoPhase::initThermoFile(), HMWSoln::m_Alpha1MX_ij, HMWSoln::m_Beta0MX_ij, HMWSoln::m_Beta1MX_ij, HMWSoln::m_CounterIJ, HMWSoln::m_CphiMX_ij, Phase::m_kk, HMWSoln::m_Psi_ijk, HMWSoln::m_Psi_ijk_coeff, HMWSoln::m_Theta_ij, HMWSoln::printCoeffs(), and Phase::speciesIndex().
|
virtual |
Member Function Documentation
Assignment operator.
Assignment operator for the object. Constructed object will be a clone of this object, but will also own all of its data.
- Parameters
-
right Object to be copied.
Definition at line 235 of file HMWSoln.cpp.
References HMWSoln::CROP_speciesCropped_, HMWSoln::IMS_cCut_, HMWSoln::IMS_gamma_k_min_, HMWSoln::IMS_gamma_o_min_, HMWSoln::IMS_lnActCoeffMolal_, HMWSoln::IMS_slopefCut_, HMWSoln::IMS_slopegCut_, HMWSoln::IMS_typeCutoff_, HMWSoln::IMS_X_o_cutoff_, HMWSoln::m_A_Debye, HMWSoln::m_Aionic, HMWSoln::m_Alpha1MX_ij, HMWSoln::m_Alpha2MX_ij, HMWSoln::m_Beta0MX_ij, HMWSoln::m_Beta0MX_ij_coeff, HMWSoln::m_Beta0MX_ij_L, HMWSoln::m_Beta0MX_ij_LL, HMWSoln::m_Beta0MX_ij_P, HMWSoln::m_Beta1MX_ij, HMWSoln::m_Beta1MX_ij_coeff, HMWSoln::m_Beta1MX_ij_L, HMWSoln::m_Beta1MX_ij_LL, HMWSoln::m_Beta1MX_ij_P, HMWSoln::m_Beta2MX_ij, HMWSoln::m_Beta2MX_ij_coeff, HMWSoln::m_Beta2MX_ij_L, HMWSoln::m_Beta2MX_ij_LL, HMWSoln::m_Beta2MX_ij_P, HMWSoln::m_BMX_IJ, HMWSoln::m_BMX_IJ_L, HMWSoln::m_BMX_IJ_LL, HMWSoln::m_BMX_IJ_P, HMWSoln::m_BphiMX_IJ, HMWSoln::m_BphiMX_IJ_L, HMWSoln::m_BphiMX_IJ_LL, HMWSoln::m_BphiMX_IJ_P, HMWSoln::m_BprimeMX_IJ, HMWSoln::m_BprimeMX_IJ_L, HMWSoln::m_BprimeMX_IJ_LL, HMWSoln::m_BprimeMX_IJ_P, HMWSoln::m_CMX_IJ, HMWSoln::m_CMX_IJ_L, HMWSoln::m_CMX_IJ_LL, HMWSoln::m_CMX_IJ_P, HMWSoln::m_CounterIJ, HMWSoln::m_CphiMX_ij, HMWSoln::m_CphiMX_ij_coeff, HMWSoln::m_CphiMX_ij_L, HMWSoln::m_CphiMX_ij_LL, HMWSoln::m_CphiMX_ij_P, HMWSoln::m_d2lnActCoeffMolaldT2_Scaled, HMWSoln::m_d2lnActCoeffMolaldT2_Unscaled, HMWSoln::m_debugCalc, HMWSoln::m_densWaterSS, HMWSoln::m_dlnActCoeffMolaldP_Scaled, HMWSoln::m_dlnActCoeffMolaldP_Unscaled, HMWSoln::m_dlnActCoeffMolaldT_Scaled, HMWSoln::m_dlnActCoeffMolaldT_Unscaled, HMWSoln::m_form_A_Debye, HMWSoln::m_formGC, HMWSoln::m_formPitzer, HMWSoln::m_formPitzerTemp, HMWSoln::m_g2func_IJ, HMWSoln::m_gamma_tmp, HMWSoln::m_gfunc_IJ, HMWSoln::m_h2func_IJ, HMWSoln::m_hfunc_IJ, HMWSoln::m_IionicMolality, HMWSoln::m_IionicMolalityStoich, HMWSoln::m_Lambda_nj, HMWSoln::m_Lambda_nj_coeff, HMWSoln::m_Lambda_nj_L, HMWSoln::m_Lambda_nj_LL, HMWSoln::m_Lambda_nj_P, HMWSoln::m_lnActCoeffMolal_Scaled, HMWSoln::m_lnActCoeffMolal_Unscaled, HMWSoln::m_maxIionicStrength, HMWSoln::m_molalitiesAreCropped, HMWSoln::m_molalitiesCropped, HMWSoln::m_Mu_nnn, HMWSoln::m_Mu_nnn_coeff, HMWSoln::m_Mu_nnn_L, HMWSoln::m_Mu_nnn_LL, HMWSoln::m_Mu_nnn_P, HMWSoln::m_Phi_IJ, HMWSoln::m_Phi_IJ_L, HMWSoln::m_Phi_IJ_LL, HMWSoln::m_Phi_IJ_P, HMWSoln::m_PhiPhi_IJ, HMWSoln::m_PhiPhi_IJ_L, HMWSoln::m_PhiPhi_IJ_LL, HMWSoln::m_PhiPhi_IJ_P, HMWSoln::m_Phiprime_IJ, HMWSoln::m_pp, HMWSoln::m_Psi_ijk, HMWSoln::m_Psi_ijk_coeff, HMWSoln::m_Psi_ijk_L, HMWSoln::m_Psi_ijk_LL, HMWSoln::m_Psi_ijk_P, HMWSoln::m_speciesCharge_Stoich, HMWSoln::m_TempPitzerRef, HMWSoln::m_Theta_ij, HMWSoln::m_Theta_ij_coeff, HMWSoln::m_Theta_ij_L, HMWSoln::m_Theta_ij_LL, HMWSoln::m_Theta_ij_P, HMWSoln::m_tmpV, HMWSoln::m_waterProps, HMWSoln::m_waterSS, HMWSoln::MC_slopepCut_, HMWSoln::MC_X_o_cutoff_, HMWSoln::MC_X_o_min_, and MolalityVPSSTP::operator=().
|
virtual |
Duplicator from the ThermoPhase parent class.
Given a pointer to a ThermoPhase object, this function will duplicate the ThermoPhase object and all underlying structures. This is basically a wrapper around the copy constructor.
- Returns
- returns a pointer to a ThermoPhase
Reimplemented from MolalityVPSSTP.
Definition at line 544 of file HMWSoln.cpp.
References HMWSoln::HMWSoln().
| void constructPhaseFile | ( | std::string | inputFile, |
| std::string | id | ||
| ) |
Import, construct, and initialize a HMWSoln phase specification from an XML tree into the current object.
Definition at line 976 of file HMWSoln_input.cpp.
References XML_Node::build(), XML_Node::copy(), Cantera::findInputFile(), and Cantera::findXMLPhase().
| void constructPhaseXML | ( | XML_Node & | phaseNode, |
| std::string | id | ||
| ) |
Import and initialize a HMWSoln phase specification in an XML tree into the current object.
Here we read an XML description of the phase. We import descriptions of the elements that make up the species in a phase. We import information about the species, including their reference state thermodynamic polynomials. We then freeze the state of the species.
Then, we read the species molar volumes from the xml tree to finish the initialization.
- 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.
Definition at line 1007 of file HMWSoln_input.cpp.
References XML_Node::attrib(), XML_Node::child(), Cantera::fpValueCheck(), ctml::getStringArray(), XML_Node::hasChild(), XML_Node::id(), Cantera::importPhase(), Cantera::lowercase(), and PITZERFORM_BASE.
Referenced by Cantera::newPhase().
|
virtual |
Equation of state type flag.
The ThermoPhase base class returns zero. Subclasses should define this to return a unique non-zero value. Known constants defined for this purpose are listed in mix_defs.h. The MolalityVPSSTP class also returns zero, as it is a non-complete class.
Reimplemented from MolalityVPSSTP.
Definition at line 549 of file HMWSoln.cpp.
References Cantera::cHMWSoln0, and HMWSoln::m_formGC.
|
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 571 of file HMWSoln.cpp.
References DATA_PTR, Phase::getMoleFractions(), HMWSoln::getPartialMolarEnthalpies(), HMWSoln::m_pp, HMWSoln::m_tmpV, and Phase::mean_X().
Referenced by HMWSoln::intEnergy_mole().
|
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 578 of file HMWSoln.cpp.
References DATA_PTR, Cantera::GasConstant, VPStandardStateTP::getEnthalpy_RT(), HMWSoln::getPartialMolarEnthalpies(), HMWSoln::m_gamma_tmp, Phase::m_kk, HMWSoln::m_tmpV, Phase::mean_X(), and Phase::temperature().
Referenced by HMWSoln::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 591 of file HMWSoln.cpp.
References Phase::charge(), DATA_PTR, Phase::getMoleFractions(), Phase::m_kk, HMWSoln::m_tmpV, Cantera::npos, and HMWSoln::relative_enthalpy().
|
virtual |
Molar internal energy. Units: J/kmol.
Molar internal energy of the solution. Units: J/kmol. (HKM -> Bump up to Parent object)
Reimplemented from ThermoPhase.
Definition at line 631 of file HMWSoln.cpp.
References HMWSoln::enthalpy_mole(), Phase::molarDensity(), and HMWSoln::pressure().
|
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
- SpeciesThermo
(HKM -> Bump up to Parent object)
Reimplemented from ThermoPhase.
Definition at line 639 of file HMWSoln.cpp.
References DATA_PTR, HMWSoln::getPartialMolarEntropies(), HMWSoln::m_tmpV, and Phase::mean_X().
|
virtual |
Molar Gibbs function. Units: J/kmol.
Reimplemented from ThermoPhase.
Definition at line 645 of file HMWSoln.cpp.
References DATA_PTR, HMWSoln::getChemPotentials(), HMWSoln::m_tmpV, and Phase::mean_X().
|
virtual |
Molar heat capacity at constant pressure. Units: J/kmol/K.
Reimplemented from ThermoPhase.
Definition at line 651 of file HMWSoln.cpp.
References DATA_PTR, HMWSoln::getPartialMolarCp(), HMWSoln::m_tmpV, and Phase::mean_X().
Referenced by HMWSoln::cv_mole().
|
virtual |
Molar heat capacity at constant volume. Units: J/kmol/K.
Reimplemented from ThermoPhase.
Definition at line 657 of file HMWSoln.cpp.
References HMWSoln::cp_mole(), HMWSoln::isothermalCompressibility(), Phase::molarVolume(), Phase::temperature(), and HMWSoln::thermalExpansionCoeff().
|
virtual |
Pressure.
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. Units: Pa. For this incompressible system, we return the internally stored independent value of the pressure.
Reimplemented from ThermoPhase.
Definition at line 671 of file HMWSoln.cpp.
References VPStandardStateTP::m_Pcurrent.
Referenced by HMWSoln::A_Debye_TP(), HMWSoln::d2A_DebyedT2_TP(), HMWSoln::dA_DebyedP_TP(), HMWSoln::dA_DebyedT_TP(), HMWSoln::intEnergy_mole(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), and HMWSoln::satPressure().
|
virtual |
Set the internally stored pressure (Pa) at constant temperature and composition.
This method sets the pressure within the object. The water model is a completely compressible model. Also, the dielectric constant is pressure dependent.
- Parameters
-
p input Pressure (Pa)
- Todo:
- Implement a variable pressure capability
Reimplemented from VPStandardStateTP.
Definition at line 676 of file HMWSoln.cpp.
References HMWSoln::setState_TP(), and Phase::temperature().
|
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 is a non-virtual function, which is not a member of the ThermoPhase base class.
Reimplemented from VPStandardStateTP.
Definition at line 681 of file HMWSoln.cpp.
References Phase::getMoleFractions(), HMWSoln::getPartialMolarVolumes(), Phase::m_kk, HMWSoln::m_pp, HMWSoln::m_tmpV, Phase::meanMolecularWeight(), and Phase::setDensity().
Referenced by HMWSoln::setState_TP().
|
virtual |
Returns the current value of the density.
- Returns
- value of the density. Units: kg/m^3
Reimplemented from Phase.
Definition at line 709 of file HMWSoln.cpp.
References Phase::density().
Referenced by HMWSoln::setDensity().
|
virtual |
Set the internally stored density (kg/m^3) of the phase.
Overwritten 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 715 of file HMWSoln.cpp.
References HMWSoln::density().
|
virtual |
Set the internally stored molar density (kmol/m^3) for the phase.
Overwritten 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 725 of file HMWSoln.cpp.
|
virtual |
Set the temperature (K)
This function sets the temperature, and makes sure that the value propagates to underlying objects, such as the water standard state model.
- Todo:
- Make Phase::setTemperature a virtual function
- Parameters
-
temp Temperature in kelvin
Reimplemented from VPStandardStateTP.
Definition at line 731 of file HMWSoln.cpp.
References VPStandardStateTP::m_Pcurrent, and HMWSoln::setState_TP().
|
virtual |
Set the temperature (K) and pressure (Pa)
Set the temperature and pressure.
- Parameters
-
t Temperature (K) p Pressure (Pa)
Reimplemented from VPStandardStateTP.
Definition at line 736 of file HMWSoln.cpp.
References HMWSoln::calcDensity(), PDSS::density(), HMWSoln::m_densWaterSS, VPStandardStateTP::m_Pcurrent, HMWSoln::m_waterSS, Phase::setTemperature(), and VPStandardStateTP::updateStandardStateThermo().
Referenced by HMWSoln::setPressure(), and HMWSoln::setTemperature().
|
virtual |
The isothermal compressibility.
Units: 1/Pa. The isothermal compressibility is defined as
\[ \kappa_T = -\frac{1}{v}\left(\frac{\partial v}{\partial P}\right)_T \]
It's equal to zero for this model, since the molar volume doesn't change with pressure or temperature.
Reimplemented from ThermoPhase.
Definition at line 695 of file HMWSoln.cpp.
Referenced by HMWSoln::cv_mole().
|
virtual |
The thermal expansion coefficient.
Units: 1/K. The thermal expansion coefficient is defined as
\[ \beta = \frac{1}{v}\left(\frac{\partial v}{\partial T}\right)_P \]
It's equal to zero for this model, since the molar volume doesn't change with pressure or temperature.
Reimplemented from ThermoPhase.
Definition at line 702 of file HMWSoln.cpp.
Referenced by HMWSoln::cv_mole().
|
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 766 of file HMWSoln.cpp.
References HMWSoln::getActivities(), Phase::m_kk, and HMWSoln::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 m3 kmol-1 s-1.
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
- Returns the standard Concentration in units of m3 kmol-1.
- Parameters
-
k Species index
Reimplemented from MolalityVPSSTP.
Definition at line 779 of file HMWSoln.cpp.
References DATA_PTR, VPStandardStateTP::getStandardVolumes(), MolalityVPSSTP::m_indexSolvent, MolalityVPSSTP::m_Mnaught, and HMWSoln::m_tmpV.
Referenced by HMWSoln::getActivityConcentrations(), and HMWSoln::logStandardConc().
|
virtual |
Returns the natural logarithm of the standard concentration of the kth species.
- Parameters
-
k Species index
Reimplemented from MolalityVPSSTP.
Definition at line 789 of file HMWSoln.cpp.
References HMWSoln::standardConcentration().
|
virtual |
Returns the units of the standard and generalized concentrations.
Note they have the same units, as their ratio is defined to be equal to the activity of the kth species in the solution, which is unitless.
This routine is used in print out applications where the units are needed. Usually, MKS units are assumed throughout the program and in the XML input files.
The base ThermoPhase class assigns the default quantities of (kmol/m3) for all species. Inherited classes are responsible for overriding the default values if necessary.
- Parameters
-
uA Output vector containing the units uA[0] = kmol units - default = 1 uA[1] = m units - default = -nDim(), the number of spatial dimensions in the Phase class. uA[2] = kg units - default = 0; uA[3] = Pa(pressure) units - default = 0; uA[4] = Temperature units - default = 0; uA[5] = time units - default = 0 k species index. Defaults to 0. sizeUA output int containing the size of the vector. Currently, this is equal to 6.
Reimplemented from MolalityVPSSTP.
Definition at line 795 of file HMWSoln.cpp.
References Phase::nDim().
|
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 819 of file HMWSoln.cpp.
References MolalityVPSSTP::m_indexSolvent, Phase::m_kk, HMWSoln::m_lnActCoeffMolal_Scaled, MolalityVPSSTP::m_molalities, Phase::moleFraction(), and VPStandardStateTP::updateStandardStateThermo().
Referenced by HMWSoln::getActivityConcentrations().
|
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 860 of file HMWSoln.cpp.
References Cantera::GasConstant, VPStandardStateTP::getStandardChemPotentials(), MolalityVPSSTP::m_indexSolvent, Phase::m_kk, HMWSoln::m_lnActCoeffMolal_Scaled, MolalityVPSSTP::m_molalities, Phase::moleFraction(), Cantera::SmallNumber, and Phase::temperature().
Referenced by HMWSoln::gibbs_mole().
|
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 888 of file HMWSoln.cpp.
References Cantera::GasConstant, VPStandardStateTP::getEnthalpy_RT(), HMWSoln::m_dlnActCoeffMolaldT_Scaled, Phase::m_kk, HMWSoln::s_update_dlnMolalityActCoeff_dT(), and Phase::temperature().
Referenced by HMWSoln::enthalpy_mole(), and HMWSoln::relative_enthalpy().
|
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 915 of file HMWSoln.cpp.
References Cantera::GasConstant, VPStandardStateTP::getEntropy_R(), HMWSoln::m_dlnActCoeffMolaldT_Scaled, MolalityVPSSTP::m_indexSolvent, Phase::m_kk, HMWSoln::m_lnActCoeffMolal_Scaled, MolalityVPSSTP::m_molalities, Phase::moleFraction(), HMWSoln::s_update_dlnMolalityActCoeff_dT(), Cantera::SmallNumber, and Phase::temperature().
Referenced by HMWSoln::entropy_mole().
|
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 960 of file HMWSoln.cpp.
References Cantera::GasConstant, VPStandardStateTP::getStandardVolumes(), HMWSoln::m_dlnActCoeffMolaldP_Scaled, Phase::m_kk, HMWSoln::s_update_dlnMolalityActCoeff_dP(), and Phase::temperature().
Referenced by HMWSoln::calcDensity().
|
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 978 of file HMWSoln.cpp.
References Cantera::GasConstant, VPStandardStateTP::getCp_R(), HMWSoln::m_d2lnActCoeffMolaldT2_Scaled, HMWSoln::m_dlnActCoeffMolaldT_Scaled, Phase::m_kk, HMWSoln::s_update_d2lnMolalityActCoeff_dT2(), HMWSoln::s_update_dlnMolalityActCoeff_dT(), and Phase::temperature().
Referenced by HMWSoln::cp_mole().
|
inlinevirtual |
This method is used by the ChemEquil equilibrium solver.
It sets the state such that the chemical potentials satisfy
\[ \frac{\mu_k}{\hat R T} = \sum_m A_{k,m} \left(\frac{\lambda_m} {\hat R T}\right) \]
where \( \lambda_m \) is the element potential of element m. The temperature is unchanged. Any phase (ideal or not) that implements this method can be equilibrated by ChemEquil.
- Parameters
-
lambda_RT Input vector of dimensionless element potentials The length is equal to nElements().
Reimplemented from MolalityVPSSTP.
Definition at line 1893 of file HMWSoln.h.
References HMWSoln::err(), and VPStandardStateTP::updateStandardStateThermo().
|
virtual |
Set the equation of state parameters.
The number and meaning of these depends on the subclass.
- Parameters
-
n number of parameters c array of n coefficients
- Deprecated:
- Unimplemented
Reimplemented from ThermoPhase.
Definition at line 1009 of file HMWSoln.cpp.
References Cantera::warn_deprecated().
|
virtual |
Get the equation of state parameters in a vector.
The number and meaning of these depends on the subclass.
- Parameters
-
n number of parameters c array of n coefficients
- Deprecated:
- Unimplemented
Reimplemented from ThermoPhase.
Definition at line 1014 of file HMWSoln.cpp.
References Cantera::warn_deprecated().
|
virtual |
Set equation of state parameter values from XML entries.
This method is called by function importPhase in file importCTML.cpp when processing a phase definition in an input file. It should be overloaded in subclasses to set any parameters that are specific to that particular phase model.
HKM -> Right now, the parameters are set elsewhere (initThermoXML) It just didn't seem to fit.
- Parameters
-
eosdata An XML_Node object corresponding to the "thermo" entry for this phase in the input file.
Reimplemented from VPStandardStateTP.
Definition at line 1019 of file HMWSoln.cpp.
|
inlinevirtual |
Critical temperature (K).
Reimplemented from ThermoPhase.
Definition at line 1945 of file HMWSoln.h.
References HMWSoln::err().
|
inlinevirtual |
Critical pressure (Pa).
Reimplemented from ThermoPhase.
Definition at line 1951 of file HMWSoln.h.
References HMWSoln::err().
|
inlinevirtual |
Critical density (kg/m3).
Reimplemented from ThermoPhase.
Definition at line 1957 of file HMWSoln.h.
References HMWSoln::err().
|
inlinevirtual |
Return the saturation temperature given the pressure.
- Parameters
-
p Pressure (Pa)
Reimplemented from ThermoPhase.
Definition at line 1968 of file HMWSoln.h.
References HMWSoln::err().
|
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 1023 of file HMWSoln.cpp.
References HMWSoln::m_waterSS, HMWSoln::pressure(), PDSS::satPressure(), PDSS::setState_TP(), and Phase::temperature().
|
inlinevirtual |
Return the fraction of vapor at the current conditions.
Reimplemented from ThermoPhase.
Definition at line 1990 of file HMWSoln.h.
References HMWSoln::err().
|
inlinevirtual |
Set the state to a saturated system at a particular temperature.
- Parameters
-
t Temperature (kelvin) x Fraction of vapor
Reimplemented from ThermoPhase.
Definition at line 1995 of file HMWSoln.h.
References HMWSoln::err().
|
inlinevirtual |
Set the state to a saturated system at a particular pressure.
- Parameters
-
p Pressure (Pa) x Fraction of vapor
Reimplemented from ThermoPhase.
Definition at line 1999 of file HMWSoln.h.
References HMWSoln::err().
|
virtual |
Internal initialization required after all species have been added.
Initialize. This method is provided to allow subclasses to perform any initialization required after all species have been added. For example, it might be used to resize internal work arrays that must have an entry for each species. The base class implementation does nothing, and subclasses that do not require initialization do not need to overload this method. When importing a CTML phase description, this method is called just prior to returning from function importPhase.
- See Also
- importCTML.cpp
Reimplemented from MolalityVPSSTP.
Definition at line 970 of file HMWSoln_input.cpp.
|
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 VPStandardStateTP.
Definition at line 1136 of file HMWSoln_input.cpp.
References XML_Node::attrib(), Cantera::cEST_solvent, XML_Node::child(), DATA_PTR, XML_Node::findByAttr(), XML_Node::findByName(), Cantera::fpValue(), Cantera::fpValueCheck(), Cantera::get_XML_NameID(), ctml::getChildValue(), ctml::getFloat(), ctml::getMap(), ctml::getOptionalFloat(), ctml::getStringArray(), XML_Node::hasAttrib(), XML_Node::hasChild(), XML_Node::id(), Cantera::interp_est(), Cantera::lowercase(), XML_Node::name(), XML_Node::nChildren(), Cantera::npos, Cantera::OneAtm, PITZERFORM_BASE, XML_Node::root(), and Cantera::toSI().
|
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 1034 of file HMWSoln.cpp.
References WaterProps::ADebye(), HMWSoln::m_A_Debye, HMWSoln::m_form_A_Debye, HMWSoln::m_waterProps, HMWSoln::pressure(), and Phase::temperature().
Referenced by HMWSoln::getUnscaledMolalityActivityCoefficients().
|
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 1061 of file HMWSoln.cpp.
References WaterProps::ADebye(), HMWSoln::m_form_A_Debye, HMWSoln::m_waterProps, HMWSoln::pressure(), and Phase::temperature().
Referenced by HMWSoln::ADebye_L(), HMWSoln::s_NBS_CLM_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT().
|
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 1087 of file HMWSoln.cpp.
References WaterProps::ADebye(), HMWSoln::m_form_A_Debye, HMWSoln::m_waterProps, HMWSoln::pressure(), and Phase::temperature().
Referenced by HMWSoln::ADebye_V(), HMWSoln::s_NBS_CLM_dlnMolalityActCoeff_dP(), and HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP().
| 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 1112 of file HMWSoln.cpp.
References HMWSoln::dA_DebyedT_TP(), Cantera::GasConstant, and Phase::temperature().
Referenced by HMWSoln::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 1134 of file HMWSoln.cpp.
References HMWSoln::ADebye_L(), HMWSoln::d2A_DebyedT2_TP(), Cantera::GasConstant, and Phase::temperature().
| 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 1123 of file HMWSoln.cpp.
References HMWSoln::dA_DebyedP_TP(), Cantera::GasConstant, and Phase::temperature().
|
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 1146 of file HMWSoln.cpp.
References WaterProps::ADebye(), HMWSoln::m_form_A_Debye, HMWSoln::m_waterProps, HMWSoln::pressure(), and Phase::temperature().
Referenced by HMWSoln::ADebye_J(), HMWSoln::s_NBS_CLM_d2lnMolalityActCoeff_dT2(), and HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2().
| double AionicRadius | ( | int | k = 0 | ) | const |
Reports the ionic radius of the kth species.
- Parameters
-
k Species index
Definition at line 1174 of file HMWSoln.cpp.
References HMWSoln::m_Aionic.
|
inline |
Returns the form of the Pitzer parameterization used
Definition at line 2182 of file HMWSoln.h.
References HMWSoln::m_formPitzer.
| void printCoeffs | ( | ) | const |
Print out all of the input Pitzer coefficients.
Definition at line 5653 of file HMWSoln.cpp.
References MolalityVPSSTP::calcMolalities(), Phase::charge(), DATA_PTR, Phase::getMoleFractions(), Cantera::int2str(), HMWSoln::m_Alpha1MX_ij, 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(), and Phase::speciesName().
Referenced by HMWSoln::HMWSoln().
|
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 overwritten 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 845 of file HMWSoln.cpp.
References HMWSoln::A_Debye_TP(), Phase::m_kk, HMWSoln::m_lnActCoeffMolal_Unscaled, and VPStandardStateTP::updateStandardStateThermo().
|
private |
Apply the current phScale to a set of activity Coefficients.
See the Eq3/6 Manual for a thorough discussion.
Definition at line 5725 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().
|
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 5740 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().
|
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 5755 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().
|
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 5770 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().
|
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 5785 of file HMWSoln.cpp.
References HMWSoln::m_A_Debye, and HMWSoln::m_IionicMolality.
Referenced by HMWSoln::applyphScale(), and HMWSoln::s_updateScaling_pHScaling().
|
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 5793 of file HMWSoln.cpp.
References HMWSoln::dA_DebyedT_TP(), and HMWSoln::m_IionicMolality.
Referenced by HMWSoln::s_updateScaling_pHScaling_dT().
|
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 5800 of file HMWSoln.cpp.
References HMWSoln::d2A_DebyedT2_TP(), and HMWSoln::m_IionicMolality.
Referenced by HMWSoln::s_updateScaling_pHScaling_dT2().
|
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 5807 of file HMWSoln.cpp.
References HMWSoln::dA_DebyedP_TP(), and HMWSoln::m_IionicMolality.
Referenced by HMWSoln::s_updateScaling_pHScaling_dP().
|
private |
Local error routine.
- Parameters
-
msg print out a message and error exit
Definition at line 1183 of file HMWSoln.cpp.
Referenced by HMWSoln::critDensity(), HMWSoln::critPressure(), HMWSoln::critTemperature(), HMWSoln::satTemperature(), HMWSoln::setState_Psat(), HMWSoln::setState_Tsat(), HMWSoln::setToEquilState(), and HMWSoln::vaporFraction().
|
private |
Initialize all of the species-dependent lengths in the object.
Definition at line 1190 of file HMWSoln.cpp.
References HMWSoln::counterIJ_setup(), HMWSoln::CROP_speciesCropped_, HMWSoln::IMS_lnActCoeffMolal_, HMWSoln::m_Aionic, HMWSoln::m_Alpha1MX_ij, HMWSoln::m_Alpha2MX_ij, HMWSoln::m_Beta0MX_ij, HMWSoln::m_Beta0MX_ij_coeff, HMWSoln::m_Beta0MX_ij_L, HMWSoln::m_Beta0MX_ij_LL, HMWSoln::m_Beta0MX_ij_P, HMWSoln::m_Beta1MX_ij, HMWSoln::m_Beta1MX_ij_coeff, HMWSoln::m_Beta1MX_ij_L, HMWSoln::m_Beta1MX_ij_LL, HMWSoln::m_Beta1MX_ij_P, HMWSoln::m_Beta2MX_ij, HMWSoln::m_Beta2MX_ij_coeff, HMWSoln::m_Beta2MX_ij_L, HMWSoln::m_Beta2MX_ij_LL, HMWSoln::m_Beta2MX_ij_P, HMWSoln::m_BMX_IJ, HMWSoln::m_BMX_IJ_L, HMWSoln::m_BMX_IJ_LL, HMWSoln::m_BMX_IJ_P, HMWSoln::m_BphiMX_IJ, HMWSoln::m_BphiMX_IJ_L, HMWSoln::m_BphiMX_IJ_LL, HMWSoln::m_BphiMX_IJ_P, HMWSoln::m_BprimeMX_IJ, HMWSoln::m_BprimeMX_IJ_L, HMWSoln::m_BprimeMX_IJ_LL, HMWSoln::m_BprimeMX_IJ_P, HMWSoln::m_CMX_IJ, HMWSoln::m_CMX_IJ_L, HMWSoln::m_CMX_IJ_LL, HMWSoln::m_CMX_IJ_P, HMWSoln::m_CounterIJ, HMWSoln::m_CphiMX_ij, HMWSoln::m_CphiMX_ij_coeff, HMWSoln::m_CphiMX_ij_L, HMWSoln::m_CphiMX_ij_LL, HMWSoln::m_CphiMX_ij_P, HMWSoln::m_d2lnActCoeffMolaldT2_Scaled, HMWSoln::m_d2lnActCoeffMolaldT2_Unscaled, HMWSoln::m_dlnActCoeffMolaldP_Scaled, HMWSoln::m_dlnActCoeffMolaldP_Unscaled, HMWSoln::m_dlnActCoeffMolaldT_Scaled, HMWSoln::m_dlnActCoeffMolaldT_Unscaled, HMWSoln::m_electrolyteSpeciesType, HMWSoln::m_formPitzerTemp, HMWSoln::m_g2func_IJ, HMWSoln::m_gamma_tmp, HMWSoln::m_gfunc_IJ, HMWSoln::m_h2func_IJ, HMWSoln::m_hfunc_IJ, Phase::m_kk, HMWSoln::m_Lambda_nj, HMWSoln::m_Lambda_nj_coeff, HMWSoln::m_Lambda_nj_L, HMWSoln::m_Lambda_nj_LL, HMWSoln::m_Lambda_nj_P, HMWSoln::m_lnActCoeffMolal_Scaled, HMWSoln::m_lnActCoeffMolal_Unscaled, HMWSoln::m_molalitiesCropped, HMWSoln::m_Mu_nnn, HMWSoln::m_Mu_nnn_coeff, HMWSoln::m_Mu_nnn_L, HMWSoln::m_Mu_nnn_LL, HMWSoln::m_Mu_nnn_P, HMWSoln::m_Phi_IJ, HMWSoln::m_Phi_IJ_L, HMWSoln::m_Phi_IJ_LL, HMWSoln::m_Phi_IJ_P, HMWSoln::m_PhiPhi_IJ, HMWSoln::m_PhiPhi_IJ_L, HMWSoln::m_PhiPhi_IJ_LL, HMWSoln::m_PhiPhi_IJ_P, HMWSoln::m_Phiprime_IJ, HMWSoln::m_pp, HMWSoln::m_Psi_ijk, HMWSoln::m_Psi_ijk_coeff, HMWSoln::m_Psi_ijk_L, HMWSoln::m_Psi_ijk_LL, HMWSoln::m_Psi_ijk_P, HMWSoln::m_speciesCharge_Stoich, Phase::m_speciesSize, HMWSoln::m_Theta_ij, HMWSoln::m_Theta_ij_coeff, HMWSoln::m_Theta_ij_L, HMWSoln::m_Theta_ij_LL, HMWSoln::m_Theta_ij_P, HMWSoln::m_tmpV, Phase::nSpecies(), and Array2D::resize().
|
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 5711 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().
|
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 2897 of file HMWSoln.cpp.
References HMWSoln::CROP_speciesCropped_, HMWSoln::m_dlnActCoeffMolaldT_Unscaled, Phase::m_kk, HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updateScaling_pHScaling_dT().
Referenced by HMWSoln::getPartialMolarCp(), HMWSoln::getPartialMolarEnthalpies(), and HMWSoln::getPartialMolarEntropies().
|
private |
This function calculates the temperature second derivative of the natural logarithm of the molality activity coefficients.
Definition at line 3746 of file HMWSoln.cpp.
References HMWSoln::CROP_speciesCropped_, HMWSoln::m_d2lnActCoeffMolaldT2_Unscaled, Phase::m_kk, HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), and HMWSoln::s_updateScaling_pHScaling_dT2().
Referenced by HMWSoln::getPartialMolarCp().
|
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 4600 of file HMWSoln.cpp.
References HMWSoln::CROP_speciesCropped_, HMWSoln::m_dlnActCoeffMolaldP_Unscaled, Phase::m_kk, HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), and HMWSoln::s_updateScaling_pHScaling_dP().
Referenced by HMWSoln::getPartialMolarVolumes().
|
private |
This function will be called to update the internally stored natural logarithm of the molality activity coefficients.
Definition at line 5542 of file HMWSoln.cpp.
References MolalityVPSSTP::calcMolalities(), HMWSoln::IMS_cCut_, HMWSoln::IMS_gamma_k_min_, HMWSoln::IMS_gamma_o_min_, HMWSoln::IMS_lnActCoeffMolal_, HMWSoln::IMS_typeCutoff_, HMWSoln::IMS_X_o_cutoff_, MolalityVPSSTP::m_indexSolvent, Phase::m_kk, MolalityVPSSTP::m_xmolSolventMIN, and Phase::moleFraction().
|
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 1867 of file HMWSoln.cpp.
References HMWSoln::calc_lambdas(), HMWSoln::calc_thetas(), Phase::charge(), HMWSoln::counterIJ_setup(), DATA_PTR, HMWSoln::m_A_Debye, HMWSoln::m_Alpha1MX_ij, HMWSoln::m_Alpha2MX_ij, HMWSoln::m_Beta0MX_ij, HMWSoln::m_Beta1MX_ij, HMWSoln::m_Beta2MX_ij, HMWSoln::m_BMX_IJ, HMWSoln::m_BphiMX_IJ, HMWSoln::m_BprimeMX_IJ, HMWSoln::m_CMX_IJ, HMWSoln::m_CounterIJ, HMWSoln::m_CphiMX_ij, HMWSoln::m_debugCalc, HMWSoln::m_g2func_IJ, HMWSoln::m_gamma_tmp, HMWSoln::m_gfunc_IJ, HMWSoln::m_h2func_IJ, HMWSoln::m_hfunc_IJ, HMWSoln::m_IionicMolality, MolalityVPSSTP::m_indexSolvent, Phase::m_kk, HMWSoln::m_Lambda_nj, HMWSoln::m_lnActCoeffMolal_Unscaled, MolalityVPSSTP::m_molalities, HMWSoln::m_molalitiesCropped, HMWSoln::m_Mu_nnn, HMWSoln::m_Phi_IJ, HMWSoln::m_PhiPhi_IJ, HMWSoln::m_Phiprime_IJ, HMWSoln::m_Psi_ijk, HMWSoln::m_Theta_ij, MolalityVPSSTP::m_weightSolvent, MolalityVPSSTP::m_xmolSolventMIN, Phase::moleFraction(), Phase::speciesName(), and Phase::temperature().
|
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 2930 of file HMWSoln.cpp.
References HMWSoln::calc_lambdas(), HMWSoln::calc_thetas(), Phase::charge(), HMWSoln::counterIJ_setup(), HMWSoln::dA_DebyedT_TP(), DATA_PTR, HMWSoln::m_Alpha1MX_ij, HMWSoln::m_Alpha2MX_ij, HMWSoln::m_Beta0MX_ij_L, HMWSoln::m_Beta1MX_ij_L, HMWSoln::m_Beta2MX_ij_L, HMWSoln::m_BMX_IJ_L, HMWSoln::m_BphiMX_IJ_L, HMWSoln::m_BprimeMX_IJ_L, HMWSoln::m_CMX_IJ_L, HMWSoln::m_CounterIJ, HMWSoln::m_CphiMX_ij_L, HMWSoln::m_debugCalc, HMWSoln::m_dlnActCoeffMolaldT_Unscaled, HMWSoln::m_g2func_IJ, HMWSoln::m_gamma_tmp, HMWSoln::m_gfunc_IJ, HMWSoln::m_h2func_IJ, HMWSoln::m_hfunc_IJ, HMWSoln::m_IionicMolality, MolalityVPSSTP::m_indexSolvent, Phase::m_kk, HMWSoln::m_Lambda_nj_L, HMWSoln::m_molalitiesCropped, HMWSoln::m_Mu_nnn_L, HMWSoln::m_Phi_IJ_L, HMWSoln::m_PhiPhi_IJ_L, HMWSoln::m_Phiprime_IJ, HMWSoln::m_Psi_ijk_L, HMWSoln::m_Theta_ij_L, MolalityVPSSTP::m_weightSolvent, and Phase::speciesName().
Referenced by HMWSoln::s_update_dlnMolalityActCoeff_dT().
|
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 3777 of file HMWSoln.cpp.
References HMWSoln::calc_lambdas(), HMWSoln::calc_thetas(), Phase::charge(), HMWSoln::counterIJ_setup(), HMWSoln::d2A_DebyedT2_TP(), DATA_PTR, HMWSoln::m_Alpha1MX_ij, HMWSoln::m_Alpha2MX_ij, HMWSoln::m_Beta0MX_ij_LL, HMWSoln::m_Beta1MX_ij_LL, HMWSoln::m_Beta2MX_ij_LL, HMWSoln::m_BMX_IJ_LL, HMWSoln::m_BphiMX_IJ_LL, HMWSoln::m_BprimeMX_IJ_LL, HMWSoln::m_CMX_IJ_LL, HMWSoln::m_CounterIJ, HMWSoln::m_CphiMX_ij_LL, HMWSoln::m_d2lnActCoeffMolaldT2_Unscaled, HMWSoln::m_debugCalc, HMWSoln::m_g2func_IJ, HMWSoln::m_gfunc_IJ, HMWSoln::m_h2func_IJ, HMWSoln::m_hfunc_IJ, HMWSoln::m_IionicMolality, MolalityVPSSTP::m_indexSolvent, Phase::m_kk, HMWSoln::m_Lambda_nj_LL, HMWSoln::m_molalitiesCropped, HMWSoln::m_Mu_nnn_LL, HMWSoln::m_Phi_IJ_LL, HMWSoln::m_PhiPhi_IJ_LL, HMWSoln::m_Phiprime_IJ, HMWSoln::m_Psi_ijk_LL, HMWSoln::m_Theta_ij_LL, MolalityVPSSTP::m_weightSolvent, and Phase::speciesName().
Referenced by HMWSoln::s_update_d2lnMolalityActCoeff_dT2().
|
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 4618 of file HMWSoln.cpp.
References HMWSoln::calc_lambdas(), HMWSoln::calc_thetas(), Phase::charge(), HMWSoln::counterIJ_setup(), HMWSoln::dA_DebyedP_TP(), DATA_PTR, HMWSoln::m_Alpha1MX_ij, HMWSoln::m_Alpha2MX_ij, HMWSoln::m_Beta0MX_ij_P, HMWSoln::m_Beta1MX_ij_P, HMWSoln::m_Beta2MX_ij_P, HMWSoln::m_BMX_IJ_P, HMWSoln::m_BphiMX_IJ_P, HMWSoln::m_BprimeMX_IJ_P, HMWSoln::m_CMX_IJ_P, HMWSoln::m_CounterIJ, HMWSoln::m_CphiMX_ij_P, HMWSoln::m_debugCalc, HMWSoln::m_dlnActCoeffMolaldP_Unscaled, HMWSoln::m_g2func_IJ, HMWSoln::m_gfunc_IJ, HMWSoln::m_h2func_IJ, HMWSoln::m_hfunc_IJ, HMWSoln::m_IionicMolality, MolalityVPSSTP::m_indexSolvent, Phase::m_kk, HMWSoln::m_Lambda_nj_P, HMWSoln::m_molalitiesCropped, HMWSoln::m_Mu_nnn_P, HMWSoln::m_Phi_IJ_P, HMWSoln::m_PhiPhi_IJ_P, HMWSoln::m_Phiprime_IJ, HMWSoln::m_Psi_ijk_P, HMWSoln::m_Theta_ij_P, MolalityVPSSTP::m_weightSolvent, HMWSoln::pressure(), Phase::speciesName(), and Phase::temperature().
Referenced by HMWSoln::s_update_dlnMolalityActCoeff_dP().
|
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 1593 of file HMWSoln.cpp.
References Phase::charge(), HMWSoln::m_Beta0MX_ij, HMWSoln::m_Beta0MX_ij_coeff, HMWSoln::m_Beta0MX_ij_L, HMWSoln::m_Beta0MX_ij_LL, HMWSoln::m_Beta1MX_ij, HMWSoln::m_Beta1MX_ij_coeff, HMWSoln::m_Beta1MX_ij_L, HMWSoln::m_Beta1MX_ij_LL, HMWSoln::m_Beta2MX_ij, HMWSoln::m_Beta2MX_ij_coeff, HMWSoln::m_Beta2MX_ij_L, HMWSoln::m_Beta2MX_ij_LL, HMWSoln::m_CounterIJ, HMWSoln::m_CphiMX_ij, HMWSoln::m_CphiMX_ij_coeff, HMWSoln::m_CphiMX_ij_L, HMWSoln::m_CphiMX_ij_LL, HMWSoln::m_formPitzerTemp, Phase::m_kk, HMWSoln::m_Lambda_nj, HMWSoln::m_Lambda_nj_coeff, HMWSoln::m_Lambda_nj_L, HMWSoln::m_Lambda_nj_LL, HMWSoln::m_Mu_nnn, HMWSoln::m_Mu_nnn_coeff, HMWSoln::m_Mu_nnn_L, HMWSoln::m_Mu_nnn_LL, HMWSoln::m_Psi_ijk, HMWSoln::m_Psi_ijk_coeff, HMWSoln::m_Psi_ijk_L, HMWSoln::m_Psi_ijk_LL, HMWSoln::m_TempPitzerRef, HMWSoln::m_Theta_ij, HMWSoln::m_Theta_ij_coeff, HMWSoln::m_Theta_ij_L, HMWSoln::m_Theta_ij_LL, Array2D::ptrColumn(), and Phase::temperature().
Referenced by HMWSoln::printCoeffs().
|
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 5437 of file HMWSoln.cpp.
References HMWSoln::elambda, HMWSoln::elambda1, and HMWSoln::m_debugCalc.
Referenced by HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
|
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[].
There is no prohibition against calling
Definition at line 5498 of file HMWSoln.cpp.
References 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().
|
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 1569 of file HMWSoln.cpp.
References HMWSoln::m_CounterIJ, and Phase::m_kk.
Referenced by HMWSoln::initLengths(), HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
|
private |
Calculate the cropped molalities.
This is an internal routine that calculates values of m_molalitiesCropped from m_molalities
Definition at line 1407 of file HMWSoln.cpp.
References Phase::charge(), DATA_PTR, Phase::getMoleFractions(), HMWSoln::m_gamma_tmp, MolalityVPSSTP::m_indexSolvent, Phase::m_kk, HMWSoln::m_maxIionicStrength, MolalityVPSSTP::m_Mnaught, MolalityVPSSTP::m_molalities, HMWSoln::m_molalitiesAreCropped, HMWSoln::m_molalitiesCropped, HMWSoln::MC_X_o_cutoff_, and Cantera::npos.
|
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 53 of file HMWSoln_input.cpp.
References XML_Node::attrib(), XML_Node::child(), Cantera::fpValueCheck(), ctml::getFloatArray(), Cantera::lowercase(), XML_Node::name(), XML_Node::nChildren(), Cantera::npos, and XML_Node::value().
|
private |
Process an XML node called "thetaAnion".
This node contains all of the parameters necessary to describe the binary interactions between two anions.
- Parameters
-
BinSalt reference to the XML_Node named thetaAnion containing the anion - anion interaction
Definition at line 253 of file HMWSoln_input.cpp.
References XML_Node::attrib(), XML_Node::child(), ctml::getFloatArray(), Cantera::lowercase(), XML_Node::name(), XML_Node::nChildren(), and Cantera::npos.
|
private |
Process an XML node called "thetaCation".
This node contains all of the parameters necessary to describe the binary interactions between two cations.
- Parameters
-
BinSalt reference to the XML_Node named thetaCation containing the cation - cation interaction
Definition at line 334 of file HMWSoln_input.cpp.
References XML_Node::attrib(), XML_Node::child(), ctml::getFloatArray(), Cantera::lowercase(), XML_Node::name(), XML_Node::nChildren(), and Cantera::npos.
|
private |
Process an XML node called "psiCommonAnion".
This node contains all of the parameters necessary to describe the ternary interactions between one anion and two cations.
- Parameters
-
BinSalt reference to the XML_Node named psiCommonAnion containing the anion - cation1 - cation2 interaction
Definition at line 555 of file HMWSoln_input.cpp.
References XML_Node::attrib(), XML_Node::child(), Cantera::fpValueCheck(), ctml::getFloatArray(), Cantera::lowercase(), XML_Node::name(), XML_Node::nChildren(), Cantera::npos, and XML_Node::value().
|
private |
Process an XML node called "psiCommonCation".
This node contains all of the parameters necessary to describe the ternary interactions between one cation and two anions.
- Parameters
-
BinSalt reference to the XML_Node named psiCommonCation containing the cation - anion1 - anion2 interaction
Definition at line 415 of file HMWSoln_input.cpp.
References XML_Node::attrib(), XML_Node::child(), Cantera::fpValueCheck(), ctml::getFloatArray(), Cantera::lowercase(), XML_Node::name(), XML_Node::nChildren(), Cantera::npos, and XML_Node::value().
|
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 696 of file HMWSoln_input.cpp.
References XML_Node::attrib(), XML_Node::child(), ctml::getFloatArray(), Cantera::lowercase(), XML_Node::name(), XML_Node::nChildren(), and Cantera::npos.
|
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 776 of file HMWSoln_input.cpp.
References XML_Node::attrib(), XML_Node::child(), ctml::getFloatArray(), Cantera::lowercase(), XML_Node::name(), XML_Node::nChildren(), and Cantera::npos.
|
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 845 of file HMWSoln_input.cpp.
References XML_Node::attrib(), XML_Node::child(), ctml::getFloatArray(), Cantera::lowercase(), XML_Node::name(), XML_Node::nChildren(), and Cantera::npos.
|
private |
Process an XML node called "croppingCoefficients" for the cropping coefficients values.
- Parameters
-
acNode Activity Coefficient XML Node
Definition at line 944 of file HMWSoln_input.cpp.
References XML_Node::child(), ctml::getOptionalFloat(), and XML_Node::hasChild().
|
private |
Precalculate the IMS Cutoff parameters for typeCutoff = 2.
Definition at line 1693 of file HMWSoln_input.cpp.
|
private |
Calculate molality cut-off parameters.
Definition at line 1743 of file HMWSoln_input.cpp.
|
staticprivate |
Utility function to assign an integer value from a string for the ElectrolyteSpeciesType field.
- Parameters
-
estString string name of the electrolyte species type
Definition at line 28 of file HMWSoln_input.cpp.
References Cantera::cEST_solvent, and Cantera::lowercase().
| int debugPrinting | ( | ) |
Return int specifying the amount of debug printing.
This will return 0 if DEBUG_MODE is not turned on
Definition at line 5814 of file HMWSoln.cpp.
References HMWSoln::m_debugCalc.
Member Data Documentation
|
private |
This is the form of the Pitzer parameterization used in this model.
The options are described at the top of this document, and in the general documentation. The list is repeated here:
PITZERFORM_BASE = 0 (only one supported atm)
Definition at line 2271 of file HMWSoln.h.
Referenced by HMWSoln::formPitzer(), and HMWSoln::operator=().
|
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 2281 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_CoeffWRTemp().
|
private |
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 2312 of file HMWSoln.h.
Referenced by HMWSoln::eosType(), and HMWSoln::operator=().
|
private |
Vector containing the electrolyte species type.
The possible types are:
- solvent
- Charged Species
- weakAcidAssociated
- strongAcidAssociated
- polarNeutral
- nonpolarNeutral .
Definition at line 2324 of file HMWSoln.h.
Referenced by HMWSoln::initLengths().
|
private |
a_k = Size of the ionic species in the DH formulation units = meters
Definition at line 2330 of file HMWSoln.h.
Referenced by HMWSoln::AionicRadius(), HMWSoln::initLengths(), and HMWSoln::operator=().
|
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 2338 of file HMWSoln.h.
Referenced by HMWSoln::operator=(), 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().
|
private |
Maximum value of the ionic strength allowed in the calculation of the activity coefficients.
Definition at line 2344 of file HMWSoln.h.
Referenced by HMWSoln::calcMolalitiesCropped(), and HMWSoln::operator=().
|
private |
Reference Temperature for the Pitzer formulations.
Definition at line 2347 of file HMWSoln.h.
Referenced by HMWSoln::operator=(), and HMWSoln::s_updatePitzer_CoeffWRTemp().
|
mutableprivate |
Stoichiometric ionic strength on the molality scale.
This differs from m_IionicMolality in the sense that associated salts are treated as unassociated salts, when calculating the Ionic strength by this method.
Definition at line 2355 of file HMWSoln.h.
Referenced by HMWSoln::operator=().
| 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 2374 of file HMWSoln.h.
Referenced by HMWSoln::A_Debye_TP(), HMWSoln::d2A_DebyedT2_TP(), HMWSoln::dA_DebyedP_TP(), HMWSoln::dA_DebyedT_TP(), and HMWSoln::operator=().
|
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
Definition at line 2408 of file HMWSoln.h.
Referenced by HMWSoln::A_Debye_TP(), HMWSoln::operator=(), HMWSoln::s_NBS_CLM_lnMolalityActCoeff(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
|
private |
Water standard state calculator.
derived from the equation of state for water.
Definition at line 2414 of file HMWSoln.h.
Referenced by HMWSoln::operator=(), HMWSoln::satPressure(), and HMWSoln::setState_TP().
|
private |
density of standard-state water
internal temporary variable
Definition at line 2420 of file HMWSoln.h.
Referenced by HMWSoln::operator=(), and HMWSoln::setState_TP().
|
private |
Pointer to the water property calculator.
Definition at line 2423 of file HMWSoln.h.
Referenced by HMWSoln::A_Debye_TP(), HMWSoln::d2A_DebyedT2_TP(), HMWSoln::dA_DebyedP_TP(), HMWSoln::dA_DebyedT_TP(), HMWSoln::operator=(), and HMWSoln::~HMWSoln().
|
mutableprivate |
Temporary array used in equilibrium calculations.
Definition at line 2426 of file HMWSoln.h.
Referenced by HMWSoln::calcDensity(), HMWSoln::enthalpy_mole(), HMWSoln::initLengths(), and HMWSoln::operator=().
|
mutableprivate |
vector of size m_kk, used as a temporary holding area.
Definition at line 2429 of file HMWSoln.h.
Referenced by HMWSoln::calcDensity(), HMWSoln::cp_mole(), HMWSoln::enthalpy_mole(), HMWSoln::entropy_mole(), HMWSoln::gibbs_mole(), HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::printCoeffs(), HMWSoln::relative_enthalpy(), HMWSoln::relative_molal_enthalpy(), and HMWSoln::standardConcentration().
|
private |
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, its equal to the m_speciesCharge[] value.
Definition at line 2443 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), and HMWSoln::operator=().
|
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 2454 of file HMWSoln.h.
Referenced by HMWSoln::HMWSoln(), HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::printCoeffs(), HMWSoln::s_updatePitzer_CoeffWRTemp(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
|
mutableprivate |
Derivative of Beta0_ij[i][j] wrt T.
vector index is counterIJ
Definition at line 2460 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::s_updatePitzer_CoeffWRTemp(), and HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT().
|
mutableprivate |
Derivative of Beta0_ij[i][j] wrt TT.
vector index is counterIJ
Definition at line 2466 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::s_updatePitzer_CoeffWRTemp(), and HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2().
|
mutableprivate |
Derivative of Beta0_ij[i][j] wrt P.
vector index is counterIJ
Definition at line 2472 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP().
|
mutableprivate |
Array of coefficients for Beta0, a variable in Pitzer's papers.
column index is counterIJ m_Beta0MX_ij_coeff.ptrColumn(counterIJ) is a double* containing the vector of coefficients for the counterIJ interaction.
Definition at line 2480 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_CoeffWRTemp().
|
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 2491 of file HMWSoln.h.
Referenced by HMWSoln::HMWSoln(), HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::printCoeffs(), HMWSoln::s_updatePitzer_CoeffWRTemp(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
|
mutableprivate |
Derivative of Beta1_ij[i][j] wrt T.
vector index is counterIJ
Definition at line 2497 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::s_updatePitzer_CoeffWRTemp(), and HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT().
|
mutableprivate |
Derivative of Beta1_ij[i][j] wrt TT.
vector index is counterIJ
Definition at line 2503 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::s_updatePitzer_CoeffWRTemp(), and HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2().
|
mutableprivate |
Derivative of Beta1_ij[i][j] wrt P.
vector index is counterIJ
Definition at line 2509 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP().
|
mutableprivate |
Array of coefficients for Beta1, a variable in Pitzer's papers.
column index is counterIJ m_Beta1MX_ij_coeff.ptrColumn(counterIJ) is a double* containing the vector of coefficients for the counterIJ interaction.
Definition at line 2517 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_CoeffWRTemp().
|
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 2529 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::printCoeffs(), HMWSoln::s_updatePitzer_CoeffWRTemp(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
|
mutableprivate |
Derivative of Beta2_ij[i][j] wrt T.
vector index is counterIJ
Definition at line 2535 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::s_updatePitzer_CoeffWRTemp(), and HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT().
|
mutableprivate |
Derivative of Beta2_ij[i][j] wrt TT.
vector index is counterIJ
Definition at line 2541 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::s_updatePitzer_CoeffWRTemp(), and HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2().
|
mutableprivate |
Derivative of Beta2_ij[i][j] wrt P.
vector index is counterIJ
Definition at line 2547 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP().
|
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.
Definition at line 2557 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_CoeffWRTemp().
|
private |
Array of 2D data used in the Pitzer/HMW formulation.
Alpha1MX_ij[i][j] is the value of the alpha1 coefficient for the ij interaction. It will be nonzero iff i and j are both charged and have opposite sign. It is symmetric wrt i, j. counterIJ where counterIJ = m_counterIJ[i][j] is used to access this array.
Definition at line 2568 of file HMWSoln.h.
Referenced by HMWSoln::HMWSoln(), HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::printCoeffs(), HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
|
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.
Definition at line 2580 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
|
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 2592 of file HMWSoln.h.
Referenced by HMWSoln::HMWSoln(), HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::printCoeffs(), HMWSoln::s_updatePitzer_CoeffWRTemp(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
|
mutableprivate |
Derivative of Cphi_ij[i][j] wrt T.
vector index is counterIJ
Definition at line 2598 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::s_updatePitzer_CoeffWRTemp(), and HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT().
|
mutableprivate |
Derivative of Cphi_ij[i][j] wrt TT.
vector index is counterIJ
Definition at line 2604 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::s_updatePitzer_CoeffWRTemp(), and HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2().
|
mutableprivate |
Derivative of Cphi_ij[i][j] wrt P.
vector index is counterIJ
Definition at line 2610 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP().
|
mutableprivate |
Array of coefficients for CphiMX, a parameter in the activity coefficient formulation.
Column index is counterIJ m_CphiMX_ij_coeff.ptrColumn(counterIJ) is a double* containing the vector of coefficients for the counterIJ interaction.
Definition at line 2619 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_CoeffWRTemp().
|
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 2633 of file HMWSoln.h.
Referenced by HMWSoln::HMWSoln(), HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::printCoeffs(), HMWSoln::s_updatePitzer_CoeffWRTemp(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
|
mutableprivate |
Derivative of Theta_ij[i][j] wrt T.
vector index is counterIJ
Definition at line 2639 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::s_updatePitzer_CoeffWRTemp(), and HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT().
|
mutableprivate |
Derivative of Theta_ij[i][j] wrt TT.
vector index is counterIJ
Definition at line 2645 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::s_updatePitzer_CoeffWRTemp(), and HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2().
|
mutableprivate |
Derivative of Theta_ij[i][j] wrt P.
vector index is counterIJ
Definition at line 2651 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP().
|
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.
Definition at line 2665 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_CoeffWRTemp().
|
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 2678 of file HMWSoln.h.
Referenced by HMWSoln::HMWSoln(), HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::printCoeffs(), HMWSoln::s_updatePitzer_CoeffWRTemp(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
|
mutableprivate |
Derivative of Psi_ijk[n] wrt T.
see m_Psi_ijk for reference on the indexing into this variable.
Definition at line 2684 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::s_updatePitzer_CoeffWRTemp(), and HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT().
|
mutableprivate |
Derivative of Psi_ijk[n] wrt TT.
see m_Psi_ijk for reference on the indexing into this variable.
Definition at line 2690 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::s_updatePitzer_CoeffWRTemp(), and HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2().
|
mutableprivate |
Derivative of Psi_ijk[n] wrt P.
see m_Psi_ijk for reference on the indexing into this variable.
Definition at line 2696 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP().
|
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.
Definition at line 2713 of file HMWSoln.h.
Referenced by HMWSoln::HMWSoln(), HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_CoeffWRTemp().
|
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.
Definition at line 2724 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::s_updatePitzer_CoeffWRTemp(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
|
mutableprivate |
Derivative of Lambda_nj[i][j] wrt T. see m_Lambda_ij.
Definition at line 2727 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::s_updatePitzer_CoeffWRTemp(), and HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT().
|
mutableprivate |
Derivative of Lambda_nj[i][j] wrt TT.
Definition at line 2730 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::s_updatePitzer_CoeffWRTemp(), and HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2().
|
mutableprivate |
Derivative of Lambda_nj[i][j] wrt P.
Definition at line 2733 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP().
|
private |
Array of coefficients for Lambda_nj[i][j] in the Pitzer/HMW formulation.
Lambda_ij[i][j] is the value of the theta coefficient for the ij interaction. 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.
Definition at line 2751 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_CoeffWRTemp().
|
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.
Definition at line 2760 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::s_updatePitzer_CoeffWRTemp(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
|
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.
Definition at line 2769 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::s_updatePitzer_CoeffWRTemp(), and HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT().
|
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.
Definition at line 2778 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::s_updatePitzer_CoeffWRTemp(), and HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2().
|
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.
Definition at line 2787 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP().
|
private |
Array of coefficients form_Mu_nnn term.
Definition at line 2790 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_CoeffWRTemp().
|
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 2800 of file HMWSoln.h.
Referenced by HMWSoln::getActivities(), HMWSoln::getChemPotentials(), HMWSoln::getPartialMolarEntropies(), HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updateScaling_pHScaling().
|
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 2810 of file HMWSoln.h.
Referenced by HMWSoln::applyphScale(), HMWSoln::getUnscaledMolalityActivityCoefficients(), HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::s_updatePitzer_lnMolalityActCoeff(), and HMWSoln::s_updateScaling_pHScaling().
|
mutableprivate |
Derivative of the Logarithm of the activity coefficients on the molality scale wrt T.
index is the species index
Definition at line 2817 of file HMWSoln.h.
Referenced by HMWSoln::getPartialMolarCp(), HMWSoln::getPartialMolarEnthalpies(), HMWSoln::getPartialMolarEntropies(), HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updateScaling_pHScaling_dT().
|
mutableprivate |
Derivative of the Logarithm of the activity coefficients on the molality scale wrt T.
index is the species index
Definition at line 2824 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::s_update_dlnMolalityActCoeff_dT(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updateScaling_pHScaling_dT().
|
mutableprivate |
Derivative of the Logarithm of the activity coefficients on the molality scale wrt TT.
index is the species index
Definition at line 2831 of file HMWSoln.h.
Referenced by HMWSoln::getPartialMolarCp(), HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updateScaling_pHScaling_dT2().
|
mutableprivate |
Derivative of the Logarithm of the activity coefficients on the molality scale wrt TT.
index is the species index
Definition at line 2838 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::s_update_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), and HMWSoln::s_updateScaling_pHScaling_dT2().
|
mutableprivate |
Derivative of the Logarithm of the activity coefficients on the molality scale wrt P.
index is the species index
Definition at line 2845 of file HMWSoln.h.
Referenced by HMWSoln::getPartialMolarVolumes(), HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updateScaling_pHScaling_dP().
|
mutableprivate |
Derivative of the Logarithm of the activity coefficients on the molality scale wrt P.
index is the species index
Definition at line 2852 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::s_update_dlnMolalityActCoeff_dP(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), and HMWSoln::s_updateScaling_pHScaling_dP().
|
mutableprivate |
Cropped and modified values of the molalities used in activity coefficient calculations.
Definition at line 2860 of file HMWSoln.h.
Referenced by HMWSoln::calcMolalitiesCropped(), HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::printCoeffs(), HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
|
mutableprivate |
Boolean indicating whether the molalities are cropped or are modified.
Definition at line 2863 of file HMWSoln.h.
Referenced by HMWSoln::calcMolalitiesCropped(), and HMWSoln::operator=().
|
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 2871 of file HMWSoln.h.
Referenced by HMWSoln::counterIJ_setup(), HMWSoln::HMWSoln(), HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::printCoeffs(), HMWSoln::s_updatePitzer_CoeffWRTemp(), HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
|
mutableprivate |
This is elambda, MEC.
Definition at line 2874 of file HMWSoln.h.
Referenced by HMWSoln::calc_lambdas(), HMWSoln::calc_thetas(), and HMWSoln::HMWSoln().
|
mutableprivate |
This is elambda1, MEC.
Definition at line 2877 of file HMWSoln.h.
Referenced by HMWSoln::calc_lambdas(), HMWSoln::calc_thetas(), and HMWSoln::HMWSoln().
|
mutableprivate |
Various temporary arrays used in the calculation of the Pitzer activity coefficients.
The subscript, L, denotes the same quantity's derivative wrt temperatureThis is the value of g(x) in Pitzer's papers
vector index is counterIJ
Definition at line 2890 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
|
mutableprivate |
This is the value of g2(x2) in Pitzer's papers.
vector index is counterIJ
Definition at line 2896 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
|
mutableprivate |
hfunc, was called gprime in Pitzer's paper.
However, it's not the derivative of gfunc(x), so I renamed it.
vector index is counterIJ
Definition at line 2903 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
|
mutableprivate |
hfunc2, was called gprime in Pitzer's paper.
However, it's not the derivative of gfunc(x), so I renamed it.
vector index is counterIJ
Definition at line 2910 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
|
mutableprivate |
Intermediate variable called BMX in Pitzer's paper This is the basic cation - anion interaction.
vector index is counterIJ
Definition at line 2917 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
|
mutableprivate |
Derivative of BMX_IJ wrt T.
vector index is counterIJ
Definition at line 2923 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT().
|
mutableprivate |
Derivative of BMX_IJ wrt TT.
vector index is counterIJ
Definition at line 2929 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2().
|
mutableprivate |
Derivative of BMX_IJ wrt P.
vector index is counterIJ
Definition at line 2935 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP().
|
mutableprivate |
Intermediate variable called BprimeMX in Pitzer's paper.
vector index is counterIJ
Definition at line 2941 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
|
mutableprivate |
Derivative of BprimeMX wrt T.
vector index is counterIJ
Definition at line 2947 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT().
|
mutableprivate |
Derivative of BprimeMX wrt TT.
vector index is counterIJ
Definition at line 2953 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2().
|
mutableprivate |
Derivative of BprimeMX wrt P.
vector index is counterIJ
Definition at line 2959 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP().
|
mutableprivate |
Intermediate variable called BphiMX in Pitzer's paper.
vector index is counterIJ
Definition at line 2965 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
|
mutableprivate |
Derivative of BphiMX_IJ wrt T.
vector index is counterIJ
Definition at line 2971 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT().
|
mutableprivate |
Derivative of BphiMX_IJ wrt TT.
vector index is counterIJ
Definition at line 2977 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2().
|
mutableprivate |
Derivative of BphiMX_IJ wrt P.
vector index is counterIJ
Definition at line 2983 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP().
|
mutableprivate |
Intermediate variable called Phi in Pitzer's paper.
vector index is counterIJ
Definition at line 2989 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
|
mutableprivate |
Derivative of m_Phi_IJ wrt T.
vector index is counterIJ
Definition at line 2995 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT().
|
mutableprivate |
Derivative of m_Phi_IJ wrt TT.
vector index is counterIJ
Definition at line 3001 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2().
|
mutableprivate |
Derivative of m_Phi_IJ wrt P.
vector index is counterIJ
Definition at line 3007 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP().
|
mutableprivate |
Intermediate variable called Phiprime in Pitzer's paper.
vector index is counterIJ
Definition at line 3013 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
|
mutableprivate |
Intermediate variable called PhiPhi in Pitzer's paper.
vector index is counterIJ
Definition at line 3019 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
|
mutableprivate |
Derivative of m_PhiPhi_IJ wrt T.
vector index is counterIJ
Definition at line 3025 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT().
|
mutableprivate |
Derivative of m_PhiPhi_IJ wrt TT.
vector index is counterIJ
Definition at line 3031 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2().
|
mutableprivate |
Derivative of m_PhiPhi_IJ wrt P.
vector index is counterIJ
Definition at line 3037 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP().
|
mutableprivate |
Intermediate variable called CMX in Pitzer's paper.
vector index is counterIJ
Definition at line 3043 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
|
mutableprivate |
Derivative of m_CMX_IJ wrt T.
vector index is counterIJ
Definition at line 3049 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT().
|
mutableprivate |
Derivative of m_CMX_IJ wrt TT.
vector index is counterIJ
Definition at line 3055 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2().
|
mutableprivate |
Derivative of m_CMX_IJ wrt P.
vector index is counterIJ
Definition at line 3061 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP().
|
mutableprivate |
Intermediate storage of the activity coefficient itself.
vector index is the species index
Definition at line 3067 of file HMWSoln.h.
Referenced by HMWSoln::calcMolalitiesCropped(), HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::relative_enthalpy(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
|
mutableprivate |
Logarithm of the molal activity coefficients.
Normally these are all one. However, stability schemes will change that
Definition at line 3073 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), and HMWSoln::s_updateIMS_lnMolalityActCoeff().
|
private |
IMS Cutoff type.
Definition at line 3076 of file HMWSoln.h.
Referenced by HMWSoln::operator=(), and HMWSoln::s_updateIMS_lnMolalityActCoeff().
|
private |
value of the solute mole fraction that centers the cutoff polynomials for the cutoff =1 process;
Definition at line 3080 of file HMWSoln.h.
Referenced by HMWSoln::operator=(), and HMWSoln::s_updateIMS_lnMolalityActCoeff().
|
private |
gamma_o value for the cutoff process at the zero solvent point
Definition at line 3083 of file HMWSoln.h.
Referenced by HMWSoln::operator=(), and HMWSoln::s_updateIMS_lnMolalityActCoeff().
|
private |
gamma_k minimum for the cutoff process at the zero solvent point
Definition at line 3086 of file HMWSoln.h.
Referenced by HMWSoln::operator=(), and HMWSoln::s_updateIMS_lnMolalityActCoeff().
|
private |
Parameter in the polyExp cutoff treatment having to do with rate of exp decay.
Definition at line 3089 of file HMWSoln.h.
Referenced by HMWSoln::operator=(), and HMWSoln::s_updateIMS_lnMolalityActCoeff().
|
private |
Parameter in the polyExp cutoff treatment.
This is the slope of the f function at the zero solvent point Default value is 0.6
Definition at line 3096 of file HMWSoln.h.
Referenced by HMWSoln::operator=().
|
private |
Parameter in the polyExp cutoff treatment.
This is the slope of the g function at the zero solvent point Default value is 0.0
Definition at line 3103 of file HMWSoln.h.
Referenced by HMWSoln::operator=().
|
private |
value of the solvent mole fraction that centers the cutoff polynomials for the cutoff =1 process;
Definition at line 3119 of file HMWSoln.h.
Referenced by HMWSoln::calcMolalitiesCropped(), and HMWSoln::operator=().
|
private |
gamma_o value for the cutoff process at the zero solvent point
Definition at line 3122 of file HMWSoln.h.
Referenced by HMWSoln::operator=().
|
private |
Parameter in the Molality Exp cutoff treatment.
This is the slope of the p function at the zero solvent point Default value is 0.0
Definition at line 3129 of file HMWSoln.h.
Referenced by HMWSoln::operator=().
|
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 3152 of file HMWSoln.h.
Referenced by HMWSoln::initLengths(), HMWSoln::operator=(), HMWSoln::s_update_d2lnMolalityActCoeff_dT2(), HMWSoln::s_update_dlnMolalityActCoeff_dP(), and HMWSoln::s_update_dlnMolalityActCoeff_dT().
|
mutable |
Turn on copious debug printing when this is true and DEBUG_MODE is turned on.
Definition at line 3433 of file HMWSoln.h.
Referenced by HMWSoln::calc_lambdas(), HMWSoln::debugPrinting(), HMWSoln::operator=(), HMWSoln::s_updatePitzer_d2lnMolalityActCoeff_dT2(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dP(), HMWSoln::s_updatePitzer_dlnMolalityActCoeff_dT(), and HMWSoln::s_updatePitzer_lnMolalityActCoeff().
The documentation for this class was generated from the following files:
