Cantera  2.3.0

Class HMWSoln represents a dilute or concentrated liquid electrolyte phase which obeys the Pitzer formulation for nonideality. More...

#include <HMWSoln.h>

Inheritance diagram for HMWSoln:
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Collaboration diagram for HMWSoln:
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## 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)

HMWSolnoperator= (const HMWSoln &right)

virtual ThermoPhaseduplMyselfAsThermoPhase () const
Duplication routine for objects which inherit from ThermoPhase. 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 doublereal satPressure (doublereal T)
Get the saturation pressure for a given temperature. More...

virtual void initThermo ()

virtual void initThermoXML (XML_Node &phaseNode, const std::string &id)
Initialize the phase parameters from an XML file. More...

virtual double A_Debye_TP (double temperature=-1.0, double pressure=-1.0) const
Value of the Debye Huckel constant as a function of temperature and pressure. More...

virtual double dA_DebyedT_TP (double temperature=-1.0, double pressure=-1.0) const
Value of the derivative of the Debye Huckel constant with respect to temperature as a function of temperature and pressure. More...

virtual double dA_DebyedP_TP (double temperature=-1.0, double pressure=-1.0) const
Value of the derivative of the Debye Huckel constant with respect to pressure, as a function of temperature and pressure. More...

double ADebye_L (double temperature=-1.0, double pressure=-1.0) const
Return Pitzer's definition of A_L. More...

double ADebye_J (double temperature=-1.0, double pressure=-1.0) const
Return Pitzer's definition of A_J. More...

double ADebye_V (double temperature=-1.0, double pressure=-1.0) const
Return Pitzer's definition of A_V. More...

virtual double d2A_DebyedT2_TP (double temperature=-1.0, double pressure=-1.0) const
Value of the 2nd derivative of the Debye Huckel constant with respect to temperature as a function of temperature and pressure. More...

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...

virtual std::string type () const
String indicating the thermodynamic model implemented. More...

Molar Thermodynamic Properties of the Solution
virtual doublereal enthalpy_mole () const
Molar enthalpy. Units: J/kmol. More...

virtual doublereal relative_enthalpy () const
Excess molar enthalpy of the solution from the mixing process. More...

virtual doublereal relative_molal_enthalpy () const
Excess molar enthalpy of the solution from the mixing process on a molality basis. More...

virtual doublereal entropy_mole () const
Molar entropy. Units: J/kmol/K. More...

virtual doublereal gibbs_mole () const
Molar Gibbs function. Units: J/kmol. More...

virtual doublereal cp_mole () const
Molar heat capacity at constant pressure. Units: J/kmol/K. More...

virtual doublereal cv_mole () const
Molar heat capacity at constant volume. Units: J/kmol/K. More...

Activities, Standard States, and Activity Concentrations

The activity $$a_k$$ of a species in solution is related to the chemical potential by

$\mu_k = \mu_k^0(T) + \hat R T \log a_k.$

The quantity $$\mu_k^0(T,P)$$ is the chemical potential at unit activity, which depends only on temperature and the pressure.

Activity is assumed to be molality-based here.

virtual void getActivityConcentrations (doublereal *c) const
This method returns an array of generalized activity concentrations. More...

virtual doublereal standardConcentration (size_t k=0) const
Return the standard concentration for the kth species. More...

virtual void getActivities (doublereal *ac) const
Get the array of non-dimensional activities at the current solution temperature, pressure, and solution concentration. More...

Partial Molar Properties of the Solution
virtual void getChemPotentials (doublereal *mu) const
Get the species chemical potentials. Units: J/kmol. More...

virtual void getPartialMolarEnthalpies (doublereal *hbar) const
Returns an array of partial molar enthalpies for the species in the mixture. More...

virtual void getPartialMolarEntropies (doublereal *sbar) const
Returns an array of partial molar entropies of the species in the solution. More...

virtual void getPartialMolarVolumes (doublereal *vbar) const
Return an array of partial molar volumes for the species in the mixture. More...

virtual void getPartialMolarCp (doublereal *cpbar) const
Return an array of partial molar heat capacities for the species in the mixture. More...

Public Member Functions inherited from MolalityVPSSTP
MolalityVPSSTP ()
Default Constructor. More...

MolalityVPSSTP (const MolalityVPSSTP &b)

MolalityVPSSTPoperator= (const MolalityVPSSTP &b)

virtual void setStateFromXML (const XML_Node &state)
Set equation of state parameter values from XML entries. More...

void setState_TPM (doublereal t, doublereal p, const doublereal *const molalities)
Set the temperature (K), pressure (Pa), and molalities (gmol kg-1) of the solutes. More...

void setState_TPM (doublereal t, doublereal p, const compositionMap &m)
Set the temperature (K), pressure (Pa), and molalities. More...

void setState_TPM (doublereal t, doublereal p, const std::string &m)
Set the temperature (K), pressure (Pa), and molalities. More...

virtual void getdlnActCoeffdlnN (const size_t ld, doublereal *const dlnActCoeffdlnN)
Get the array of derivatives of the log activity coefficients with respect to the log of the species mole numbers. More...

virtual std::string report (bool show_thermo=true, doublereal threshold=1e-14) const
returns a summary of the state of the phase as a string More...

void setpHScale (const int pHscaleType)
Set the pH scale, which determines the scale for single-ion activity coefficients. More...

int pHScale () const
Reports the pH scale, which determines the scale for single-ion activity coefficients. More...

void setSolvent (size_t k)
This routine sets the index number of the solvent for the phase. More...

size_t solventIndex () const
Returns the solvent index. More...

void setMoleFSolventMin (doublereal xmolSolventMIN)
Sets the minimum mole fraction in the molality formulation. More...

doublereal moleFSolventMin () const
Returns the minimum mole fraction in the molality formulation. More...

void calcMolalities () const
Calculates the molality of all species and stores the result internally. More...

void getMolalities (doublereal *const molal) const
This function will return the molalities of the species. More...

void setMolalities (const doublereal *const molal)
Set the molalities of the solutes in a phase. More...

void setMolalitiesByName (const compositionMap &xMap)
Set the molalities of a phase. More...

void setMolalitiesByName (const std::string &name)
Set the molalities of a phase. More...

int activityConvention () const
We set the convention to molality here. More...

virtual void getActivityCoefficients (doublereal *ac) const
Get the array of non-dimensional activity coefficients at the current solution temperature, pressure, and solution concentration. More...

virtual void getMolalityActivityCoefficients (doublereal *acMolality) const
Get the array of non-dimensional molality based activity coefficients at the current solution temperature, pressure, and solution concentration. More...

virtual double osmoticCoefficient () const
Calculate the osmotic coefficient. More...

virtual bool addSpecies (shared_ptr< Species > spec)

Public Member Functions inherited from VPStandardStateTP
VPStandardStateTP ()
Constructor. More...

VPStandardStateTP (const VPStandardStateTP &b)

VPStandardStateTPoperator= (const VPStandardStateTP &b)

virtual int standardStateConvention () const
This method returns the convention used in specification of the standard state, of which there are currently two, temperature based, and variable pressure based. More...

virtual void getdlnActCoeffdlnN_diag (doublereal *dlnActCoeffdlnN_diag) const
Get the array of log species mole number derivatives of the log activity coefficients. More...

virtual void getChemPotentials_RT (doublereal *mu) const
Get the array of non-dimensional species chemical potentials. More...

virtual void getStandardChemPotentials (doublereal *mu) const
Get the array of chemical potentials at unit activity for the species at their standard states at the current T and P of the solution. More...

virtual void getEnthalpy_RT (doublereal *hrt) const
Get the nondimensional Enthalpy functions for the species at their standard states at the current T and P of the solution. More...

virtual void getEntropy_R (doublereal *sr) const
Get the array of nondimensional Entropy functions for the standard state species at the current T and P of the solution. More...

virtual void getGibbs_RT (doublereal *grt) const
Get the nondimensional Gibbs functions for the species in their standard states at the current T and P of the solution. More...

virtual void getPureGibbs (doublereal *gpure) const
Get the Gibbs functions for the standard state of the species at the current T and P of the solution. More...

virtual void getIntEnergy_RT (doublereal *urt) const
Returns the vector of nondimensional Internal Energies of the standard state species at the current T and P of the solution. More...

virtual void getCp_R (doublereal *cpr) const
Get the nondimensional Heat Capacities at constant pressure for the species standard states at the current T and P of the solution. More...

virtual void getStandardVolumes (doublereal *vol) const
Get the molar volumes of the species standard states at the current T and P of the solution. More...

virtual const vector_fpgetStandardVolumes () const

virtual void setTemperature (const doublereal temp)
Set the temperature of the phase. More...

virtual void setPressure (doublereal p)
Set the internally stored pressure (Pa) at constant temperature and composition. More...

virtual void setState_TP (doublereal T, doublereal pres)
Set the temperature and pressure at the same time. More...

virtual doublereal pressure () const
Returns the current pressure of the phase. More...

Updates the standard state thermodynamic functions at the current T and P of the solution. More...

void setVPSSMgr (VPSSMgr *vp_ptr)
set the VPSS Mgr More...

VPSSMgrprovideVPSSMgr ()
Return a pointer to the VPSSMgr for this phase. More...

void createInstallPDSS (size_t k, const XML_Node &s, const XML_Node *phaseNode_ptr)

PDSSprovidePDSS (size_t k)

const PDSSprovidePDSS (size_t k) const

virtual bool addSpecies (shared_ptr< Species > spec)
Add a Species to this Phase. More...

virtual void getEnthalpy_RT_ref (doublereal *hrt) const

virtual void getGibbs_RT_ref (doublereal *grt) const
Returns the vector of nondimensional Gibbs Free Energies of the reference state at the current temperature of the solution and the reference pressure for the species. More...

virtual void getGibbs_ref (doublereal *g) const
Returns the vector of the Gibbs function of the reference state at the current temperature of the solution and the reference pressure for the species. More...

virtual void getEntropy_R_ref (doublereal *er) const
Returns the vector of nondimensional entropies of the reference state at the current temperature of the solution and the reference pressure for each species. More...

virtual void getCp_R_ref (doublereal *cprt) const
Returns the vector of nondimensional constant pressure heat capacities of the reference state at the current temperature of the solution and reference pressure for each species. More...

virtual void getStandardVolumes_ref (doublereal *vol) const
Get the molar volumes of the species reference states at the current T and P_ref of the solution. More...

Public Member Functions inherited from ThermoPhase
ThermoPhase ()
Constructor. More...

ThermoPhase (const ThermoPhase &right)

ThermoPhaseoperator= (const ThermoPhase &right)

doublereal _RT () const
Return the Gas Constant multiplied by the current temperature. More...

doublereal RT () const
Return the Gas Constant multiplied by the current temperature. More...

virtual doublereal refPressure () const
Returns the reference pressure in Pa. More...

virtual doublereal minTemp (size_t k=npos) const
Minimum temperature for which the thermodynamic data for the species or phase are valid. More...

doublereal Hf298SS (const size_t k) const
Report the 298 K Heat of Formation of the standard state of one species (J kmol-1) More...

virtual void modifyOneHf298SS (const size_t k, const doublereal Hf298New)
Modify the value of the 298 K Heat of Formation of one species in the phase (J kmol-1) More...

virtual void resetHf298 (const size_t k=npos)
Restore the original heat of formation of one or more species. More...

virtual doublereal maxTemp (size_t k=npos) const
Maximum temperature for which the thermodynamic data for the species are valid. More...

bool chargeNeutralityNecessary () const
Returns the chargeNeutralityNecessity boolean. More...

virtual doublereal intEnergy_mole () const
Molar internal energy. Units: J/kmol. More...

virtual doublereal isothermalCompressibility () const
Returns the isothermal compressibility. Units: 1/Pa. More...

virtual doublereal thermalExpansionCoeff () const
Return the volumetric thermal expansion coefficient. Units: 1/K. More...

void setElectricPotential (doublereal v)
Set the electric potential of this phase (V). More...

doublereal electricPotential () const
Returns the electric potential of this phase (V). More...

virtual doublereal logStandardConc (size_t k=0) const
Natural logarithm of the standard concentration of the kth species. More...

virtual void getLnActivityCoefficients (doublereal *lnac) const
Get the array of non-dimensional molar-based ln activity coefficients at the current solution temperature, pressure, and solution concentration. More...

void getElectrochemPotentials (doublereal *mu) const
Get the species electrochemical potentials. More...

virtual void getPartialMolarIntEnergies (doublereal *ubar) const
Return an array of partial molar internal energies for the species in the mixture. More...

virtual void getIntEnergy_RT_ref (doublereal *urt) const
Returns the vector of nondimensional internal Energies of the reference state at the current temperature of the solution and the reference pressure for each species. More...

virtual void setReferenceComposition (const doublereal *const x)
Sets the reference composition. More...

virtual void getReferenceComposition (doublereal *const x) const
Gets the reference composition. More...

doublereal enthalpy_mass () const
Specific enthalpy. Units: J/kg. More...

doublereal intEnergy_mass () const
Specific internal energy. Units: J/kg. More...

doublereal entropy_mass () const
Specific entropy. Units: J/kg/K. More...

doublereal gibbs_mass () const
Specific Gibbs function. Units: J/kg. More...

doublereal cp_mass () const
Specific heat at constant pressure. Units: J/kg/K. More...

doublereal cv_mass () const
Specific heat at constant volume. Units: J/kg/K. More...

virtual void setState_TPX (doublereal t, doublereal p, const doublereal *x)
Set the temperature (K), pressure (Pa), and mole fractions. More...

virtual void setState_TPX (doublereal t, doublereal p, const compositionMap &x)
Set the temperature (K), pressure (Pa), and mole fractions. More...

virtual void setState_TPX (doublereal t, doublereal p, const std::string &x)
Set the temperature (K), pressure (Pa), and mole fractions. More...

virtual void setState_TPY (doublereal t, doublereal p, const doublereal *y)
Set the internally stored temperature (K), pressure (Pa), and mass fractions of the phase. More...

virtual void setState_TPY (doublereal t, doublereal p, const compositionMap &y)
Set the internally stored temperature (K), pressure (Pa), and mass fractions of the phase. More...

virtual void setState_TPY (doublereal t, doublereal p, const std::string &y)
Set the internally stored temperature (K), pressure (Pa), and mass fractions of the phase. More...

virtual void setState_PX (doublereal p, doublereal *x)
Set the pressure (Pa) and mole fractions. More...

virtual void setState_PY (doublereal p, doublereal *y)
Set the internally stored pressure (Pa) and mass fractions. More...

virtual void setState_HP (double h, double p, double tol=1e-9)
Set the internally stored specific enthalpy (J/kg) and pressure (Pa) of the phase. More...

virtual void setState_UV (double u, double v, double tol=1e-9)
Set the specific internal energy (J/kg) and specific volume (m^3/kg). More...

virtual void setState_SP (double s, double p, double tol=1e-9)
Set the specific entropy (J/kg/K) and pressure (Pa). More...

virtual void setState_SV (double s, double v, double tol=1e-9)
Set the specific entropy (J/kg/K) and specific volume (m^3/kg). More...

virtual void setState_ST (double s, double t, double tol=1e-9)
Set the specific entropy (J/kg/K) and temperature (K). More...

virtual void setState_TV (double t, double v, double tol=1e-9)
Set the temperature (K) and specific volume (m^3/kg). More...

virtual void setState_PV (double p, double v, double tol=1e-9)
Set the pressure (Pa) and specific volume (m^3/kg). More...

virtual void setState_UP (double u, double p, double tol=1e-9)
Set the specific internal energy (J/kg) and pressure (Pa). More...

virtual void setState_VH (double v, double h, double tol=1e-9)
Set the specific volume (m^3/kg) and the specific enthalpy (J/kg) More...

virtual void setState_TH (double t, double h, double tol=1e-9)
Set the temperature (K) and the specific enthalpy (J/kg) More...

virtual void setState_SH (double s, double h, double tol=1e-9)
Set the specific entropy (J/kg/K) and the specific enthalpy (J/kg) More...

virtual void setState_RP (doublereal rho, doublereal p)
Set the density (kg/m**3) and pressure (Pa) at constant composition. More...

virtual void setState_RPX (doublereal rho, doublereal p, const doublereal *x)
Set the density (kg/m**3), pressure (Pa) and mole fractions. More...

virtual void setState_RPX (doublereal rho, doublereal p, const compositionMap &x)
Set the density (kg/m**3), pressure (Pa) and mole fractions. More...

virtual void setState_RPX (doublereal rho, doublereal p, const std::string &x)
Set the density (kg/m**3), pressure (Pa) and mole fractions. More...

virtual void setState_RPY (doublereal rho, doublereal p, const doublereal *y)
Set the density (kg/m**3), pressure (Pa) and mass fractions. More...

virtual void setState_RPY (doublereal rho, doublereal p, const compositionMap &y)
Set the density (kg/m**3), pressure (Pa) and mass fractions. More...

virtual void setState_RPY (doublereal rho, doublereal p, const std::string &y)
Set the density (kg/m**3), pressure (Pa) and mass fractions. More...

void equilibrate (const std::string &XY, const std::string &solver="auto", double rtol=1e-9, int max_steps=50000, int max_iter=100, int estimate_equil=0, int log_level=0)
Equilibrate a ThermoPhase object. More...

virtual void setToEquilState (const doublereal *lambda_RT)
This method is used by the ChemEquil equilibrium solver. More...

void setElementPotentials (const vector_fp &lambda)
Stores the element potentials in the ThermoPhase object. More...

bool getElementPotentials (doublereal *lambda) const
Returns the element potentials stored in the ThermoPhase object. More...

virtual bool compatibleWithMultiPhase () const
Indicates whether this phase type can be used with class MultiPhase for equilibrium calculations. More...

virtual doublereal critTemperature () const
Critical temperature (K). More...

virtual doublereal critPressure () const
Critical pressure (Pa). More...

virtual doublereal critVolume () const
Critical volume (m3/kmol). More...

virtual doublereal critCompressibility () const
Critical compressibility (unitless). More...

virtual doublereal critDensity () const
Critical density (kg/m3). More...

virtual doublereal satTemperature (doublereal p) const
Return the saturation temperature given the pressure. More...

virtual doublereal vaporFraction () const
Return the fraction of vapor at the current conditions. More...

virtual void setState_Tsat (doublereal t, doublereal x)
Set the state to a saturated system at a particular temperature. More...

virtual void setState_Psat (doublereal p, doublereal x)
Set the state to a saturated system at a particular pressure. More...

virtual void modifySpecies (size_t k, shared_ptr< Species > spec)
Modify the thermodynamic data associated with a species. More...

void saveSpeciesData (const size_t k, const XML_Node *const data)
Store a reference pointer to the XML tree containing the species data for this phase. More...

const std::vector< const XML_Node * > & speciesData () const
Return a pointer to the vector of XML nodes containing the species data for this phase. More...

void setSpeciesThermo (MultiSpeciesThermo *spthermo)
Install a species thermodynamic property manager. More...

virtual MultiSpeciesThermospeciesThermo (int k=-1)
Return a changeable reference to the calculation manager for species reference-state thermodynamic properties. More...

virtual void initThermoFile (const std::string &inputFile, const std::string &id)

virtual void installSlavePhases (XML_Node *phaseNode)
Add in species from Slave phases. More...

virtual void setParameters (int n, doublereal *const c)
Set the equation of state parameters. More...

virtual void getParameters (int &n, doublereal *const c) const
Get the equation of state parameters in a vector. More...

virtual void setParametersFromXML (const XML_Node &eosdata)
Set equation of state parameter values from XML entries. More...

virtual void getdlnActCoeffds (const doublereal dTds, const doublereal *const dXds, doublereal *dlnActCoeffds) const
Get the change in activity coefficients wrt changes in state (temp, mole fraction, etc) along a line in parameter space or along a line in physical space. More...

virtual void getdlnActCoeffdlnX_diag (doublereal *dlnActCoeffdlnX_diag) const
Get the array of ln mole fraction derivatives of the log activity coefficients - diagonal component only. More...

virtual void getdlnActCoeffdlnN_numderiv (const size_t ld, doublereal *const dlnActCoeffdlnN)

virtual void reportCSV (std::ofstream &csvFile) const
returns a summary of the state of the phase to a comma separated file. More...

Public Member Functions inherited from Phase
Phase ()
Default constructor. More...

Phase (const Phase &right)

Phaseoperator= (const Phase &right)

XML_Nodexml () const
Returns a const reference to the XML_Node that describes the phase. More...

void setXMLdata (XML_Node &xmlPhase)
Stores the XML tree information for the current phase. More...

void saveState (vector_fp &state) const
Save the current internal state of the phase. More...

void saveState (size_t lenstate, doublereal *state) const
Write to array 'state' the current internal state. More...

void restoreState (const vector_fp &state)
Restore a state saved on a previous call to saveState. More...

void restoreState (size_t lenstate, const doublereal *state)
Restore the state of the phase from a previously saved state vector. More...

doublereal molecularWeight (size_t k) const
Molecular weight of species k. More...

void getMolecularWeights (vector_fp &weights) const
Copy the vector of molecular weights into vector weights. More...

void getMolecularWeights (doublereal *weights) const
Copy the vector of molecular weights into array weights. More...

const vector_fpmolecularWeights () 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...

Returns a bool indicating whether the object is ready for use. More...

int stateMFNumber () const
Return the State Mole Fraction Number. More...

std::string id () const
Return the string id for the phase. More...

void setID (const std::string &id)
Set the string id for the phase. More...

std::string name () const
Return the name of the phase. More...

void setName (const std::string &nm)
Sets the string name for the phase. More...

std::string elementName (size_t m) const
Name of the element with index m. More...

size_t elementIndex (const std::string &name) const
Return the index of element named 'name'. More...

const std::vector< std::string > & elementNames () const
Return a read-only reference to the vector of element names. More...

doublereal atomicWeight (size_t m) const
Atomic weight of element m. More...

doublereal entropyElement298 (size_t m) const
Entropy of the element in its standard state at 298 K and 1 bar. More...

int atomicNumber (size_t m) const
Atomic number of element m. More...

int elementType (size_t m) const
Return the element constraint type Possible types include: More...

int changeElementType (int m, int elem_type)
Change the element type of the mth constraint Reassigns an element type. More...

const vector_fpatomicWeights () const
Return a read-only reference to the vector of atomic weights. More...

size_t nElements () const
Number of elements. More...

void checkElementIndex (size_t m) const
Check that the specified element index is in range. More...

void checkElementArraySize (size_t mm) const
Check that an array size is at least nElements(). More...

doublereal nAtoms (size_t k, size_t m) const
Number of atoms of element m in species k. More...

void getAtoms (size_t k, double *atomArray) const
Get a vector containing the atomic composition of species k. More...

size_t speciesIndex (const std::string &name) const
Returns the index of a species named 'name' within the Phase object. More...

std::string speciesName (size_t k) const
Name of the species with index k. More...

std::string speciesSPName (int k) const
Returns the expanded species name of a species, including the phase name This is guaranteed to be unique within a Cantera problem. More...

const std::vector< std::string > & speciesNames () const
Return a const reference to the vector of species names. More...

size_t nSpecies () const
Returns the number of species in the phase. More...

void checkSpeciesIndex (size_t k) const
Check that the specified species index is in range. More...

void checkSpeciesArraySize (size_t kk) const
Check that an array size is at least nSpecies(). More...

void setMoleFractionsByName (const compositionMap &xMap)
Set the species mole fractions by name. More...

void setMoleFractionsByName (const std::string &x)
Set the mole fractions of a group of species by name. More...

void setMassFractionsByName (const compositionMap &yMap)
Set the species mass fractions by name. More...

void setMassFractionsByName (const std::string &x)
Set the species mass fractions by name. More...

void setState_TRX (doublereal t, doublereal dens, const doublereal *x)
Set the internally stored temperature (K), density, and mole fractions. More...

void setState_TRX (doublereal t, doublereal dens, const compositionMap &x)
Set the internally stored temperature (K), density, and mole fractions. More...

void setState_TRY (doublereal t, doublereal dens, const doublereal *y)
Set the internally stored temperature (K), density, and mass fractions. More...

void setState_TRY (doublereal t, doublereal dens, const compositionMap &y)
Set the internally stored temperature (K), density, and mass fractions. More...

void setState_TNX (doublereal t, doublereal n, const doublereal *x)
Set the internally stored temperature (K), molar density (kmol/m^3), and mole fractions. More...

void setState_TR (doublereal t, doublereal rho)
Set the internally stored temperature (K) and density (kg/m^3) More...

void setState_TX (doublereal t, doublereal *x)
Set the internally stored temperature (K) and mole fractions. More...

void setState_TY (doublereal t, doublereal *y)
Set the internally stored temperature (K) and mass fractions. More...

void setState_RX (doublereal rho, doublereal *x)
Set the density (kg/m^3) and mole fractions. More...

void setState_RY (doublereal rho, doublereal *y)
Set the density (kg/m^3) and mass fractions. More...

compositionMap getMoleFractionsByName (double threshold=0.0) const
Get the mole fractions by name. More...

doublereal moleFraction (size_t k) const
Return the mole fraction of a single species. More...

doublereal moleFraction (const std::string &name) const
Return the mole fraction of a single species. More...

compositionMap getMassFractionsByName (double threshold=0.0) const
Get the mass fractions by name. More...

doublereal massFraction (size_t k) const
Return the mass fraction of a single species. More...

doublereal massFraction (const std::string &name) const
Return the mass fraction of a single species. More...

void getMoleFractions (doublereal *const x) const
Get the species mole fraction vector. More...

virtual void setMoleFractions (const doublereal *const x)
Set the mole fractions to the specified values. More...

virtual void setMoleFractions_NoNorm (const doublereal *const x)
Set the mole fractions to the specified values without normalizing. More...

void getMassFractions (doublereal *const y) const
Get the species mass fractions. More...

const doublereal * massFractions () const
Return a const pointer to the mass fraction array. More...

virtual void setMassFractions (const doublereal *const y)
Set the mass fractions to the specified values and normalize them. More...

virtual void setMassFractions_NoNorm (const doublereal *const y)
Set the mass fractions to the specified values without normalizing. More...

void getConcentrations (doublereal *const c) const
Get the species concentrations (kmol/m^3). More...

doublereal concentration (const size_t k) const
Concentration of species k. More...

virtual void setConcentrations (const doublereal *const conc)
Set the concentrations to the specified values within the phase. More...

virtual void setConcentrationsNoNorm (const double *const conc)
Set the concentrations without ignoring negative concentrations. More...

doublereal elementalMassFraction (const size_t m) const
Elemental mass fraction of element m. More...

doublereal elementalMoleFraction (const size_t m) const
Elemental mole fraction of element m. More...

const doublereal * moleFractdivMMW () const
Returns a const pointer to the start of the moleFraction/MW array. More...

doublereal temperature () const
Temperature (K). More...

virtual doublereal density () const
Density (kg/m^3). More...

doublereal molarDensity () const
Molar density (kmol/m^3). More...

doublereal molarVolume () const
Molar volume (m^3/kmol). More...

doublereal mean_X (const doublereal *const Q) const
Evaluate the mole-fraction-weighted mean of an array Q. More...

doublereal mean_X (const vector_fp &Q) const
Evaluate the mole-fraction-weighted mean of an array Q. More...

doublereal meanMolecularWeight () const
The mean molecular weight. Units: (kg/kmol) More...

doublereal sum_xlogx () const
Evaluate $$\sum_k X_k \log X_k$$. More...

size_t addElement (const std::string &symbol, doublereal weight=-12345.0, int atomicNumber=0, doublereal entropy298=ENTROPY298_UNKNOWN, int elem_type=CT_ELEM_TYPE_ABSPOS)

shared_ptr< Speciesspecies (const std::string &name) const
Return the Species object for the named species. More...

shared_ptr< Speciesspecies (size_t k) const
Return the Species object for species whose index is k. More...

void ignoreUndefinedElements ()
Set behavior when adding a species containing undefined elements to just skip the species. More...

Set behavior when adding a species containing undefined elements to add those elements to the phase. More...

void throwUndefinedElements ()
Set the behavior when adding a species containing undefined elements to throw an exception. More...

## Public Attributes

int m_form_A_Debye
Form of the constant outside the Debye-Huckel term called A. More...

int m_debugCalc
Turn on copious debug printing when this is true. More...

## Private Member Functions

Apply the current phScale to a set of activity Coefficients. More...

Apply the current phScale to a set of derivatives of the activity Coefficients wrt temperature. More...

Apply the current phScale to a set of 2nd derivatives of the activity Coefficients wrt temperature. More...

Apply the current phScale to a set of derivatives of the activity Coefficients wrt pressure. More...

doublereal s_NBS_CLM_lnMolalityActCoeff () const
Calculate the Chlorine activity coefficient on the NBS scale. More...

doublereal s_NBS_CLM_dlnMolalityActCoeff_dT () const
Calculate the temperature derivative of the Chlorine activity coefficient on the NBS scale. More...

doublereal s_NBS_CLM_d2lnMolalityActCoeff_dT2 () const
Calculate the second temperature derivative of the Chlorine activity coefficient on the NBS scale. More...

doublereal s_NBS_CLM_dlnMolalityActCoeff_dP () const
Calculate the pressure derivative of the Chlorine activity coefficient. More...

void initLengths ()
Initialize all of the species-dependent lengths in the object. More...

virtual void applyphScale (doublereal *acMolality) const
Apply the current phScale to a set of activity Coefficients or activities. More...

void s_update_lnMolalityActCoeff () const

void s_update_dlnMolalityActCoeff_dT () const
This function calculates the temperature derivative of the natural logarithm of the molality activity coefficients. More...

void s_update_d2lnMolalityActCoeff_dT2 () const
This function calculates the temperature second derivative of the natural logarithm of the molality activity coefficients. More...

void s_update_dlnMolalityActCoeff_dP () const
This function calculates the pressure derivative of the natural logarithm of the molality activity coefficients. More...

void s_updateIMS_lnMolalityActCoeff () const
This function will be called to update the internally stored natural logarithm of the molality activity coefficients. More...

void s_updatePitzer_lnMolalityActCoeff () const
Calculate the Pitzer portion of the activity coefficients. More...

void s_updatePitzer_dlnMolalityActCoeff_dT () const
Calculates the temperature derivative of the natural logarithm of the molality activity coefficients. More...

void s_updatePitzer_d2lnMolalityActCoeff_dT2 () const
This function calculates the temperature second derivative of the natural logarithm of the molality activity coefficients. More...

void s_updatePitzer_dlnMolalityActCoeff_dP () const
Calculates the Pressure derivative of the natural logarithm of the molality activity coefficients. More...

void s_updatePitzer_CoeffWRTemp (int doDerivs=2) const
Calculates the Pitzer coefficients' dependence on the temperature. More...

void calc_lambdas (double is) const
Calculate the lambda interactions. More...

void calc_thetas (int z1, int z2, double *etheta, double *etheta_prime) const
Calculate etheta and etheta_prime. More...

void counterIJ_setup () const
Set up a counter variable for keeping track of symmetric binary interactions amongst the solute species. More...

void calcMolalitiesCropped () const
Calculate the cropped molalities. More...

Process an XML node called "binarySaltParameters". More...

Process an XML node called "thetaAnion". More...

Process an XML node called "thetaCation". More...

Process an XML node called "psiCommonAnion". More...

Process an XML node called "psiCommonCation". More...

Process an XML node called "lambdaNeutral". More...

Process an XML node called "MunnnNeutral". More...

Process an XML node called "zetaCation". More...

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...

Water standard state calculator. More...

density of standard-state water More...

std::unique_ptr< WaterPropsm_waterProps
Pointer to the water property calculator. More...

vector_fp m_tmpV
vector of size m_kk, used as a temporary holding area. More...

vector_fp m_speciesCharge_Stoich
Stoichiometric species charge -> This is for calculations of the ionic strength which ignore ion-ion pairing into neutral molecules. More...

vector_fp m_Beta0MX_ij
Array of 2D data used in the Pitzer/HMW formulation. More...

vector_fp m_Beta0MX_ij_L
Derivative of Beta0_ij[i][j] wrt T. Vector index is counterIJ. More...

vector_fp m_Beta0MX_ij_LL
Derivative of Beta0_ij[i][j] wrt TT. Vector index is counterIJ. More...

vector_fp m_Beta0MX_ij_P
Derivative of Beta0_ij[i][j] wrt P. Vector index is counterIJ. More...

Array2D m_Beta0MX_ij_coeff
Array of coefficients for Beta0, a variable in Pitzer's papers. More...

vector_fp m_Beta1MX_ij
Array of 2D data used in the Pitzer/HMW formulation. More...

vector_fp m_Beta1MX_ij_L
Derivative of Beta1_ij[i][j] wrt T. Vector index is counterIJ. More...

vector_fp m_Beta1MX_ij_LL
Derivative of Beta1_ij[i][j] wrt TT. Vector index is counterIJ. More...

vector_fp m_Beta1MX_ij_P
Derivative of Beta1_ij[i][j] wrt P. Vector index is counterIJ. More...

Array2D m_Beta1MX_ij_coeff
Array of coefficients for Beta1, a variable in Pitzer's papers. More...

vector_fp m_Beta2MX_ij
Array of 2D data used in the Pitzer/HMW formulation. More...

vector_fp m_Beta2MX_ij_L
Derivative of Beta2_ij[i][j] wrt T. Vector index is counterIJ. More...

vector_fp m_Beta2MX_ij_LL
Derivative of Beta2_ij[i][j] wrt TT. Vector index is counterIJ. More...

vector_fp m_Beta2MX_ij_P
Derivative of Beta2_ij[i][j] wrt P. Vector index is counterIJ. More...

Array2D m_Beta2MX_ij_coeff
Array of coefficients for Beta2, a variable in Pitzer's papers. More...

vector_fp m_Alpha1MX_ij

vector_fp m_Alpha2MX_ij
Array of 2D data used in the Pitzer/HMW formulation. More...

vector_fp m_CphiMX_ij
Array of 2D data used in the Pitzer/HMW formulation. More...

vector_fp m_CphiMX_ij_L
Derivative of Cphi_ij[i][j] wrt T. Vector index is counterIJ. More...

vector_fp m_CphiMX_ij_LL
Derivative of Cphi_ij[i][j] wrt TT. Vector index is counterIJ. More...

vector_fp m_CphiMX_ij_P
Derivative of Cphi_ij[i][j] wrt P. Vector index is counterIJ. More...

Array2D m_CphiMX_ij_coeff
Array of coefficients for CphiMX, a parameter in the activity coefficient formulation. More...

vector_fp m_Theta_ij
Array of 2D data for Theta_ij[i][j] in the Pitzer/HMW formulation. More...

vector_fp m_Theta_ij_L
Derivative of Theta_ij[i][j] wrt T. Vector index is counterIJ. More...

vector_fp m_Theta_ij_LL
Derivative of Theta_ij[i][j] wrt TT. Vector index is counterIJ. More...

vector_fp m_Theta_ij_P
Derivative of Theta_ij[i][j] wrt P. Vector index is counterIJ. More...

Array2D m_Theta_ij_coeff
Array of coefficients for Theta_ij[i][j] in the Pitzer/HMW formulation. More...

vector_fp m_Psi_ijk
Array of 3D data used in the Pitzer/HMW formulation. More...

vector_fp m_Psi_ijk_L
Derivative of Psi_ijk[n] wrt T. More...

vector_fp m_Psi_ijk_LL
Derivative of Psi_ijk[n] wrt TT. More...

vector_fp m_Psi_ijk_P
Derivative of Psi_ijk[n] wrt P. More...

Array2D m_Psi_ijk_coeff
Array of coefficients for Psi_ijk[n] in the Pitzer/HMW formulation. More...

Array2D m_Lambda_nj
Lambda coefficient for the ij interaction. More...

Array2D m_Lambda_nj_L
Derivative of Lambda_nj[i][j] wrt T. see m_Lambda_ij. More...

Array2D m_Lambda_nj_LL
Derivative of Lambda_nj[i][j] wrt TT. More...

Array2D m_Lambda_nj_P
Derivative of Lambda_nj[i][j] wrt P. More...

Array2D m_Lambda_nj_coeff
Array of coefficients for Lambda_nj[i][j] in the Pitzer/HMW formulation. More...

vector_fp m_Mu_nnn
Mu coefficient for the self-ternary neutral coefficient. More...

vector_fp m_Mu_nnn_L
Mu coefficient temperature derivative for the self-ternary neutral coefficient. More...

vector_fp m_Mu_nnn_LL
Mu coefficient 2nd temperature derivative for the self-ternary neutral coefficient. More...

vector_fp m_Mu_nnn_P
Mu coefficient pressure derivative for the self-ternary neutral coefficient. More...

Array2D m_Mu_nnn_coeff
Array of coefficients form_Mu_nnn term. More...

vector_fp m_lnActCoeffMolal_Scaled
Logarithm of the activity coefficients on the molality scale. More...

vector_fp m_lnActCoeffMolal_Unscaled
Logarithm of the activity coefficients on the molality scale. More...

vector_fp m_dlnActCoeffMolaldT_Scaled
Derivative of the Logarithm of the activity coefficients on the molality scale wrt T. More...

vector_fp m_dlnActCoeffMolaldT_Unscaled
Derivative of the Logarithm of the activity coefficients on the molality scale wrt T. More...

vector_fp m_d2lnActCoeffMolaldT2_Scaled
Derivative of the Logarithm of the activity coefficients on the molality scale wrt TT. More...

vector_fp m_d2lnActCoeffMolaldT2_Unscaled
Derivative of the Logarithm of the activity coefficients on the molality scale wrt TT. More...

vector_fp m_dlnActCoeffMolaldP_Scaled
Derivative of the Logarithm of the activity coefficients on the molality scale wrt P. More...

vector_fp m_dlnActCoeffMolaldP_Unscaled
Derivative of the Logarithm of the activity coefficients on the molality scale wrt P. More...

vector_fp m_molalitiesCropped
Cropped and modified values of the molalities used in activity coefficient calculations. More...

bool m_molalitiesAreCropped
Boolean indicating whether the molalities are cropped or are modified. More...

vector_int m_CounterIJ
a counter variable for keeping track of symmetric binary interactions amongst the solute species. More...

double elambda [17]
This is elambda, MEC. More...

double elambda1 [17]
This is elambda1, MEC. More...

vector_fp m_gfunc_IJ
Various temporary arrays used in the calculation of the Pitzer activity coefficients. More...

vector_fp m_g2func_IJ
This is the value of g2(x2) in Pitzer's papers. Vector index is counterIJ. More...

vector_fp m_hfunc_IJ
hfunc, was called gprime in Pitzer's paper. More...

vector_fp m_h2func_IJ
hfunc2, was called gprime in Pitzer's paper. More...

vector_fp m_BMX_IJ
Intermediate variable called BMX in Pitzer's paper. More...

vector_fp m_BMX_IJ_L
Derivative of BMX_IJ wrt T. Vector index is counterIJ. More...

vector_fp m_BMX_IJ_LL
Derivative of BMX_IJ wrt TT. Vector index is counterIJ. More...

vector_fp m_BMX_IJ_P
Derivative of BMX_IJ wrt P. Vector index is counterIJ. More...

vector_fp m_BprimeMX_IJ
Intermediate variable called BprimeMX in Pitzer's paper. More...

vector_fp m_BprimeMX_IJ_L
Derivative of BprimeMX wrt T. Vector index is counterIJ. More...

vector_fp m_BprimeMX_IJ_LL
Derivative of BprimeMX wrt TT. Vector index is counterIJ. More...

vector_fp m_BprimeMX_IJ_P
Derivative of BprimeMX wrt P. Vector index is counterIJ. More...

vector_fp m_BphiMX_IJ
Intermediate variable called BphiMX in Pitzer's paper. More...

vector_fp m_BphiMX_IJ_L
Derivative of BphiMX_IJ wrt T. Vector index is counterIJ. More...

vector_fp m_BphiMX_IJ_LL
Derivative of BphiMX_IJ wrt TT. Vector index is counterIJ. More...

vector_fp m_BphiMX_IJ_P
Derivative of BphiMX_IJ wrt P. Vector index is counterIJ. More...

vector_fp m_Phi_IJ
Intermediate variable called Phi in Pitzer's paper. More...

vector_fp m_Phi_IJ_L
Derivative of m_Phi_IJ wrt T. Vector index is counterIJ. More...

vector_fp m_Phi_IJ_LL
Derivative of m_Phi_IJ wrt TT. Vector index is counterIJ. More...

vector_fp m_Phi_IJ_P
Derivative of m_Phi_IJ wrt P. Vector index is counterIJ. More...

vector_fp m_Phiprime_IJ
Intermediate variable called Phiprime in Pitzer's paper. More...

vector_fp m_PhiPhi_IJ
Intermediate variable called PhiPhi in Pitzer's paper. More...

vector_fp m_PhiPhi_IJ_L
Derivative of m_PhiPhi_IJ wrt T. Vector index is counterIJ. More...

vector_fp m_PhiPhi_IJ_LL
Derivative of m_PhiPhi_IJ wrt TT. Vector index is counterIJ. More...

vector_fp m_PhiPhi_IJ_P
Derivative of m_PhiPhi_IJ wrt P. Vector index is counterIJ. More...

vector_fp m_CMX_IJ
Intermediate variable called CMX in Pitzer's paper. More...

vector_fp m_CMX_IJ_L
Derivative of m_CMX_IJ wrt T. Vector index is counterIJ. More...

vector_fp m_CMX_IJ_LL
Derivative of m_CMX_IJ wrt TT. Vector index is counterIJ. More...

vector_fp m_CMX_IJ_P
Derivative of m_CMX_IJ wrt P. Vector index is counterIJ. More...

vector_fp m_gamma_tmp
Intermediate storage of the activity coefficient itself. More...

vector_fp IMS_lnActCoeffMolal_
Logarithm of the molal activity coefficients. More...

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...

doublereal m_last_is

Parameters in the polyExp cutoff treatment having to do with rate of exp decay
doublereal IMS_dfCut_

doublereal IMS_efCut_

doublereal IMS_afCut_

doublereal IMS_bfCut_

doublereal IMS_dgCut_

doublereal IMS_egCut_

doublereal IMS_agCut_

doublereal IMS_bgCut_

Parameters in the Molality Exp cutoff treatment
doublereal MC_dpCut_

doublereal MC_epCut_

doublereal MC_apCut_

doublereal MC_bpCut_

doublereal MC_cpCut_

doublereal CROP_ln_gamma_o_min

doublereal CROP_ln_gamma_o_max

doublereal CROP_ln_gamma_k_min

doublereal CROP_ln_gamma_k_max

vector_int CROP_speciesCropped_
This is a boolean-type vector indicating whether a species's activity coefficient is in the cropped regime. More...

## Mechanical Equation of State Properties

virtual void setDensity (const doublereal rho)
Set the internally stored density (kg/m^3) of the phase. More...

virtual void setMolarDensity (const doublereal conc)
Set the internally stored molar density (kmol/m^3) for the phase. More...

void calcDensity ()
Calculate the density of the mixture using the partial molar volumes and mole fractions as input. More...

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
Updates the standard state thermodynamic functions at the current T and P of the solution. More...

virtual void invalidateCache ()
Invalidate any cached values which are normally updated only when a change in state is detected. More...

const vector_fpGibbs_RT_ref () const

Protected Member Functions inherited from Phase
void setMolecularWeight (const int k, const double mw)
Set the molecular weight of a single species to a given value. More...

virtual void compositionChanged ()
Apply changes to the state which are needed after the composition changes. More...

Protected Attributes inherited from MolalityVPSSTP
size_t m_indexSolvent
Index of the solvent. More...

int m_pHScalingType
Scaling to be used for output of single-ion species activity coefficients. More...

size_t m_indexCLM
Index of the phScale species. More...

doublereal m_weightSolvent
Molecular weight of the Solvent. More...

doublereal m_xmolSolventMIN

doublereal m_Mnaught
This is the multiplication factor that goes inside log expressions involving the molalities of species. More...

vector_fp m_molalities
Current value of the molalities of the species in the phase. More...

Protected Attributes inherited from VPStandardStateTP
doublereal m_Pcurrent
Current value of the pressure - state variable. More...

doublereal m_Tlast_ss
The last temperature at which the standard statethermodynamic properties were calculated at. More...

doublereal m_Plast_ss
The last pressure at which the Standard State thermodynamic properties were calculated at. More...

doublereal m_P0

std::unique_ptr< VPSSMgrm_VPSS_ptr
Pointer to the VPSS manager that calculates all of the standard state info efficiently. More...

std::vector< std::unique_ptr< PDSS > > m_PDSS_storage
Storage for the PDSS objects for the species. More...

Protected Attributes inherited from ThermoPhase
MultiSpeciesThermom_spthermo
Pointer to the calculation manager for species reference-state thermodynamic properties. More...

std::vector< const XML_Node * > m_speciesData
Vector of pointers to the species databases. More...

doublereal m_phi
Stored value of the electric potential for this phase. Units are Volts. More...

vector_fp m_lambdaRRT
Vector of element potentials. Length equal to number of elements. More...

bool m_hasElementPotentials
Boolean indicating whether there is a valid set of saved element potentials for this phase. More...

bool m_chargeNeutralityNecessary
Boolean indicating whether a charge neutrality condition is a necessity. More...

int m_ssConvention
Contains the standard state convention. More...

vector_fp xMol_Ref
Reference Mole Fraction Composition. More...

doublereal m_tlast
last value of the temperature processed by reference state More...

Protected Attributes inherited from Phase
ValueCache m_cache
Cached for saved calculations within each ThermoPhase. More...

size_t m_kk
Number of species in the phase. More...

size_t m_ndim
Dimensionality of the phase. More...

vector_fp m_speciesComp
Atomic composition of the species. More...

vector_fp m_speciesSize
Vector of species sizes. More...

vector_fp m_speciesCharge
Vector of species charges. length m_kk. More...

std::map< std::string, shared_ptr< Species > > m_species

UndefElement::behavior m_undefinedElementBehavior
Flag determining behavior when adding species with an undefined element. More...

## Detailed Description

Class HMWSoln represents a dilute or concentrated liquid electrolyte phase which obeys the Pitzer formulation for nonideality.

As a prerequisite to the specification of thermodynamic quantities, The concentrations of the ionic species are assumed to obey the electroneutrality condition.

## Specification of Species Standard State Properties

The solvent is assumed to be liquid water. A real model for liquid water (IAPWS 1995 formulation) is used as its standard state. All standard state properties for the solvent are based on this real model for water, and involve function calls to the object that handles the real water model, Cantera::WaterPropsIAPWS.

The standard states for solutes are on the unit molality basis. Therefore, in the documentation below, the normal $$o$$ superscript is replaced with the $$\triangle$$ symbol. The reference state symbol is now $$\triangle, ref$$.

It is assumed that the reference state thermodynamics may be obtained by a pointer to a populated species thermodynamic property manager class (see ThermoPhase::m_spthermo). How to relate pressure changes to the reference state thermodynamics is resolved at this level.

For solutes that rely on ThermoPhase::m_spthermo, are assumed to have an incompressible standard state mechanical property. In other words, the molar volumes are independent of temperature and pressure.

For these incompressible, standard states, the molar internal energy is independent of pressure. Since the thermodynamic properties are specified by giving the standard-state enthalpy, the term $$P_0 \hat v$$ is subtracted from the specified molar enthalpy to compute the molar internal energy. The entropy is assumed to be independent of the pressure.

The enthalpy function is given by the following relation.

$h^\triangle_k(T,P) = h^{\triangle,ref}_k(T) + \tilde{v}_k \left( P - P_{ref} \right)$

For an incompressible, stoichiometric substance, the molar internal energy is independent of pressure. Since the thermodynamic properties are specified by giving the standard-state enthalpy, the term $$P_{ref} \tilde v$$ is subtracted from the specified reference molar enthalpy to compute the molar internal energy.

$u^\triangle_k(T,P) = h^{\triangle,ref}_k(T) - P_{ref} \tilde{v}_k$

The solute standard state heat capacity and entropy are independent of pressure. The solute standard state Gibbs free energy is obtained from the enthalpy and entropy functions.

The 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.

### Ionic Strength

Most of the parameterizations within the model use the ionic strength as a key variable. The ionic strength, $$I$$ is defined as follows

$I = \frac{1}{2} \sum_k{m_k z_k^2}$

$$m_k$$ is the molality of the kth species. $$z_k$$ is the charge of the kth species. Note, the ionic strength is a defined units quantity. The molality has defined units of gmol kg-1, and therefore the ionic strength has units of sqrt(gmol/kg).

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:

<stoichIsMods>
NaCl(aq):-1.0
</stoichIsMods>

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

<electrolyteSpeciesType>
H2L(L):solvent
H+:chargedSpecies
NaOH(aq):weakAcidAssociated
NaCl(aq):strongAcidAssociated
NH3(aq):polarNeutral
O2(aq):nonpolarNeutral
</electrolyteSpeciesType>

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.

### Specification of the Excess Gibbs Free Energy

Pitzer's formulation may best be represented as a specification of the excess Gibbs free energy, $$G^{ex}$$, defined as the deviation of the total Gibbs free energy from that of an ideal molal solution.

$G = G^{id} + G^{ex}$

The ideal molal solution contribution, not equal to an ideal solution contribution and in fact containing a singularity at the zero solvent mole fraction limit, is given below.

$G^{id} = n_o \mu^o_o + \sum_{k\ne o} n_k \mu_k^{\triangle} + \tilde{M}_o n_o ( RT (\sum{m_i(\ln(m_i)-1)}))$

From the excess Gibbs free energy formulation, the activity coefficient expression and the osmotic coefficient expression for the solvent may be defined, by taking the appropriate derivatives. Using this approach guarantees that the entire system will obey the Gibbs-Duhem relations.

Pitzer employs the following general expression for the excess Gibbs free energy

$\begin{array}{cclc} \frac{G^{ex}}{\tilde{M}_o n_o RT} &= & \left( \frac{4A_{Debye}I}{3b} \right) \ln(1 + b \sqrt{I}) + 2 \sum_c \sum_a m_c m_a B_{ca} + \sum_c \sum_a m_c m_a Z C_{ca} \\&& + \sum_{c < c'} \sum m_c m_{c'} \left[ 2 \Phi_{c{c'}} + \sum_a m_a \Psi_{c{c'}a} \right] + \sum_{a < a'} \sum m_a m_{a'} \left[ 2 \Phi_{a{a'}} + \sum_c m_c \Psi_{a{a'}c} \right] \\&& + 2 \sum_n \sum_c m_n m_c \lambda_{nc} + 2 \sum_n \sum_a m_n m_a \lambda_{na} + 2 \sum_{n < n'} \sum m_n m_{n'} \lambda_{n{n'}} + \sum_n m^2_n \lambda_{nn} \end{array}$

a is a subscript over all anions, c is a subscript extending over all cations, and i is a subscript that extends over all anions and cations. n is a subscript that extends only over neutral solute molecules. The second line contains cross terms where cations affect cations and/or cation/anion pairs, and anions affect anions or cation/anion pairs. Note part of the coefficients, $$\Phi_{c{c'}}$$ and $$\Phi_{a{a'}}$$ stem from the theory of unsymmetrical mixing of electrolytes with different charges. This theory depends on the total ionic strength of the solution, and therefore, $$\Phi_{c{c'}}$$ and $$\Phi_{a{a'}}$$ will depend on I, the ionic strength. $$B_{ca}$$ is a strong function of the total ionic strength, I, of the electrolyte. The rest of the coefficients are assumed to be independent of the molalities or ionic strengths. However, all coefficients are potentially functions of the temperature and pressure of the solution.

A is the Debye-Huckel constant. Its specification is described in its own section below.

$$I$$ is the ionic strength of the solution, and is given by:

$I = \frac{1}{2} \sum_k{m_k z_k^2}$

In contrast to several other Debye-Huckel implementations (see DebyeHuckel), the parameter $$b$$ in the above equation is a constant that does not vary with respect to ion identity. This is an important simplification as it avoids troubles with satisfaction of the Gibbs-Duhem analysis.

The function $$Z$$ is given by

$Z = \sum_i m_i \left| z_i \right|$

The value of $$B_{ca}$$ is given by the following function

$B_{ca} = \beta^{(0)}_{ca} + \beta^{(1)}_{ca} g(\alpha^{(1)}_{ca} \sqrt{I}) + \beta^{(2)}_{ca} g(\alpha^{(2)}_{ca} \sqrt{I})$

where

$g(x) = 2 \frac{(1 - (1 + x)\exp[-x])}{x^2}$

The formulation for $$B_{ca}$$ combined with the formulation of the Debye- Huckel term in the eqn. for the excess Gibbs free energy stems essentially from an empirical fit to the ionic strength dependent data based over a wide sampling of binary electrolyte systems. $$C_{ca}$$, $$\lambda_{nc}$$, $$\lambda_{na}$$, $$\lambda_{nn}$$, $$\Psi_{c{c'}a}$$, $$\Psi_{a{a'}c}$$ are experimentally derived coefficients that may have pressure and/or temperature dependencies.

The $$\Phi_{c{c'}}$$ and $$\Phi_{a{a'}}$$ formulations are slightly more complicated. $$b$$ is a universal constant defined to be equal to $$1.2\ kg^{1/2}\ gmol^{-1/2}$$. The exponential coefficient $$\alpha^{(1)}_{ca}$$ is usually fixed at $$\alpha^{(1)}_{ca} = 2.0\ kg^{1/2} gmol^{-1/2}$$ except for 2-2 electrolytes, while other parameters were fit to experimental data. For 2-2 electrolytes, $$\alpha^{(1)}_{ca} = 1.4\ kg^{1/2}\ gmol^{-1/2}$$ is used in combination with either $$\alpha^{(2)}_{ca} = 12\ kg^{1/2}\ gmol^{-1/2}$$ or $$\alpha^{(2)}_{ca} = k A_\psi$$, where k is a constant. For electrolytes other than 2-2 electrolytes the $$\beta^{(2)}_{ca} g(\alpha^{(2)}_{ca} \sqrt{I})$$ term is not used in the fitting procedure; it is only used for divalent metal solfates and other high-valence electrolytes which exhibit significant association at low ionic strengths.

The $$\beta^{(0)}_{ca}$$, $$\beta^{(1)}_{ca}$$, $$\beta^{(2)}_{ca}$$, and $$C_{ca}$$ binary coefficients are referred to as ion- interaction or Pitzer parameters. These Pitzer parameters may vary with temperature and pressure but they do not depend on the ionic strength. Their values and temperature derivatives of their values have been tabulated for a range of electrolytes

The $$\Phi_{c{c'}}$$ and $$\Phi_{a{a'}}$$ contributions, which capture cation-cation and anion-anion interactions, also have an ionic strength dependence.

Ternary contributions $$\Psi_{c{c'}a}$$ and $$\Psi_{a{a'}c}$$ have been measured also for some systems. The success of the Pitzer method lies in its ability to model nonlinear activity coefficients of complex multicomponent systems with just binary and minor ternary contributions, which can be independently measured in binary or ternary subsystems.

### Multicomponent Activity Coefficients for Solutes

The formulas for activity coefficients of solutes may be obtained by taking the following derivative of the excess Gibbs Free Energy formulation described above:

$\ln(\gamma_k^\triangle) = \frac{d\left( \frac{G^{ex}}{M_o n_o RT} \right)}{d(m_k)}\Bigg|_{n_i}$

In the formulas below the following conventions are used. The subscript M refers to a particular cation. The subscript X refers to a particular anion, whose activity is being currently evaluated. the subscript a refers to a summation over all anions in the solution, while the subscript c refers to a summation over all cations in the solutions.

The activity coefficient for a particular cation M is given by

$\ln(\gamma_M^\triangle) = -z_M^2(F) + \sum_a m_a \left( 2 B_{Ma} + Z C_{Ma} \right) + z_M \left( \sum_a \sum_c m_a m_c C_{ca} \right) + \sum_c m_c \left[ 2 \Phi_{Mc} + \sum_a m_a \Psi_{Mca} \right] + \sum_{a < a'} \sum m_a m_{a'} \Psi_{Ma{a'}} + 2 \sum_n m_n \lambda_{nM}$

The activity coefficient for a particular anion X is given by

$\ln(\gamma_X^\triangle) = -z_X^2(F) + \sum_a m_c \left( 2 B_{cX} + Z C_{cX} \right) + \left|z_X \right| \left( \sum_a \sum_c m_a m_c C_{ca} \right) + \sum_a m_a \left[ 2 \Phi_{Xa} + \sum_c m_c \Psi_{cXa} \right] + \sum_{c < c'} \sum m_c m_{c'} \Psi_{c{c'}X} + 2 \sum_n m_n \lambda_{nM}$

where the function $$F$$ is given by

$F = - A_{\phi} \left[ \frac{\sqrt{I}}{1 + b \sqrt{I}} + \frac{2}{b} \ln{\left(1 + b\sqrt{I}\right)} \right] + \sum_a \sum_c m_a m_c B'_{ca} + \sum_{c < c'} \sum m_c m_{c'} \Phi'_{c{c'}} + \sum_{a < a'} \sum m_a m_{a'} \Phi'_{a{a'}}$

We have employed the definition of $$A_{\phi}$$, also used by Pitzer which is equal to

$A_{\phi} = \frac{A_{Debye}}{3}$

In the above formulas, $$\Phi'_{c{c'}}$$ and $$\Phi'_{a{a'}}$$ are the ionic strength derivatives of $$\Phi_{c{c'}}$$ and $$\Phi_{a{a'}}$$, respectively.

The function $$B'_{MX}$$ is defined as:

$B'_{MX} = \left( \frac{\beta^{(1)}_{MX} h(\alpha^{(1)}_{MX} \sqrt{I})}{I} \right) \left( \frac{\beta^{(2)}_{MX} h(\alpha^{(2)}_{MX} \sqrt{I})}{I} \right)$

where $$h(x)$$ is defined as

$h(x) = g'(x) \frac{x}{2} = \frac{2\left(1 - \left(1 + x + \frac{x^2}{2} \right)\exp(-x) \right)}{x^2}$

The activity coefficient for neutral species N is given by

$\ln(\gamma_N^\triangle) = 2 \left( \sum_i m_i \lambda_{iN}\right)$

### Activity of the Water Solvent

The activity for the solvent water, $$a_o$$, is not independent and must be determined either from the Gibbs-Duhem relation or from taking the appropriate derivative of the same excess Gibbs free energy function as was used to formulate the solvent activity coefficients. Pitzer's description follows the later approach to derive a formula for the osmotic coefficient, $$\phi$$.

$\phi - 1 = - \left( \frac{d\left(\frac{G^{ex}}{RT} \right)}{d(\tilde{M}_o n_o)} \right) \frac{1}{\sum_{i \ne 0} m_i}$

The osmotic coefficient may be related to the water activity by the following relation:

$\phi = - \frac{1}{\tilde{M}_o \sum_{i \neq o} m_i} \ln(a_o) = - \frac{n_o}{\sum_{i \neq o}n_i} \ln(a_o)$

The result is the following

$\begin{array}{ccclc} \phi - 1 &= & \frac{2}{\sum_{i \ne 0} m_i} \bigg[ & - A_{\phi} \frac{I^{3/2}}{1 + b \sqrt{I}} + \sum_c \sum_a m_c m_a \left( B^{\phi}_{ca} + Z C_{ca}\right) \\&&& + \sum_{c < c'} \sum m_c m_{c'} \left[ \Phi^{\phi}_{c{c'}} + \sum_a m_a \Psi_{c{c'}a} \right] + \sum_{a < a'} \sum m_a m_{a'} \left[ \Phi^{\phi}_{a{a'}} + \sum_c m_c \Psi_{a{a'}c} \right] \\&&& + \sum_n \sum_c m_n m_c \lambda_{nc} + \sum_n \sum_a m_n m_a \lambda_{na} + \sum_{n < n'} \sum m_n m_{n'} \lambda_{n{n'}} + \frac{1}{2} \left( \sum_n m^2_n \lambda_{nn}\right) \bigg] \end{array}$

It can be shown that the expression

$B^{\phi}_{ca} = \beta^{(0)}_{ca} + \beta^{(1)}_{ca} \exp{(- \alpha^{(1)}_{ca} \sqrt{I})} + \beta^{(2)}_{ca} \exp{(- \alpha^{(2)}_{ca} \sqrt{I} )}$

is consistent with the expression $$B_{ca}$$ in the $$G^{ex}$$ expression after carrying out the derivative wrt $$m_M$$.

Also taking into account that $${\Phi}_{c{c'}}$$ and $${\Phi}_{a{a'}}$$ has an ionic strength dependence.

$\Phi^{\phi}_{c{c'}} = {\Phi}_{c{c'}} + I \frac{d{\Phi}_{c{c'}}}{dI}$

$\Phi^{\phi}_{a{a'}} = \Phi_{a{a'}} + I \frac{d\Phi_{a{a'}}}{dI}$

### Temperature and Pressure Dependence of the Pitzer Parameters

In general most of the coefficients introduced in the previous section may have a temperature and pressure dependence. The temperature and pressure dependence of these coefficients strongly influence the value of the excess Enthalpy and excess Volumes of Pitzer solutions. Therefore, these are readily measurable quantities. HMWSoln provides several different methods for putting these dependencies into the coefficients. HMWSoln has an implementation described by Silverter and Pitzer (1977), which was used to fit experimental data for NaCl over an extensive range, below the critical temperature of water. They found a temperature functional form for fitting the 3 following coefficients that describe the Pitzer parameterization for a single salt to be adequate to describe how the excess Gibbs free energy values for the binary salt changes with respect to temperature. The following functional form was used to fit the temperature dependence of the Pitzer Coefficients for each cation - anion pair, M X.

$\beta^{(0)}_{MX} = q^{b0}_0 + q^{b0}_1 \left( T - T_r \right) + q^{b0}_2 \left( T^2 - T_r^2 \right) + q^{b0}_3 \left( \frac{1}{T} - \frac{1}{T_r}\right) + q^{b0}_4 \ln \left( \frac{T}{T_r} \right)$

$\beta^{(1)}_{MX} = q^{b1}_0 + q^{b1}_1 \left( T - T_r \right) + q^{b1}_{2} \left( T^2 - T_r^2 \right)$

$C^{\phi}_{MX} = q^{Cphi}_0 + q^{Cphi}_1 \left( T - T_r \right) + q^{Cphi}_2 \left( T^2 - T_r^2 \right) + q^{Cphi}_3 \left( \frac{1}{T} - \frac{1}{T_r}\right) + q^{Cphi}_4 \ln \left( \frac{T}{T_r} \right)$

where

$C^{\phi}_{MX} = 2 {\left| z_M z_X \right|}^{1/2} C_{MX}$

In later papers, Pitzer has added additional temperature dependencies to all of the other remaining second and third order virial coefficients. Some of these dependencies are justified and motivated by theory. Therefore, a formalism wherein all of the coefficients in the base theory have temperature dependencies associated with them has been implemented within the HMWSoln object. Much of the formalism, however, has been unexercised.

In the HMWSoln object, the temperature dependence of the Pitzer parameters are specified in the following way.

• PIZTER_TEMP_CONSTANT - string name "CONSTANT"
• Assumes that all coefficients are independent of temperature and pressure
• PIZTER_TEMP_COMPLEX1 - string name "COMPLEX" or "COMPLEX1"
• Uses the full temperature dependence for the $$\beta^{(0)}_{MX}$$ (5 coeffs), the $$\beta^{(1)}_{MX}$$ (3 coeffs), and $$C^{\phi}_{MX}$$ (5 coeffs) parameters described above.
• PITZER_TEMP_LINEAR - string name "LINEAR"
• Uses just the temperature dependence for the $$\beta^{(0)}_{MX}$$, the $$\beta^{(1)}_{MX}$$, and $$C^{\phi}_{MX}$$ coefficients described above. There are 2 coefficients for each term.

The temperature dependence is specified in an attributes field in the activityCoefficients XML block, called TempModel. Permissible values for that attribute are CONSTANT, COMPLEX1, and LINEAR.

The specification of the binary interaction between a cation and an anion is given by the coefficients, $$B_{MX}$$ and $$C_{MX}$$ The specification of $$B_{MX}$$ is a function of $$\beta^{(0)}_{MX}$$, $$\beta^{(1)}_{MX}$$, $$\beta^{(2)}_{MX}$$, $$\alpha^{(1)}_{MX}$$, and $$\alpha^{(2)}_{MX}$$. $$C_{MX}$$ is calculated from $$C^{\phi}_{MX}$$ from the formula above. All of the underlying coefficients are specified in the XML element block binarySaltParameters, which has the attribute cation and anion to identify the interaction. XML elements named beta0, beta1, beta2, Cphi, Alpha1, Alpha2 within each binarySaltParameters block specify the parameters. Within each of these blocks multiple parameters describing temperature or pressure dependence are serially listed in the order that they appear in the equation in this document. An example of the beta0 block that fits the COMPLEX1 temperature dependence given above is

<binarySaltParameters cation="Na+" anion="OH-">
<beta0> q0, q1, q2, q3, q4 </beta0>
</binarySaltParameters>

The parameters for $$\beta^{(0)}$$ fit the following equation:

$\beta^{(0)} = q_0^{{\beta}0} + q_1^{{\beta}0} \left( T - T_r \right) + q_2^{{\beta}0} \left( T^2 - T_r^2 \right) + q_3^{{\beta}0} \left( \frac{1}{T} - \frac{1}{T_r} \right) + q_4^{{\beta}0} \ln \left( \frac{T}{T_r} \right)$

This same COMPLEX1 temperature dependence given above is used for the following parameters: $$\beta^{(0)}_{MX}$$, $$\beta^{(1)}_{MX}$$, $$\beta^{(2)}_{MX}$$, $$\Theta_{cc'}$$, $$\Theta_{aa'}$$, $$\Psi_{c{c'}a}$$ and $$\Psi_{ca{a'}}$$.

### Like-Charged Binary Ion Parameters and the Mixing Parameters

The previous section contained the functions, $$\Phi_{c{c'}}$$, $$\Phi_{a{a'}}$$ and their derivatives wrt the ionic strength, $$\Phi'_{c{c'}}$$ and $$\Phi'_{a{a'}}$$. Part of these terms come from theory.

Since like charged ions repel each other and are generally not near each other, the virial coefficients for same-charged ions are small. However, Pitzer doesn't ignore these in his formulation. Relatively larger and longer range terms between like-charged ions exist however, which appear only for unsymmetrical mixing of same-sign charged ions with different charges. $$\Phi_{ij}$$, where $$ij$$ is either $$a{a'}$$ or $$c{c'}$$ is given by

${\Phi}_{ij} = \Theta_{ij} + \,^E \Theta_{ij}(I)$

$$\Theta_{ij}$$ is the small virial coefficient expansion term. Dependent in general on temperature and pressure, its ionic strength dependence is ignored in Pitzer's approach. $$\,^E\Theta_{ij}(I)$$ accounts for the electrostatic unsymmetrical mixing effects and is dependent only on the charges of the ions i, j, the total ionic strength and on the dielectric constant and density of the solvent. This seems to be a relatively well- documented part of the theory. They theory below comes from Pitzer summation (Pitzer) in the appendix. It's also mentioned in Bethke's book (Bethke), and the equations are summarized in Harvie & Weare (1980). Within the code, $$\,^E\Theta_{ij}(I)$$ is evaluated according to the algorithm described in Appendix B [Pitzer] as

$\,^E\Theta_{ij}(I) = \left( \frac{z_i z_j}{4I} \right) \left( J(x_{ij}) - \frac{1}{2} J(x_{ii}) - \frac{1}{2} J(x_{jj}) \right)$

where $$x_{ij} = 6 z_i z_j A_{\phi} \sqrt{I}$$ and

$J(x) = \frac{1}{x} \int_0^{\infty}{\left( 1 + q + \frac{1}{2} q^2 - e^q \right) y^2 dy}$

and $$q = - (\frac{x}{y}) e^{-y}$$. $$J(x)$$ is evaluated by numerical integration.

The $$\Theta_{ij}$$ term is a constant that is specified by the XML element thetaCation and thetaAnion, which has the attribute cation1, cation2 and anion1, anion2 respectively to identify the interaction. No temperature or pressure dependence of this parameter is currently allowed. An example of the block is presented below.

<thetaCation cation1="Na+" cation2="H+">
<Theta> 0.036 </Theta>
</thetaCation>

### Ternary Pitzer Parameters

The $$\Psi_{c{c'}a}$$ and $$\Psi_{ca{a'}}$$ terms represent ternary interactions between two cations and an anion and two anions and a cation, respectively. In Pitzer's implementation these terms are usually small in absolute size. Currently these parameters do not have any dependence on temperature, pressure, or ionic strength.

Their values are input using the XML element psiCommonCation and psiCommonAnion. The species id's are specified in attribute fields in the XML element. The fields cation, anion1, and anion2 are used for psiCommonCation. The fields anion, cation1 and cation2 are used for psiCommonAnion. An example block is given below. The Theta field below is a duplicate of the thetaAnion field mentioned above. The two fields are input into the same block for convenience, and because their data are highly correlated, in practice. It is an error for the two blocks to specify different information about thetaAnion (or thetaCation) in different blocks. It's ok to specify duplicate but consistent information in multiple blocks.

<psiCommonCation cation="Na+" anion1="Cl-" anion2="OH-">
<Theta> -0.05 </Theta>
<Psi> -0.006 </Psi>
</psiCommonCation>

### 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.

<lambdaNeutral species1="CO2" species2="CH4">
<lambda> 0.05 </lambda>
</lambdaNeutral>

## 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" />
<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

An example of a fixed value implementation is given below.

<activityCoefficients model="Pitzer">
<!-- A_Debye units = sqrt(kg/gmol) -->
<A_Debye> 1.172576 </A_Debye>
<!-- object description continues -->
</activityCoefficients>

An example of a variable value implementation within the HMWSoln object is given below. The model attribute, "water", triggers the full implementation.

<activityCoefficients model="Pitzer">
<!-- A_Debye units = sqrt(kg/gmol) -->
<A_Debye model="water" />
<!-- object description continues -->
</activityCoefficients>

### Temperature and Pressure Dependence of the Activity Coefficients

Temperature dependence of the activity coefficients leads to nonzero terms for the excess enthalpy and entropy of solution. This means that the partial molar enthalpies, entropies, and heat capacities are all non-trivial to compute. The following formulas are used.

The partial molar enthalpy, $$\bar s_k(T,P)$$:

$\bar h_k(T,P) = h^{\triangle}_k(T,P) - R T^2 \frac{d \ln(\gamma_k^\triangle)}{dT}$

The solvent partial molar enthalpy is equal to

$\bar h_o(T,P) = h^{o}_o(T,P) - R T^2 \frac{d \ln(a_o)}{dT} = h^{o}_o(T,P) + R T^2 (\sum_{k \neq o} m_k) \tilde{M_o} (\frac{d \phi}{dT})$

The partial molar entropy, $$\bar s_k(T,P)$$:

$\bar s_k(T,P) = s^{\triangle}_k(T,P) - R \ln( \gamma^{\triangle}_k \frac{m_k}{m^{\triangle}})) - R T \frac{d \ln(\gamma^{\triangle}_k) }{dT}$

$\bar s_o(T,P) = s^o_o(T,P) - R \ln(a_o) - R T \frac{d \ln(a_o)}{dT}$

The partial molar heat capacity, $$C_{p,k}(T,P)$$:

$\bar C_{p,k}(T,P) = C^{\triangle}_{p,k}(T,P) - 2 R T \frac{d \ln( \gamma^{\triangle}_k)}{dT} - R T^2 \frac{d^2 \ln(\gamma^{\triangle}_k) }{{dT}^2}$

$\bar C_{p,o}(T,P) = C^o_{p,o}(T,P) - 2 R T \frac{d \ln(a_o)}{dT} - R T^2 \frac{d^2 \ln(a_o)}{{dT}^2}$

The pressure dependence of the activity coefficients leads to non-zero terms for the excess Volume of the solution. Therefore, the partial molar volumes are functions of the pressure derivatives of the activity coefficients.

$\bar V_k(T,P) = V^{\triangle}_k(T,P) + R T \frac{d \ln(\gamma^{\triangle}_k) }{dP}$

$\bar V_o(T,P) = V^o_o(T,P) + R T \frac{d \ln(a_o)}{dP}$

The majority of work for these functions take place in the internal routines that calculate the first and second derivatives of the log of the activity coefficients wrt temperature, s_update_dlnMolalityActCoeff_dT(), s_update_d2lnMolalityActCoeff_dT2(), and the first derivative of the log activity coefficients wrt pressure, s_update_dlnMolalityActCoeff_dP().

## Application within Kinetics Managers

For the time being, we have set the standard concentration for all solute species in this phase equal to the default concentration of the solvent at the system temperature and pressure multiplied by Mnaught (kg solvent / gmol solvent). The solvent standard concentration is just equal to its standard state concentration.

This means that the kinetics operator essentially works on an generalized concentration basis (kmol / m3), with units for the kinetic rate constant specified as if all reactants (solvent or solute) are on a concentration basis (kmol /m3). The concentration will be modified by the activity coefficients.

For example, a bulk-phase binary reaction between liquid solute species j and k, producing a new liquid solute species l would have the following equation for its rate of progress variable, $$R^1$$, which has units of kmol m-3 s-1.

$R^1 = k^1 C_j^a C_k^a = k^1 (C^o_o \tilde{M}_o a_j) (C^o_o \tilde{M}_o a_k)$

where

$C_j^a = C^o_o \tilde{M}_o a_j \quad and \quad C_k^a = C^o_o \tilde{M}_o a_k$

$$C_j^a$$ is the activity concentration of species j, and $$C_k^a$$ is the activity concentration of species k. $$C^o_o$$ is the concentration of water at 298 K and 1 atm. $$\tilde{M}_o$$ has units of kg solvent per gmol solvent and is equal to

$\tilde{M}_o = \frac{M_o}{1000}$

$$a_j$$ is the activity of species j at the current temperature and pressure and concentration of the liquid phase is given by the molality based activity coefficient multiplied by the molality of the jth species.

$a_j = \gamma_j^\triangle m_j = \gamma_j^\triangle \frac{n_j}{\tilde{M}_o n_o}$

$$k^1$$ has units of m^3/kmol/s.

Therefore the generalized activity concentration of a solute species has the following form

$C_j^a = C^o_o \frac{\gamma_j^\triangle n_j}{n_o}$

The generalized activity concentration of the solvent has the same units, but it's a simpler form

$C_o^a = C^o_o a_o$

The reverse rate constant can then be obtained from the law of microscopic reversibility and the equilibrium expression for the system.

$\frac{a_j a_k}{ a_l} = K^{o,1} = \exp(\frac{\mu^o_l - \mu^o_j - \mu^o_k}{R T} )$

$$K^{o,1}$$ is the dimensionless form of the equilibrium constant.

$R^{-1} = k^{-1} C_l^a = k^{-1} (C_o \tilde{M}_o a_l)$

where

$k^{-1} = k^1 K^{o,1} C_o \tilde{M}_o$

$$k^{-1}$$ has units of 1/s.

Note, this treatment may be modified in the future, as events dictate.

## Instantiation of the Class

The constructor for this phase is now located in the default ThermoFactory for Cantera. The following code snippet may be used to initialize the phase using the default construction technique within Cantera.

ThermoPhase *HMW = newPhase("HMW_NaCl.xml", "NaCl_electrolyte");

A new HMWSoln object may be created by the following code snippets:

HMWSoln *HMW = new HMWSoln("HMW_NaCl.xml", "NaCl_electrolyte");

or

XML_Node *xm = get_XML_NameID("phase", "HMW_NaCl.xml#NaCl_electrolyte", 0);
HMWSoln *dh = new HMWSoln(*xm);

or by the following call to importPhase():

XML_Node *xm = get_XML_NameID("phase", "HMW_NaCl.xml#NaCl_electrolyte", 0);
HMWSoln dhphase;
importPhase(*xm, &dhphase);

## 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" />
<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>

Definition at line 1145 of file HMWSoln.h.

## ◆ HMWSoln() [1/3]

 HMWSoln ( )

Default Constructor.

Definition at line 27 of file HMWSoln.cpp.

Referenced by HMWSoln::duplMyselfAsThermoPhase().

## ◆ HMWSoln() [2/3]

 HMWSoln ( const std::string & inputFile, const std::string & id = "" )

Construct and initialize an HMWSoln ThermoPhase object directly from an ASCII input file.

This constructor is a shell that calls the routine initThermo(), with a reference to the XML database to get the info for the phase.

Parameters
 inputFile Name of the input file containing the phase XML data to set up the object id ID of the phase in the input file. Defaults to the empty string.

Definition at line 72 of file HMWSoln.cpp.

## ◆ HMWSoln() [3/3]

 HMWSoln ( XML_Node & phaseRef, const std::string & id = "" )

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 118 of file HMWSoln.cpp.

## ◆ duplMyselfAsThermoPhase()

 ThermoPhase * duplMyselfAsThermoPhase ( ) const
virtual

Duplication routine for objects which inherit from ThermoPhase.

This virtual routine can be used to duplicate ThermoPhase objects inherited from ThermoPhase even if the application only has a pointer to ThermoPhase to work with.

These routines are basically wrappers around the derived copy constructor.

Deprecated:
To be removed after Cantera 2.3 for all classes derived from ThermoPhase.

Reimplemented from MolalityVPSSTP.

Definition at line 367 of file HMWSoln.cpp.

References HMWSoln::HMWSoln().

## ◆ constructPhaseFile()

 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 911 of file HMWSoln_input.cpp.

References Cantera::warn_deprecated().

## ◆ constructPhaseXML()

 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.
Deprecated:
Use importPhase() instead. To be removed after Cantera 2.3.

Definition at line 919 of file HMWSoln_input.cpp.

References Cantera::importPhase(), and Cantera::warn_deprecated().

## ◆ eosType()

 int eosType ( ) const
virtual

Equation of state type flag.

The base class returns zero. Subclasses should define this to return a unique non-zero value. Constants defined for this purpose are listed in mix_defs.h.

Deprecated:
To be removed after Cantera 2.3. Use type() instead.

Reimplemented from ThermoPhase.

Definition at line 372 of file HMWSoln.cpp.

References Cantera::cHMWSoln0, HMWSoln::m_formGC, and Cantera::warn_deprecated().

## ◆ type()

 virtual std::string type ( ) const
inlinevirtual

String indicating the thermodynamic model implemented.

Usually corresponds to the name of the derived class, less any suffixes such as "Phase", TP", "VPSS", etc.

Reimplemented from ThermoPhase.

Definition at line 1218 of file HMWSoln.h.

## ◆ enthalpy_mole()

 doublereal enthalpy_mole ( ) const
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 395 of file HMWSoln.cpp.

References HMWSoln::getPartialMolarEnthalpies(), HMWSoln::m_tmpV, and Phase::mean_X().

## ◆ relative_enthalpy()

 doublereal relative_enthalpy ( ) const
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 401 of file HMWSoln.cpp.

Referenced by HMWSoln::relative_molal_enthalpy().

## ◆ relative_molal_enthalpy()

 doublereal relative_molal_enthalpy ( ) const
virtual

Excess molar enthalpy of the solution from the mixing process on a molality basis.

Note this is kmol of the guessed at salt composition

Definition at line 413 of file HMWSoln.cpp.

## ◆ entropy_mole()

 doublereal entropy_mole ( ) const
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.

MultiSpeciesThermo
 (HKM -> Bump up to Parent object)

Reimplemented from ThermoPhase.

Definition at line 453 of file HMWSoln.cpp.

References HMWSoln::getPartialMolarEntropies(), HMWSoln::m_tmpV, and Phase::mean_X().

## ◆ gibbs_mole()

 doublereal gibbs_mole ( ) const
virtual

Molar Gibbs function. Units: J/kmol.

(HKM -> Bump up to Parent object)

Reimplemented from ThermoPhase.

Definition at line 459 of file HMWSoln.cpp.

References HMWSoln::getChemPotentials(), HMWSoln::m_tmpV, and Phase::mean_X().

## ◆ cp_mole()

 doublereal cp_mole ( ) const
virtual

Molar heat capacity at constant pressure. Units: J/kmol/K.

Reimplemented from ThermoPhase.

Definition at line 465 of file HMWSoln.cpp.

References HMWSoln::getPartialMolarCp(), HMWSoln::m_tmpV, and Phase::mean_X().

## ◆ cv_mole()

 doublereal cv_mole ( ) const
virtual

Molar heat capacity at constant volume. Units: J/kmol/K.

(HKM -> Bump up to Parent object)

Reimplemented from ThermoPhase.

Definition at line 471 of file HMWSoln.cpp.

References ThermoPhase::isothermalCompressibility().

## ◆ calcDensity()

 void calcDensity ( )
protectedvirtual

Calculate the density of the mixture using the partial molar volumes and mole fractions as input.

In this equation of state implementation, the density is a function only of the mole fractions. Therefore, it can't be an independent variable. Instead, the pressure is used as the independent variable. Functions which try to set the thermodynamic state by calling setDensity() may cause an exception to be thrown.The formula for this is

$\rho = \frac{\sum_k{X_k W_k}}{\sum_k{X_k V_k}}$

where $$X_k$$ are the mole fractions, $$W_k$$ are the molecular weights, and $$V_k$$ are the pure species molar volumes.

Note, the basis behind this formula is that in an ideal solution the partial molar volumes are equal to the pure species molar volumes. We have additionally specified in this class that the pure species molar volumes are independent of temperature and pressure.

NOTE: This is a non-virtual function, which is not a member of the ThermoPhase base class.

Reimplemented from VPStandardStateTP.

Definition at line 483 of file HMWSoln.cpp.

## ◆ setDensity()

 void setDensity ( const doublereal rho )
virtual

Set the internally stored density (kg/m^3) of the phase.

Overridden setDensity() function is necessary because the density is not an independent variable.

This function will now throw an error condition.

Note, in general, setting the phase density is now a nonlinear calculation. P and T are the fundamental variables. This routine should be revamped to do the nonlinear problem.

Todo:

May have to adjust the strategy here to make the eos for these materials slightly compressible, in order to create a condition where the density is a function of the pressure.

Now have a compressible ss equation for liquid water. Therefore, this phase is compressible. May still want to change the independent variable however.

Parameters
 rho Input density (kg/m^3).

Reimplemented from Phase.

Definition at line 502 of file HMWSoln.cpp.

References Phase::density().

## ◆ setMolarDensity()

 void setMolarDensity ( const doublereal conc )
virtual

Set the internally stored molar density (kmol/m^3) for the phase.

Overridden setMolarDensity() function is necessary because of the underlying water model.

This function will now throw an error condition if the input isn't exactly equal to the current molar density.

Parameters
 conc Input molar density (kmol/m^3).

Reimplemented from Phase.

Definition at line 511 of file HMWSoln.cpp.

## ◆ getActivityConcentrations()

 void getActivityConcentrations ( doublereal * c ) const
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 519 of file HMWSoln.cpp.

## ◆ standardConcentration()

 doublereal standardConcentration ( size_t k = 0 ) const
virtual

Return the standard concentration for the kth species.

The standard concentration $$C^0_k$$ used to normalize the activity (i.e., generalized) concentration for use

We have set the standard concentration for all solute species in this phase equal to the default concentration of the solvent at the system temperature and pressure multiplied by Mnaught (kg solvent / gmol solvent). The solvent standard concentration is just equal to its standard state concentration.

$C_j^0 = C^o_o \tilde{M}_o \quad and C_o^0 = C^o_o$

The consequence of this is that the standard concentrations have unequal units between the solvent and the solute. However, both the solvent and the solute activity concentrations will have the same units of kmol/kg^3.

This means that the kinetics operator essentially works on an generalized concentration basis (kmol / m3), with units for the kinetic rate constant specified as if all reactants (solvent or solute) are on a concentration basis (kmol /m3). The concentration will be modified by the activity coefficients.

For example, a bulk-phase binary reaction between liquid solute species j and k, producing a new liquid solute species l would have the following equation for its rate of progress variable, $$R^1$$, which has units of kmol m-3 s-1.

$R^1 = k^1 C_j^a C_k^a = k^1 (C^o_o \tilde{M}_o a_j) (C^o_o \tilde{M}_o a_k)$

where

$C_j^a = C^o_o \tilde{M}_o a_j \quad and \quad C_k^a = C^o_o \tilde{M}_o a_k$

$$C_j^a$$ is the activity concentration of species j, and $$C_k^a$$ is the activity concentration of species k. $$C^o_o$$ is the concentration of water at 298 K and 1 atm. $$\tilde{M}_o$$ has units of kg solvent per gmol solvent and is equal to

$\tilde{M}_o = \frac{M_o}{1000}$

$$a_j$$ is the activity of species j at the current temperature and pressure and concentration of the liquid phase is given by the molality based activity coefficient multiplied by the molality of the jth species.

$a_j = \gamma_j^\triangle m_j = \gamma_j^\triangle \frac{n_j}{\tilde{M}_o n_o}$

$$k^1$$ has units of m^3/kmol/s.

Therefore the generalized activity concentration of a solute species has the following form

$C_j^a = C^o_o \frac{\gamma_j^\triangle n_j}{n_o}$

The generalized activity concentration of the solvent has the same units, but it's a simpler form

$C_o^a = C^o_o a_o$

Parameters
 k Optional parameter indicating the species. The default is to assume this refers to species 0.
Returns
the standard Concentration in units of m^3/kmol.
Parameters
 k Species index

Reimplemented from MolalityVPSSTP.

Definition at line 532 of file HMWSoln.cpp.

## ◆ getActivities()

 void getActivities ( doublereal * ac ) const
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 542 of file HMWSoln.cpp.

## ◆ getChemPotentials()

 void getChemPotentials ( doublereal * mu ) const
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 574 of file HMWSoln.cpp.

Referenced by HMWSoln::gibbs_mole().

## ◆ getPartialMolarEnthalpies()

 void getPartialMolarEnthalpies ( doublereal * hbar ) const
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 597 of file HMWSoln.cpp.

Referenced by HMWSoln::enthalpy_mole(), and HMWSoln::relative_enthalpy().

## ◆ getPartialMolarEntropies()

 void getPartialMolarEntropies ( doublereal * sbar ) const
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 616 of file HMWSoln.cpp.

Referenced by HMWSoln::entropy_mole().

## ◆ getPartialMolarVolumes()

 void getPartialMolarVolumes ( doublereal * vbar ) const
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 653 of file HMWSoln.cpp.

Referenced by HMWSoln::calcDensity().

## ◆ getPartialMolarCp()

 void getPartialMolarCp ( doublereal * cpbar ) const
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 666 of file HMWSoln.cpp.

Referenced by HMWSoln::cp_mole().

## ◆ satPressure()

 doublereal satPressure ( doublereal T )
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 686 of file HMWSoln.cpp.

## ◆ initThermo()

 void initThermo ( )
virtual

The following methods are used in the process of constructing the phase and setting its parameters from a specification in an input file. They are not normally used in application programs. To see how they are used, see importPhase().

Reimplemented from MolalityVPSSTP.

Definition at line 901 of file HMWSoln_input.cpp.

## ◆ initThermoXML()

 void initThermoXML ( XML_Node & phaseNode, const std::string & id )
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 926 of file HMWSoln_input.cpp.

## ◆ A_Debye_TP()

 double A_Debye_TP ( double temperature = -1.0, double pressure = -1.0 ) const
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 696 of file HMWSoln.cpp.

Referenced by HMWSoln::getUnscaledMolalityActivityCoefficients().

## ◆ dA_DebyedT_TP()

 double dA_DebyedT_TP ( double temperature = -1.0, double pressure = -1.0 ) const
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 728 of file HMWSoln.cpp.

## ◆ dA_DebyedP_TP()

 double dA_DebyedP_TP ( double temperature = -1.0, double pressure = -1.0 ) const
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 752 of file HMWSoln.cpp.

 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 784 of file HMWSoln.cpp.

References HMWSoln::dA_DebyedT_TP().

 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 806 of file HMWSoln.cpp.

 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 795 of file HMWSoln.cpp.

References HMWSoln::dA_DebyedP_TP().

## ◆ d2A_DebyedT2_TP()

 double d2A_DebyedT2_TP ( double temperature = -1.0, double pressure = -1.0 ) const
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 818 of file HMWSoln.cpp.

Referenced by HMWSoln::s_NBS_CLM_d2lnMolalityActCoeff_dT2().

 double AionicRadius ( int k = 0 ) const

Reports the ionic radius of the kth species.

Parameters
 k Species index

Definition at line 844 of file HMWSoln.cpp.

References HMWSoln::m_Aionic.

## ◆ formPitzer()

 int formPitzer ( ) const
inline

Returns the form of the Pitzer parameterization used

Definition at line 1765 of file HMWSoln.h.

References HMWSoln::m_formPitzer.

## ◆ printCoeffs()

 void printCoeffs ( ) const

Print out all of the input Pitzer coefficients.

Definition at line 4155 of file HMWSoln.cpp.

## ◆ getUnscaledMolalityActivityCoefficients()

 void getUnscaledMolalityActivityCoefficients ( doublereal * acMolality ) const
virtual

Get the array of unscaled non-dimensional molality based activity coefficients at the current solution temperature, pressure, and solution concentration.

See Denbigh p. 278 for a thorough discussion. This class must be overridden in classes which derive from MolalityVPSSTP. This function takes over from the molar-based activity coefficient calculation, getActivityCoefficients(), in derived classes.

Parameters
 acMolality Output vector containing the molality based activity coefficients. length: m_kk.

Reimplemented from MolalityVPSSTP.

Definition at line 561 of file HMWSoln.cpp.

private

Apply the current phScale to a set of activity Coefficients.

See the Eq3/6 Manual for a thorough discussion.

Definition at line 4213 of file HMWSoln.cpp.

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 4228 of file HMWSoln.cpp.

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 4243 of file HMWSoln.cpp.

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 4258 of file HMWSoln.cpp.

Referenced by HMWSoln::s_update_dlnMolalityActCoeff_dP().

## ◆ s_NBS_CLM_lnMolalityActCoeff()

 doublereal s_NBS_CLM_lnMolalityActCoeff ( ) const
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 4273 of file HMWSoln.cpp.

References HMWSoln::m_IionicMolality.

## ◆ s_NBS_CLM_dlnMolalityActCoeff_dT()

 doublereal s_NBS_CLM_dlnMolalityActCoeff_dT ( ) const
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 4281 of file HMWSoln.cpp.

References HMWSoln::dA_DebyedT_TP(), and HMWSoln::m_IionicMolality.

## ◆ s_NBS_CLM_d2lnMolalityActCoeff_dT2()

 doublereal s_NBS_CLM_d2lnMolalityActCoeff_dT2 ( ) const
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 4288 of file HMWSoln.cpp.

References HMWSoln::d2A_DebyedT2_TP(), and HMWSoln::m_IionicMolality.

## ◆ s_NBS_CLM_dlnMolalityActCoeff_dP()

 doublereal s_NBS_CLM_dlnMolalityActCoeff_dP ( ) const
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 4295 of file HMWSoln.cpp.

References HMWSoln::dA_DebyedP_TP(), and HMWSoln::m_IionicMolality.

## ◆ initLengths()

 void initLengths ( )
private

Initialize all of the species-dependent lengths in the object.

Definition at line 851 of file HMWSoln.cpp.

## ◆ applyphScale()

 void applyphScale ( doublereal * acMolality ) const
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 4199 of file HMWSoln.cpp.

## ◆ s_update_dlnMolalityActCoeff_dT()

 void s_update_dlnMolalityActCoeff_dT ( ) const
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 2153 of file HMWSoln.cpp.

## ◆ s_update_d2lnMolalityActCoeff_dT2()

 void s_update_d2lnMolalityActCoeff_dT2 ( ) const
private

This function calculates the temperature second derivative of the natural logarithm of the molality activity coefficients.

Definition at line 2767 of file HMWSoln.cpp.

Referenced by HMWSoln::getPartialMolarCp().

## ◆ s_update_dlnMolalityActCoeff_dP()

 void s_update_dlnMolalityActCoeff_dP ( ) const
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 3373 of file HMWSoln.cpp.

Referenced by HMWSoln::getPartialMolarVolumes().

## ◆ s_updateIMS_lnMolalityActCoeff()

 void s_updateIMS_lnMolalityActCoeff ( ) const
private

This function will be called to update the internally stored natural logarithm of the molality activity coefficients.

Definition at line 4053 of file HMWSoln.cpp.

## ◆ s_updatePitzer_lnMolalityActCoeff()

 void s_updatePitzer_lnMolalityActCoeff ( ) const
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 1457 of file HMWSoln.cpp.

## ◆ s_updatePitzer_dlnMolalityActCoeff_dT()

 void s_updatePitzer_dlnMolalityActCoeff_dT ( ) const
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 2181 of file HMWSoln.cpp.

Referenced by HMWSoln::s_update_dlnMolalityActCoeff_dT().

## ◆ s_updatePitzer_d2lnMolalityActCoeff_dT2()

 void s_updatePitzer_d2lnMolalityActCoeff_dT2 ( ) const
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 2795 of file HMWSoln.cpp.

Referenced by HMWSoln::s_update_d2lnMolalityActCoeff_dT2().

## ◆ s_updatePitzer_dlnMolalityActCoeff_dP()

 void s_updatePitzer_dlnMolalityActCoeff_dP ( ) const
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 3397 of file HMWSoln.cpp.

Referenced by HMWSoln::s_update_dlnMolalityActCoeff_dP().

## ◆ s_updatePitzer_CoeffWRTemp()

 void s_updatePitzer_CoeffWRTemp ( int doDerivs = 2 ) const
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 1211 of file HMWSoln.cpp.

Referenced by HMWSoln::printCoeffs().

## ◆ calc_lambdas()

 void calc_lambdas ( double is ) const
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 3976 of file HMWSoln.cpp.

References HMWSoln::m_debugCalc, and Cantera::writelogf().

## ◆ calc_thetas()

 void calc_thetas ( int z1, int z2, double * etheta, double * etheta_prime ) const
private

Calculate etheta and etheta_prime.

This interaction accounts for the mixing effects of like-signed ions with different charges. This interaction will be nonzero for species with the same charge. this routine is not to be called for neutral species; it core dumps or error exits.

MEC implementation routine.

Parameters
 z1 charge of the first molecule z2 charge of the second molecule etheta return pointer containing etheta etheta_prime Return pointer containing etheta_prime.

This routine uses the internal variables, elambda[] and elambda1[].

Definition at line 4027 of file HMWSoln.cpp.

References AssertThrowMsg, HMWSoln::elambda, and HMWSoln::elambda1.

## ◆ counterIJ_setup()

 void counterIJ_setup ( ) const
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 1188 of file HMWSoln.cpp.

References HMWSoln::m_CounterIJ, and Phase::m_kk.

## ◆ calcMolalitiesCropped()

 void calcMolalitiesCropped ( ) const
private

Calculate the cropped molalities.

This is an internal routine that calculates values of m_molalitiesCropped from m_molalities

Definition at line 1047 of file HMWSoln.cpp.

 void readXMLBinarySalt ( XML_Node & BinSalt )
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 49 of file HMWSoln_input.cpp.

 void readXMLThetaAnion ( XML_Node & BinSalt )
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 235 of file HMWSoln_input.cpp.

 void readXMLThetaCation ( XML_Node & BinSalt )
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 311 of file HMWSoln_input.cpp.

 void readXMLPsiCommonAnion ( XML_Node & BinSalt )
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 518 of file HMWSoln_input.cpp.

 void readXMLPsiCommonCation ( XML_Node & BinSalt )
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 387 of file HMWSoln_input.cpp.

 void readXMLLambdaNeutral ( XML_Node & BinSalt )
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 648 of file HMWSoln_input.cpp.

 void readXMLMunnnNeutral ( XML_Node & BinSalt )
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 722 of file HMWSoln_input.cpp.

 void readXMLZetaCation ( const XML_Node & BinSalt )
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 783 of file HMWSoln_input.cpp.

 void readXMLCroppingCoefficients ( const XML_Node & acNode )
private

Process an XML node called "croppingCoefficients" for the cropping coefficients values.

Parameters
 acNode Activity Coefficient XML Node

Definition at line 876 of file HMWSoln_input.cpp.

References XML_Node::child(), Cantera::getOptionalFloat(), and XML_Node::hasChild().

## ◆ calcIMSCutoffParams_()

 void calcIMSCutoffParams_ ( )
private

Precalculate the IMS Cutoff parameters for typeCutoff = 2.

Definition at line 1364 of file HMWSoln_input.cpp.

## ◆ calcMCCutoffParams_()

 void calcMCCutoffParams_ ( )
private

Calculate molality cut-off parameters.

Definition at line 1413 of file HMWSoln_input.cpp.

## ◆ interp_est()

 int interp_est ( const std::string & estString )
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 27 of file HMWSoln_input.cpp.

References Cantera::cEST_solvent.

## ◆ debugPrinting()

 int debugPrinting ( )

Return int specifying the amount of debug printing.

Definition at line 4302 of file HMWSoln.cpp.

References HMWSoln::m_debugCalc.

## ◆ m_formPitzer

 int m_formPitzer
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 1850 of file HMWSoln.h.

Referenced by HMWSoln::formPitzer().

## ◆ m_formPitzerTemp

 int m_formPitzerTemp
private

This is the form of the temperature dependence of Pitzer parameterization used in the model.

PITZER_TEMP_CONSTANT 0 PITZER_TEMP_LINEAR 1 PITZER_TEMP_COMPLEX1 2

Definition at line 1860 of file HMWSoln.h.

Referenced by HMWSoln::initLengths().

## ◆ m_formGC

 int m_formGC
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 1890 of file HMWSoln.h.

Referenced by HMWSoln::eosType().

## ◆ m_electrolyteSpeciesType

 vector_int m_electrolyteSpeciesType
private

Vector containing the electrolyte species type.

The possible types are:

• solvent
• Charged Species
• weakAcidAssociated
• strongAcidAssociated
• polarNeutral
• nonpolarNeutral

Definition at line 1902 of file HMWSoln.h.

Referenced by HMWSoln::initLengths().

## ◆ m_Aionic

 vector_fp m_Aionic
private

a_k = Size of the ionic species in the DH formulation. units = meters

Definition at line 1905 of file HMWSoln.h.

## ◆ m_IionicMolality

 double m_IionicMolality
mutableprivate

Current value of the ionic strength on the molality scale Associated Salts, if present in the mechanism, don't contribute to the value of the ionic strength in this version of the Ionic strength.

Definition at line 1910 of file HMWSoln.h.

## ◆ m_maxIionicStrength

 double m_maxIionicStrength
private

Maximum value of the ionic strength allowed in the calculation of the activity coefficients.

Definition at line 1914 of file HMWSoln.h.

Referenced by HMWSoln::calcMolalitiesCropped().

## ◆ m_TempPitzerRef

 double m_TempPitzerRef
private

Reference Temperature for the Pitzer formulations.

Definition at line 1917 of file HMWSoln.h.

## ◆ m_IionicMolalityStoich

 double m_IionicMolalityStoich
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 1922 of file HMWSoln.h.

## ◆ m_form_A_Debye

 int m_form_A_Debye

Form of the constant outside the Debye-Huckel term called A.

It's normally a function of temperature and pressure. However, it can be set from the input file in order to aid in numerical comparisons. Acceptable forms:

  A_DEBYE_CONST  0
A_DEBYE_WATER  1


The A_DEBYE_WATER form may be used for water solvents with needs to cover varying temperatures and pressures. Note, the dielectric constant of water is a relatively strong function of T, and its variability must be accounted for,

Definition at line 1939 of file HMWSoln.h.

## ◆ m_A_Debye

 double m_A_Debye
mutableprivate

A_Debye: this expression appears on the top of the ln actCoeff term in the general Debye-Huckel expression It depends on temperature.

And, therefore, most be recalculated whenever T or P changes. This variable is a local copy of the calculation.

A_Debye = (F e B_Debye) / (8 Pi epsilon R T)

 where B_Debye = F / sqrt(epsilon R T/2)
(dw/1000)^(1/2)


A_Debye = (1/ (8 Pi)) (2 Na * dw/1000)^(1/2) (e * e / (epsilon * kb * T))^(3/2)

Units = sqrt(kg/gmol)

Nominal value = 1.172576 sqrt(kg/gmol) based on: epsilon/epsilon_0 = 78.54 (water at 25C) epsilon_0 = 8.854187817E-12 C2 N-1 m-2 e = 1.60217653 E-19 C F = 9.6485309E7 C kmol-1 R = 8.314472E3 kg m2 s-2 kmol-1 K-1 T = 298.15 K B_Debye = 3.28640E9 sqrt(kg/gmol)/m dw = C_0 * M_0 (density of water) (kg/m3) = 1.0E3 at 25C

Definition at line 1971 of file HMWSoln.h.

private

Water standard state calculator.

derived from the equation of state for water.

Definition at line 1977 of file HMWSoln.h.

Referenced by HMWSoln::calcDensity(), and HMWSoln::satPressure().

private

density of standard-state water

internal temporary variable

Definition at line 1983 of file HMWSoln.h.

Referenced by HMWSoln::calcDensity().

## ◆ m_waterProps

 std::unique_ptr m_waterProps
private

Pointer to the water property calculator.

Definition at line 1986 of file HMWSoln.h.

## ◆ m_tmpV

 vector_fp m_tmpV
mutableprivate

vector of size m_kk, used as a temporary holding area.

Definition at line 1989 of file HMWSoln.h.

## ◆ m_speciesCharge_Stoich

 vector_fp m_speciesCharge_Stoich
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 2004 of file HMWSoln.h.

Referenced by HMWSoln::initLengths().

## ◆ m_Beta0MX_ij

 vector_fp m_Beta0MX_ij
mutableprivate

Array of 2D data used in the Pitzer/HMW formulation.

Beta0_ij[i][j] is the value of the Beta0 coefficient for the ij salt. It will be nonzero iff i and j are both charged and have opposite sign. The array is also symmetric. counterIJ where counterIJ = m_counterIJ[i][j] is used to access this array.

Definition at line 2013 of file HMWSoln.h.

Referenced by HMWSoln::printCoeffs().

## ◆ m_Beta0MX_ij_L

 vector_fp m_Beta0MX_ij_L
mutableprivate

Derivative of Beta0_ij[i][j] wrt T. Vector index is counterIJ.

Definition at line 2016 of file HMWSoln.h.

## ◆ m_Beta0MX_ij_LL

 vector_fp m_Beta0MX_ij_LL
mutableprivate

Derivative of Beta0_ij[i][j] wrt TT. Vector index is counterIJ.

Definition at line 2019 of file HMWSoln.h.

## ◆ m_Beta0MX_ij_P

 vector_fp m_Beta0MX_ij_P
mutableprivate

Derivative of Beta0_ij[i][j] wrt P. Vector index is counterIJ.

Definition at line 2022 of file HMWSoln.h.

## ◆ m_Beta0MX_ij_coeff

 Array2D m_Beta0MX_ij_coeff
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 2030 of file HMWSoln.h.

## ◆ m_Beta1MX_ij

 vector_fp m_Beta1MX_ij
mutableprivate

Array of 2D data used in the Pitzer/HMW formulation.

Beta1_ij[i][j] is the value of the Beta1 coefficient for the ij salt. It will be nonzero iff i and j are both charged and have opposite sign. The array is also symmetric. counterIJ where counterIJ = m_counterIJ[i][j] is used to access this array.

Definition at line 2037 of file HMWSoln.h.

Referenced by HMWSoln::printCoeffs().

## ◆ m_Beta1MX_ij_L

 vector_fp m_Beta1MX_ij_L
mutableprivate

Derivative of Beta1_ij[i][j] wrt T. Vector index is counterIJ.

Definition at line 2040 of file HMWSoln.h.

## ◆ m_Beta1MX_ij_LL

 vector_fp m_Beta1MX_ij_LL
mutableprivate

Derivative of Beta1_ij[i][j] wrt TT. Vector index is counterIJ.

Definition at line 2043 of file HMWSoln.h.

## ◆ m_Beta1MX_ij_P

 vector_fp m_Beta1MX_ij_P
mutableprivate

Derivative of Beta1_ij[i][j] wrt P. Vector index is counterIJ.

Definition at line 2046 of file HMWSoln.h.

## ◆ m_Beta1MX_ij_coeff

 Array2D m_Beta1MX_ij_coeff
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 2054 of file HMWSoln.h.

## ◆ m_Beta2MX_ij

 vector_fp m_Beta2MX_ij
mutableprivate

Array of 2D data used in the Pitzer/HMW formulation.

Beta2_ij[i][j] is the value of the Beta2 coefficient for the ij salt. It will be nonzero iff i and j are both charged and have opposite sign, and i and j both have charges of 2 or more. The array is also symmetric. counterIJ where counterIJ = m_counterIJ[i][j] is used to access this array.

Definition at line 2061 of file HMWSoln.h.

Referenced by HMWSoln::printCoeffs().

## ◆ m_Beta2MX_ij_L

 vector_fp m_Beta2MX_ij_L
mutableprivate

Derivative of Beta2_ij[i][j] wrt T. Vector index is counterIJ.

Definition at line 2064 of file HMWSoln.h.

## ◆ m_Beta2MX_ij_LL

 vector_fp m_Beta2MX_ij_LL
mutableprivate

Derivative of Beta2_ij[i][j] wrt TT. Vector index is counterIJ.

Definition at line 2067 of file HMWSoln.h.

## ◆ m_Beta2MX_ij_P

 vector_fp m_Beta2MX_ij_P
mutableprivate

Derivative of Beta2_ij[i][j] wrt P. Vector index is counterIJ.

Definition at line 2070 of file HMWSoln.h.

## ◆ m_Beta2MX_ij_coeff

 Array2D m_Beta2MX_ij_coeff
mutableprivate

Array of coefficients for Beta2, a variable in Pitzer's papers.

column index is counterIJ. m_Beta2MX_ij_coeff.ptrColumn(counterIJ) is a double* containing the vector of coefficients for the counterIJ interaction. This was added for the YMP database version of the code since it contains temperature-dependent parameters for some 2-2 electrolytes.

Definition at line 2080 of file HMWSoln.h.

## ◆ m_Alpha2MX_ij

 vector_fp m_Alpha2MX_ij
private

Array of 2D data used in the Pitzer/HMW formulation.

Alpha2MX_ij[i][j] is the value of the alpha2 coefficient for the ij interaction. It will be nonzero iff i and j are both charged and have opposite sign, and i and j both have charges of 2 or more, usually. It is symmetric wrt i, j. counterIJ, where counterIJ = m_counterIJ[i][j], is used to access this array.

Definition at line 2095 of file HMWSoln.h.

## ◆ m_CphiMX_ij

 vector_fp m_CphiMX_ij
mutableprivate

Array of 2D data used in the Pitzer/HMW formulation.

CphiMX_ij[i][j] is the value of the Cphi coefficient for the ij interaction. It will be nonzero iff i and j are both charged and have opposite sign, and i and j both have charges of 2 or more. The array is also symmetric. counterIJ where counterIJ = m_counterIJ[i][j] is used to access this array.

Definition at line 2102 of file HMWSoln.h.

Referenced by HMWSoln::printCoeffs().

## ◆ m_CphiMX_ij_L

 vector_fp m_CphiMX_ij_L
mutableprivate

Derivative of Cphi_ij[i][j] wrt T. Vector index is counterIJ.

Definition at line 2105 of file HMWSoln.h.

## ◆ m_CphiMX_ij_LL

 vector_fp m_CphiMX_ij_LL
mutableprivate

Derivative of Cphi_ij[i][j] wrt TT. Vector index is counterIJ.

Definition at line 2108 of file HMWSoln.h.

## ◆ m_CphiMX_ij_P

 vector_fp m_CphiMX_ij_P
mutableprivate

Derivative of Cphi_ij[i][j] wrt P. Vector index is counterIJ.

Definition at line 2111 of file HMWSoln.h.

## ◆ m_CphiMX_ij_coeff

 Array2D m_CphiMX_ij_coeff
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 2120 of file HMWSoln.h.

## ◆ m_Theta_ij

 vector_fp m_Theta_ij
mutableprivate

Array of 2D data for Theta_ij[i][j] in the Pitzer/HMW formulation.

Array of 2D data used in the Pitzer/HMW formulation. Theta_ij[i][j] is the value of the theta coefficient for the ij interaction. It will be nonzero for charged ions with the same sign. It is symmetric. counterIJ where counterIJ = m_counterIJ[i][j] is used to access this array.

HKM Recent Pitzer papers have used a functional form for Theta_ij, which depends on the ionic strength.

Definition at line 2132 of file HMWSoln.h.

Referenced by HMWSoln::printCoeffs().

## ◆ m_Theta_ij_L

 vector_fp m_Theta_ij_L
mutableprivate

Derivative of Theta_ij[i][j] wrt T. Vector index is counterIJ.

Definition at line 2135 of file HMWSoln.h.

## ◆ m_Theta_ij_LL

 vector_fp m_Theta_ij_LL
mutableprivate

Derivative of Theta_ij[i][j] wrt TT. Vector index is counterIJ.

Definition at line 2138 of file HMWSoln.h.

## ◆ m_Theta_ij_P

 vector_fp m_Theta_ij_P
mutableprivate

Derivative of Theta_ij[i][j] wrt P. Vector index is counterIJ.

Definition at line 2141 of file HMWSoln.h.

## ◆ m_Theta_ij_coeff

 Array2D m_Theta_ij_coeff
private

Array of coefficients for Theta_ij[i][j] in the Pitzer/HMW formulation.

Theta_ij[i][j] is the value of the theta coefficient for the ij interaction. It will be nonzero for charged ions with the same sign. It is symmetric. Column index is counterIJ. counterIJ where counterIJ = m_counterIJ[i][j] is used to access this array.

m_Theta_ij_coeff.ptrColumn(counterIJ) is a double* containing the vector of coefficients for the counterIJ interaction.

Definition at line 2153 of file HMWSoln.h.

## ◆ m_Psi_ijk

 vector_fp m_Psi_ijk
mutableprivate

Array of 3D data used in the Pitzer/HMW formulation.

Psi_ijk[n] is the value of the psi coefficient for the ijk interaction where

n = k + j * m_kk + i * m_kk * m_kk;

It is potentially nonzero everywhere. The first two coordinates are symmetric wrt cations, and the last two coordinates are symmetric wrt anions.

Definition at line 2166 of file HMWSoln.h.

Referenced by HMWSoln::printCoeffs().

## ◆ m_Psi_ijk_L

 vector_fp m_Psi_ijk_L
mutableprivate

Derivative of Psi_ijk[n] wrt T.

See m_Psi_ijk for reference on the indexing into this variable.

Definition at line 2170 of file HMWSoln.h.

## ◆ m_Psi_ijk_LL

 vector_fp m_Psi_ijk_LL
mutableprivate

Derivative of Psi_ijk[n] wrt TT.

See m_Psi_ijk for reference on the indexing into this variable.

Definition at line 2174 of file HMWSoln.h.

## ◆ m_Psi_ijk_P

 vector_fp m_Psi_ijk_P
mutableprivate

Derivative of Psi_ijk[n] wrt P.

See m_Psi_ijk for reference on the indexing into this variable.

Definition at line 2178 of file HMWSoln.h.

## ◆ m_Psi_ijk_coeff

 Array2D m_Psi_ijk_coeff
private

Array of coefficients for Psi_ijk[n] in the Pitzer/HMW formulation.

Psi_ijk[n] is the value of the psi coefficient for the ijk interaction where

n = k + j * m_kk + i * m_kk * m_kk;

It is potentially nonzero everywhere. The first two coordinates are symmetric wrt cations, and the last two coordinates are symmetric wrt anions.

m_Psi_ijk_coeff.ptrColumn(n) is a double* containing the vector of coefficients for the n interaction.

Definition at line 2194 of file HMWSoln.h.

## ◆ m_Lambda_nj

 Array2D m_Lambda_nj
mutableprivate

Lambda coefficient for the ij interaction.

Array of 2D data used in the Pitzer/HMW formulation. Lambda_nj[n][j] represents the lambda coefficient for the ij interaction. This is a general interaction representing neutral species. The neutral species occupy the first index, i.e., n. The charged species occupy the j coordinate. neutral, neutral interactions are also included here.

Definition at line 2204 of file HMWSoln.h.

## ◆ m_Lambda_nj_L

 Array2D m_Lambda_nj_L
mutableprivate

Derivative of Lambda_nj[i][j] wrt T. see m_Lambda_ij.

Definition at line 2207 of file HMWSoln.h.

## ◆ m_Lambda_nj_LL

 Array2D m_Lambda_nj_LL
mutableprivate

Derivative of Lambda_nj[i][j] wrt TT.

Definition at line 2210 of file HMWSoln.h.

## ◆ m_Lambda_nj_P

 Array2D m_Lambda_nj_P
mutableprivate

Derivative of Lambda_nj[i][j] wrt P.

Definition at line 2213 of file HMWSoln.h.

## ◆ m_Lambda_nj_coeff

 Array2D m_Lambda_nj_coeff
private

Array of coefficients for Lambda_nj[i][j] in the Pitzer/HMW formulation.

Array of 2D data used in the Pitzer/HMW formulation. Lambda_ij[i][j] represents the lambda coefficient for the ij interaction. This is a general interaction representing neutral species. The neutral species occupy the first index, i.e., i. The charged species occupy the j coordinate. Neutral, neutral interactions are also included here.

n = j + m_kk * i


m_Lambda_ij_coeff.ptrColumn(n) is a double* containing the vector of coefficients for the (i,j) interaction.

Definition at line 2228 of file HMWSoln.h.

## ◆ m_Mu_nnn

 vector_fp m_Mu_nnn
mutableprivate

Mu coefficient for the self-ternary neutral coefficient.

Array of 2D data used in the Pitzer/HMW formulation. Mu_nnn[i] represents the Mu coefficient for the nnn interaction. This is a general interaction representing neutral species interacting with itself.

Definition at line 2236 of file HMWSoln.h.

## ◆ m_Mu_nnn_L

 vector_fp m_Mu_nnn_L
mutableprivate

Mu coefficient temperature derivative for the self-ternary neutral coefficient.

Array of 2D data used in the Pitzer/HMW formulation. Mu_nnn_L[i] represents the Mu coefficient temperature derivative for the nnn interaction. This is a general interaction representing neutral species interacting with itself.

Definition at line 2246 of file HMWSoln.h.

## ◆ m_Mu_nnn_LL

 vector_fp m_Mu_nnn_LL
mutableprivate

Mu coefficient 2nd temperature derivative for the self-ternary neutral coefficient.

Array of 2D data used in the Pitzer/HMW formulation. Mu_nnn_L[i] represents the Mu coefficient 2nd temperature derivative for the nnn interaction. This is a general interaction representing neutral species interacting with itself.

Definition at line 2256 of file HMWSoln.h.

## ◆ m_Mu_nnn_P

 vector_fp m_Mu_nnn_P
mutableprivate

Mu coefficient pressure derivative for the self-ternary neutral coefficient.

Array of 2D data used in the Pitzer/HMW formulation. Mu_nnn_L[i] represents the Mu coefficient pressure derivative for the nnn interaction. This is a general interaction representing neutral species interacting with itself.

Definition at line 2266 of file HMWSoln.h.

## ◆ m_Mu_nnn_coeff

 Array2D m_Mu_nnn_coeff
private

Array of coefficients form_Mu_nnn term.

Definition at line 2269 of file HMWSoln.h.

## ◆ m_lnActCoeffMolal_Scaled

 vector_fp m_lnActCoeffMolal_Scaled
mutableprivate

Logarithm of the activity coefficients on the molality scale.

mutable because we change this if the composition or temperature or pressure changes. Index is the species index

Definition at line 2276 of file HMWSoln.h.

## ◆ m_lnActCoeffMolal_Unscaled

 vector_fp m_lnActCoeffMolal_Unscaled
mutableprivate

Logarithm of the activity coefficients on the molality scale.

mutable because we change this if the composition or temperature or pressure changes. Index is the species index

Definition at line 2283 of file HMWSoln.h.

## ◆ m_dlnActCoeffMolaldT_Scaled

 vector_fp m_dlnActCoeffMolaldT_Scaled
mutableprivate

Derivative of the Logarithm of the activity coefficients on the molality scale wrt T.

Index is the species index

Definition at line 2287 of file HMWSoln.h.

## ◆ m_dlnActCoeffMolaldT_Unscaled

 vector_fp m_dlnActCoeffMolaldT_Unscaled
mutableprivate

Derivative of the Logarithm of the activity coefficients on the molality scale wrt T.

Index is the species index

Definition at line 2291 of file HMWSoln.h.

## ◆ m_d2lnActCoeffMolaldT2_Scaled

 vector_fp m_d2lnActCoeffMolaldT2_Scaled
mutableprivate

Derivative of the Logarithm of the activity coefficients on the molality scale wrt TT.

Index is the species index.

Definition at line 2295 of file HMWSoln.h.

## ◆ m_d2lnActCoeffMolaldT2_Unscaled

 vector_fp m_d2lnActCoeffMolaldT2_Unscaled
mutableprivate

Derivative of the Logarithm of the activity coefficients on the molality scale wrt TT.

Index is the species index

Definition at line 2299 of file HMWSoln.h.

## ◆ m_dlnActCoeffMolaldP_Scaled

 vector_fp m_dlnActCoeffMolaldP_Scaled
mutableprivate

Derivative of the Logarithm of the activity coefficients on the molality scale wrt P.

Index is the species index

Definition at line 2303 of file HMWSoln.h.

## ◆ m_dlnActCoeffMolaldP_Unscaled

 vector_fp m_dlnActCoeffMolaldP_Unscaled
mutableprivate

Derivative of the Logarithm of the activity coefficients on the molality scale wrt P.

Index is the species index

Definition at line 2307 of file HMWSoln.h.

## ◆ m_molalitiesCropped

 vector_fp m_molalitiesCropped
mutableprivate

Cropped and modified values of the molalities used in activity coefficient calculations.

Definition at line 2313 of file HMWSoln.h.

## ◆ m_molalitiesAreCropped

 bool m_molalitiesAreCropped
mutableprivate

Boolean indicating whether the molalities are cropped or are modified.

Definition at line 2316 of file HMWSoln.h.

Referenced by HMWSoln::calcMolalitiesCropped().

## ◆ m_CounterIJ

 vector_int m_CounterIJ
mutableprivate

a counter variable for keeping track of symmetric binary interactions amongst the solute species.

n = m_kk*i + j m_CounterIJ[n] = counterIJ

Definition at line 2324 of file HMWSoln.h.

## ◆ elambda

 double elambda[17]
mutableprivate

This is elambda, MEC.

Definition at line 2327 of file HMWSoln.h.

Referenced by HMWSoln::calc_thetas().

## ◆ elambda1

 double elambda1[17]
mutableprivate

This is elambda1, MEC.

Definition at line 2330 of file HMWSoln.h.

Referenced by HMWSoln::calc_thetas().

## ◆ m_gfunc_IJ

 vector_fp m_gfunc_IJ
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 2339 of file HMWSoln.h.

## ◆ m_g2func_IJ

 vector_fp m_g2func_IJ
mutableprivate

This is the value of g2(x2) in Pitzer's papers. Vector index is counterIJ.

Definition at line 2342 of file HMWSoln.h.

## ◆ m_hfunc_IJ

 vector_fp m_hfunc_IJ
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 2346 of file HMWSoln.h.

## ◆ m_h2func_IJ

 vector_fp m_h2func_IJ
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 2350 of file HMWSoln.h.

## ◆ m_BMX_IJ

 vector_fp m_BMX_IJ
mutableprivate

Intermediate variable called BMX in Pitzer's paper.

This is the basic cation - anion interaction. Vector index is counterIJ

Definition at line 2354 of file HMWSoln.h.

## ◆ m_BMX_IJ_L

 vector_fp m_BMX_IJ_L
mutableprivate

Derivative of BMX_IJ wrt T. Vector index is counterIJ.

Definition at line 2357 of file HMWSoln.h.

## ◆ m_BMX_IJ_LL

 vector_fp m_BMX_IJ_LL
mutableprivate

Derivative of BMX_IJ wrt TT. Vector index is counterIJ.

Definition at line 2360 of file HMWSoln.h.

## ◆ m_BMX_IJ_P

 vector_fp m_BMX_IJ_P
mutableprivate

Derivative of BMX_IJ wrt P. Vector index is counterIJ.

Definition at line 2363 of file HMWSoln.h.

## ◆ m_BprimeMX_IJ

 vector_fp m_BprimeMX_IJ
mutableprivate

Intermediate variable called BprimeMX in Pitzer's paper.

Vector index is counterIJ

Definition at line 2367 of file HMWSoln.h.

## ◆ m_BprimeMX_IJ_L

 vector_fp m_BprimeMX_IJ_L
mutableprivate

Derivative of BprimeMX wrt T. Vector index is counterIJ.

Definition at line 2370 of file HMWSoln.h.

## ◆ m_BprimeMX_IJ_LL

 vector_fp m_BprimeMX_IJ_LL
mutableprivate

Derivative of BprimeMX wrt TT. Vector index is counterIJ.

Definition at line 2373 of file HMWSoln.h.

## ◆ m_BprimeMX_IJ_P

 vector_fp m_BprimeMX_IJ_P
mutableprivate

Derivative of BprimeMX wrt P. Vector index is counterIJ.

Definition at line 2376 of file HMWSoln.h.

## ◆ m_BphiMX_IJ

 vector_fp m_BphiMX_IJ
mutableprivate

Intermediate variable called BphiMX in Pitzer's paper.

Vector index is counterIJ

Definition at line 2380 of file HMWSoln.h.

## ◆ m_BphiMX_IJ_L

 vector_fp m_BphiMX_IJ_L
mutableprivate

Derivative of BphiMX_IJ wrt T. Vector index is counterIJ.

Definition at line 2383 of file HMWSoln.h.

## ◆ m_BphiMX_IJ_LL

 vector_fp m_BphiMX_IJ_LL
mutableprivate

Derivative of BphiMX_IJ wrt TT. Vector index is counterIJ.

Definition at line 2386 of file HMWSoln.h.

## ◆ m_BphiMX_IJ_P

 vector_fp m_BphiMX_IJ_P
mutableprivate

Derivative of BphiMX_IJ wrt P. Vector index is counterIJ.

Definition at line 2389 of file HMWSoln.h.

## ◆ m_Phi_IJ

 vector_fp m_Phi_IJ
mutableprivate

Intermediate variable called Phi in Pitzer's paper.

Vector index is counterIJ

Definition at line 2393 of file HMWSoln.h.

## ◆ m_Phi_IJ_L

 vector_fp m_Phi_IJ_L
mutableprivate

Derivative of m_Phi_IJ wrt T. Vector index is counterIJ.

Definition at line 2396 of file HMWSoln.h.

## ◆ m_Phi_IJ_LL

 vector_fp m_Phi_IJ_LL
mutableprivate

Derivative of m_Phi_IJ wrt TT. Vector index is counterIJ.

Definition at line 2399 of file HMWSoln.h.

## ◆ m_Phi_IJ_P

 vector_fp m_Phi_IJ_P
mutableprivate

Derivative of m_Phi_IJ wrt P. Vector index is counterIJ.

Definition at line 2402 of file HMWSoln.h.

## ◆ m_Phiprime_IJ

 vector_fp m_Phiprime_IJ
mutableprivate

Intermediate variable called Phiprime in Pitzer's paper.

Vector index is counterIJ

Definition at line 2406 of file HMWSoln.h.

## ◆ m_PhiPhi_IJ

 vector_fp m_PhiPhi_IJ
mutableprivate

Intermediate variable called PhiPhi in Pitzer's paper.

Vector index is counterIJ

Definition at line 2410 of file HMWSoln.h.

## ◆ m_PhiPhi_IJ_L

 vector_fp m_PhiPhi_IJ_L
mutableprivate

Derivative of m_PhiPhi_IJ wrt T. Vector index is counterIJ.

Definition at line 2413 of file HMWSoln.h.

## ◆ m_PhiPhi_IJ_LL

 vector_fp m_PhiPhi_IJ_LL
mutableprivate

Derivative of m_PhiPhi_IJ wrt TT. Vector index is counterIJ.

Definition at line 2416 of file HMWSoln.h.

## ◆ m_PhiPhi_IJ_P

 vector_fp m_PhiPhi_IJ_P
mutableprivate

Derivative of m_PhiPhi_IJ wrt P. Vector index is counterIJ.

Definition at line 2419 of file HMWSoln.h.

## ◆ m_CMX_IJ

 vector_fp m_CMX_IJ
mutableprivate

Intermediate variable called CMX in Pitzer's paper.

Vector index is counterIJ

Definition at line 2423 of file HMWSoln.h.

## ◆ m_CMX_IJ_L

 vector_fp m_CMX_IJ_L
mutableprivate

Derivative of m_CMX_IJ wrt T. Vector index is counterIJ.

Definition at line 2426 of file HMWSoln.h.

## ◆ m_CMX_IJ_LL

 vector_fp m_CMX_IJ_LL
mutableprivate

Derivative of m_CMX_IJ wrt TT. Vector index is counterIJ.

Definition at line 2429 of file HMWSoln.h.

## ◆ m_CMX_IJ_P

 vector_fp m_CMX_IJ_P
mutableprivate

Derivative of m_CMX_IJ wrt P. Vector index is counterIJ.

Definition at line 2432 of file HMWSoln.h.

## ◆ m_gamma_tmp

 vector_fp m_gamma_tmp
mutableprivate

Intermediate storage of the activity coefficient itself.

Vector index is the species index

Definition at line 2436 of file HMWSoln.h.

## ◆ IMS_lnActCoeffMolal_

 vector_fp IMS_lnActCoeffMolal_
mutableprivate

Logarithm of the molal activity coefficients.

Normally these are all one. However, stability schemes will change that

Definition at line 2440 of file HMWSoln.h.

Referenced by HMWSoln::s_updateIMS_lnMolalityActCoeff().

## ◆ IMS_typeCutoff_

 int IMS_typeCutoff_
private

IMS Cutoff type.

Definition at line 2443 of file HMWSoln.h.

Referenced by HMWSoln::s_updateIMS_lnMolalityActCoeff().

## ◆ IMS_X_o_cutoff_

 doublereal IMS_X_o_cutoff_
private

value of the solute mole fraction that centers the cutoff polynomials for the cutoff =1 process;

Definition at line 2447 of file HMWSoln.h.

Referenced by HMWSoln::s_updateIMS_lnMolalityActCoeff().

## ◆ IMS_gamma_o_min_

 doublereal IMS_gamma_o_min_
private

gamma_o value for the cutoff process at the zero solvent point

Definition at line 2450 of file HMWSoln.h.

Referenced by HMWSoln::s_updateIMS_lnMolalityActCoeff().

## ◆ IMS_gamma_k_min_

 doublereal IMS_gamma_k_min_
private

gamma_k minimum for the cutoff process at the zero solvent point

Definition at line 2453 of file HMWSoln.h.

Referenced by HMWSoln::s_updateIMS_lnMolalityActCoeff().

## ◆ IMS_cCut_

 doublereal IMS_cCut_
private

Parameter in the polyExp cutoff treatment having to do with rate of exp decay.

Definition at line 2456 of file HMWSoln.h.

## ◆ IMS_slopefCut_

 doublereal IMS_slopefCut_
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 2463 of file HMWSoln.h.

## ◆ IMS_slopegCut_

 doublereal IMS_slopegCut_
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 2470 of file HMWSoln.h.

## ◆ MC_X_o_cutoff_

 doublereal MC_X_o_cutoff_
private

value of the solvent mole fraction that centers the cutoff polynomials for the cutoff =1 process;

Definition at line 2486 of file HMWSoln.h.

## ◆ MC_X_o_min_

 doublereal MC_X_o_min_
private

gamma_o value for the cutoff process at the zero solvent point

Definition at line 2489 of file HMWSoln.h.

## ◆ MC_slopepCut_

 doublereal MC_slopepCut_
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 2496 of file HMWSoln.h.

## ◆ CROP_speciesCropped_

 vector_int CROP_speciesCropped_
mutableprivate

This is a boolean-type vector indicating whether a species's activity coefficient is in the cropped regime.

• 0 = Not in cropped regime
• 1 = In a transition regime where it is altered but there still may be a temperature or pressure dependence
• 2 = In a cropped regime where there is no temperature or pressure dependence

Definition at line 2519 of file HMWSoln.h.

## ◆ m_debugCalc

 int m_debugCalc
mutable

Turn on copious debug printing when this is true.

Definition at line 2774 of file HMWSoln.h.

The documentation for this class was generated from the following files: