 |
Cantera
3.1.0a1
|
|
Cantera
3.1.0a1
|
Class DebyeHuckel represents a dilute liquid electrolyte phase which obeys the Debye Huckel formulation for nonideality. More...
#include <DebyeHuckel.h>
Class DebyeHuckel represents a dilute liquid electrolyte phase which obeys the Debye Huckel formulation for nonideality.
The concentrations of the ionic species are assumed to obey the electroneutrality condition.
The standard states are on the unit molality basis. Therefore, in the documentation below, the normal \( o \) superscript is replaced with the \( \triangle \) symbol. The reference state symbol is now \( \triangle, ref \).
It is assumed that the reference state thermodynamics may be obtained by a pointer to a populated species thermodynamic property manager class (see ThermoPhase::m_spthermo). How to relate pressure changes to the reference state thermodynamics is resolved at this level.
For an incompressible, stoichiometric substance, the molar internal energy is independent of pressure. Since the thermodynamic properties are specified by giving the standard-state enthalpy, the term \( P_0 \hat v \) is subtracted from the specified molar enthalpy to compute the molar internal energy. The entropy is assumed to be independent of the pressure.
The enthalpy function is given by the following relation.
\[ h^\triangle_k(T,P) = h^{\triangle,ref}_k(T) + \tilde v \left( P - P_{ref} \right) \]
For an incompressible, stoichiometric substance, the molar internal energy is independent of pressure. Since the thermodynamic properties are specified by giving the standard-state enthalpy, the term \( P_{ref} \tilde v \) is subtracted from the specified reference molar enthalpy to compute the molar internal energy.
\[ u^\triangle_k(T,P) = h^{\triangle,ref}_k(T) - P_{ref} \tilde v \]
The standard state heat capacity and entropy are independent of pressure. The standard state Gibbs free energy is obtained from the enthalpy and entropy functions.
The 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, that is, beyond its spinodal curve.
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.
Most of the parameterizations within the model use the ionic strength as a key variable. The ionic strength, \( I \) is defined as follows
\[ I = \frac{1}{2} \sum_k{m_k z_k^2} \]
\( m_k \) is the molality of the kth species. \( z_k \) is the charge of the kth species. Note, the ionic strength is a defined units quantity. The molality has defined units of gmol kg-1, and therefore the ionic strength has units of sqrt( gmol kg-1).
In some instances, from some authors, a different formulation is used for the ionic strength in the equations below. The different formulation is due to the possibility of the existence of weak acids and how association wrt to the weak acid equilibrium relation affects the calculation of the activity coefficients via the assumed value of the ionic strength.
If we are to assume that the association reaction doesn't have an effect on the ionic strength, then we will want to consider the associated weak acid as in effect being fully dissociated, when we calculate an effective value for the ionic strength. We will call this calculated value, the stoichiometric ionic strength, \( I_s \), putting a subscript s to denote it from the more straightforward calculation of \( I \).
\[ I_s = \frac{1}{2} \sum_k{m_k^s z_k^2} \]
Here, \( m_k^s \) is the value of the molalities calculated assuming that all weak acid-base pairs are in their fully dissociated states. This calculation may be simplified by considering that the weakly associated acid may be made up of two charged species, k1 and k2, each with their own charges, obeying the following relationship:
\[ z_k = z_{k1} + z_{k2} \]
Then, we may only need to specify one charge value, say, \( z_{k1} \), the cation charge number, in order to get both numbers, since we have already specified \( z_k \) in the definition of original species. Then, the stoichiometric ionic strength may be calculated via the following formula.
\[ I_s = \frac{1}{2} \left(\sum_{k,ions}{m_k z_k^2}+ \sum_{k,weak_assoc}(m_k z_{k1}^2 + m_k z_{k2}^2) \right) \]
The specification of which species are weakly associated acids is made in YAML input files by specifying the corresponding charge \( k1 \) as the weak-acid-charge parameter of the Debye-Huckel block in the corresponding species entry.
Because we need the concept of a weakly associated acid in order to calculate \( I_s \) we need to catalog all species in the phase. This is done using the following categories:
cEST_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 speciescEST_nonpolarNeutral Non polar neutral speciesPolar 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.
In a YAML input file, the type of species is specified in the electrolyte-species-type field of the Debye-Huckel block in the corresponding species entry. Note, this is not considered a part of the specification of the standard state for the species, at this time.
Much of the species electrolyte type information is inferred from other information in the input file. For example, as species which is charged is given the "chargedSpecies" default category. A neutral solute species is put into the "nonpolarNeutral" category by default.
The specification of solute activity coefficients depends on the model assumed for the Debye-Huckel term. The model is set by the internal parameter m_formDH. We will now describe each category in its own section.
DHFORM_DILUTE_LIMIT = 0
This form assumes a dilute limit to DH, and is mainly for informational purposes:
\[ \ln(\gamma_k^\triangle) = - z_k^2 A_{Debye} \sqrt{I} \]
where \( I \) is the ionic strength
\[ I = \frac{1}{2} \sum_k{m_k z_k^2} \]
The activity for the solvent water, \( a_o \), is not independent and must be determined from the Gibbs-Duhem relation.
\[ \ln(a_o) = \frac{X_o - 1.0}{X_o} + \frac{ 2 A_{Debye} \tilde{M}_o}{3} (I)^{3/2} \]
DHFORM_BDOT_AK = 1
This form assumes Bethke's format for the Debye Huckel activity coefficient:
\[ \ln(\gamma_k^\triangle) = -z_k^2 \frac{A_{Debye} \sqrt{I}}{ 1 + B_{Debye} a_k \sqrt{I}} + \ln(10) B^{dot}_k I \]
Note, this particular form where \( a_k \) can differ in multielectrolyte solutions has problems with respect to a Gibbs-Duhem analysis. However, we include it here because there is a lot of data fit to it.
The activity for the solvent water, \( a_o \), is not independent and must be determined from the Gibbs-Duhem relation. Here, we use:
\[ \ln(a_o) = \frac{X_o - 1.0}{X_o} + \frac{ 2 A_{Debye} \tilde{M}_o}{3} (I)^{1/2} \left[ \sum_k{\frac{1}{2} m_k z_k^2 \sigma( B_{Debye} a_k \sqrt{I} ) } \right] - \frac{\ln 10}{2} \tilde{M}_o I \sum_k{ B^{dot}_k m_k} \]
where
\[ \sigma (y) = \frac{3}{y^3} \left[ (1+y) - 2 \ln(1 + y) - \frac{1}{1+y} \right] \]
Additionally, Helgeson's formulation for the water activity is offered as an alternative.
DHFORM_BDOT_AUNIFORM = 2
This form assumes Bethke's format for the Debye-Huckel activity coefficient
\[ \ln(\gamma_k^\triangle) = -z_k^2 \frac{A_{Debye} \sqrt{I}}{ 1 + B_{Debye} a \sqrt{I}} + \ln(10) B^{dot}_k I \]
The value of a is determined at the beginning of the calculation, and not changed.
\[ \ln(a_o) = \frac{X_o - 1.0}{X_o} + \frac{ 2 A_{Debye} \tilde{M}_o}{3} (I)^{3/2} \sigma( B_{Debye} a \sqrt{I} ) - \frac{\ln 10}{2} \tilde{M}_o I \sum_k{ B^{dot}_k m_k} \]
DHFORM_BETAIJ = 3
This form assumes a linear expansion in a virial coefficient form. It is used extensively in the book by Newmann, "Electrochemistry Systems", and is the beginning of more complex treatments for stronger electrolytes, fom Pitzer and from Harvey, Moller, and Weire.
\[ \ln(\gamma_k^\triangle) = -z_k^2 \frac{A_{Debye} \sqrt{I}}{ 1 + B_{Debye} a \sqrt{I}} + 2 \sum_j \beta_{j,k} m_j \]
In the current treatment the binary interaction coefficients, \( \beta_{j,k} \), are independent of temperature and pressure.
\[ \ln(a_o) = \frac{X_o - 1.0}{X_o} + \frac{ 2 A_{Debye} \tilde{M}_o}{3} (I)^{3/2} \sigma( B_{Debye} a \sqrt{I} ) - \tilde{M}_o \sum_j \sum_k \beta_{j,k} m_j m_k \]
In this formulation the ionic radius, \( a \), is a constant, specified as part of the species definition.
The \( \beta_{j,k} \) parameters are binary interaction parameters. There are in principle \( N (N-1) /2 \) different, symmetric interaction parameters, where \( N \) are the number of solute species in the mechanism.
DHFORM_PITZER_BETAIJ = 4
This form assumes an activity coefficient formulation consistent with a truncated form of Pitzer's formulation. Pitzer's formulation is equivalent to the formulations above in the dilute limit, where rigorous theory may be applied.
\[ \ln(\gamma_k^\triangle) = -z_k^2 \frac{A_{Debye}}{3} \frac{\sqrt{I}}{ 1 + B_{Debye} a \sqrt{I}} -2 z_k^2 \frac{A_{Debye}}{3} \frac{\ln(1 + B_{Debye} a \sqrt{I})}{ B_{Debye} a} + 2 \sum_j \beta_{j,k} m_j \]
\[ \ln(a_o) = \frac{X_o - 1.0}{X_o} + \frac{ 2 A_{Debye} \tilde{M}_o}{3} \frac{(I)^{3/2} }{1 + B_{Debye} a \sqrt{I} } - \tilde{M}_o \sum_j \sum_k \beta_{j,k} m_j m_k \]
In the equations above, the formulas for \( A_{Debye} \) and \( B_{Debye} \) are needed. The DebyeHuckel object uses two methods for specifying these quantities. The default method is to assume that \( A_{Debye} \) is a constant, given in the initialization process, and stored in the member double, m_A_Debye. Optionally, a full water treatment may be employed that makes \( A_{Debye} \) a full function of T and P.
\[ A_{Debye} = \frac{F e B_{Debye}}{8 \pi \epsilon R T} {\left( C_o \tilde{M}_o \right)}^{1/2} \]
where
\[ B_{Debye} = \frac{F} {{(\frac{\epsilon R T}{2})}^{1/2}} \]
Therefore:
\[ A_{Debye} = \frac{1}{8 \pi} {\left(\frac{2 N_a \rho_o}{1000}\right)}^{1/2} {\left(\frac{N_a e^2}{\epsilon R T }\right)}^{3/2} \]
where
Nominal value at 298 K and 1 atm = 1.172576 (kg/gmol)^(1/2) based on:
Currently, \( B_{Debye} \) is a constant in the model, specified either by a default water value, or through the input file. This may have to be looked at, in the future.
Example phase and species definitions are given in the YAML API Reference.
For the time being, we have set the standard concentration for all species in this phase equal to the default concentration of the solvent at 298 K and 1 atm. This means that the kinetics operator essentially works on an activities basis, with units specified as if it were on a concentration basis.
For example, a bulk-phase binary reaction between liquid species j and k, producing a new liquid species l would have the following equation for its rate of progress variable, \( R^1 \), which has units of kmol m-3 s-1.
\[ R^1 = k^1 C_j^a C_k^a = k^1 (C_o a_j) (C_o a_k) \]
where
\[ C_j^a = C_o a_j \quad and \quad C_k^a = C_o a_k \]
\( C_j^a \) is the activity concentration of species j, and \( C_k^a \) is the activity concentration of species k. \( C_o \) is the concentration of water at 298 K and 1 atm. \( a_j \) is the activity of species j at the current temperature and pressure and concentration of the liquid phase. \( k^1 \) has units of m3 kmol-1 s-1.
The reverse rate constant can then be obtained from the law of microscopic reversibility and the equilibrium expression for the system.
\[ \frac{a_j a_k}{ a_l} = K^{o,1} = \exp(\frac{\mu^o_l - \mu^o_j - \mu^o_k}{R T} ) \]
\( K^{o,1} \) is the dimensionless form of the equilibrium constant.
\[ R^{-1} = k^{-1} C_l^a = k^{-1} (C_o a_l) \]
where
\[ k^{-1} = k^1 K^{o,1} C_o \]
\( k^{-1} \) has units of s-1.
Definition at line 414 of file DebyeHuckel.h.
Public Member Functions | |
| DebyeHuckel (const string &inputFile="", const string &id="") | |
| Full constructor for creating the phase. More... | |
| bool | addSpecies (shared_ptr< Species > spec) override |
| Add a Species to this Phase. More... | |
| void | initThermo () override |
| Initialize the ThermoPhase object after all species have been set up. More... | |
| void | getParameters (AnyMap &phaseNode) const override |
| Store the parameters of a ThermoPhase object such that an identical one could be reconstructed using the newThermo(AnyMap&) function. More... | |
| void | getSpeciesParameters (const string &name, AnyMap &speciesNode) const override |
| Get phase-specific parameters of a Species object such that an identical one could be reconstructed and added to this phase. More... | |
| virtual double | A_Debye_TP (double temperature=-1.0, double pressure=-1.0) const |
| Return the Debye Huckel constant as a function of temperature and pressure (Units = sqrt(kg/gmol)) More... | |
| virtual double | dA_DebyedT_TP (double temperature=-1.0, double pressure=-1.0) const |
| Value of the derivative of the Debye Huckel constant with respect to temperature. More... | |
| virtual double | d2A_DebyedT2_TP (double temperature=-1.0, double pressure=-1.0) const |
| Value of the 2nd derivative of the Debye Huckel constant with respect to temperature as a function of temperature and pressure. More... | |
| virtual double | dA_DebyedP_TP (double temperature=-1.0, double pressure=-1.0) const |
| Value of the derivative of the Debye Huckel constant with respect to pressure, as a function of temperature and pressure. More... | |
| double | AionicRadius (int k=0) const |
| Reports the ionic radius of the kth species. More... | |
| void | setDebyeHuckelModel (const string &form) |
| Set the DebyeHuckel parameterization form. More... | |
| int | formDH () const |
| Returns the form of the Debye-Huckel parameterization used. More... | |
| void | setA_Debye (double A) |
| Set the A_Debye parameter. More... | |
| void | setB_Debye (double B) |
| void | setB_dot (double bdot) |
| void | setMaxIonicStrength (double Imax) |
| void | useHelgesonFixedForm (bool mode=true) |
| void | setDefaultIonicRadius (double value) |
| Set the default ionic radius [m] for each species. More... | |
| void | setBeta (const string &sp1, const string &sp2, double value) |
| Set the value for the beta interaction between species sp1 and sp2. More... | |
| Array2D & | get_Beta_ij () |
| Returns a reference to M_Beta_ij. More... | |
Utilities | |
| string | type () const override |
| String indicating the thermodynamic model implemented. More... | |
Molar Thermodynamic Properties of the Solution | |
| double | enthalpy_mole () const override |
| Molar enthalpy. Units: J/kmol. More... | |
| double | entropy_mole () const override |
| Molar entropy. Units: J/kmol/K. More... | |
| double | gibbs_mole () const override |
| Molar Gibbs function. Units: J/kmol. More... | |
| double | cp_mole () const override |
| Molar heat capacity at constant pressure. Units: J/kmol/K. More... | |
Activities, Standard States, and Activity Concentrations | |
The activity \( a_k \) of a species in solution is related to the chemical potential by \[ \mu_k = \mu_k^0(T) + \hat R T \ln a_k. \] 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. | |
| void | getActivityConcentrations (double *c) const override |
| This method returns an array of generalized concentrations. More... | |
| double | standardConcentration (size_t k=0) const override |
| Return the standard concentration for the kth species. More... | |
| void | getActivities (double *ac) const override |
| Get the array of non-dimensional activities at the current solution temperature, pressure, and solution concentration. More... | |
| void | getMolalityActivityCoefficients (double *acMolality) const override |
| Get the array of non-dimensional molality-based activity coefficients at the current solution temperature, pressure, and solution concentration. More... | |
Partial Molar Properties of the Solution | |
| void | getChemPotentials (double *mu) const override |
| Get the species chemical potentials. Units: J/kmol. More... | |
| void | getPartialMolarEnthalpies (double *hbar) const override |
| Returns an array of partial molar enthalpies for the species in the mixture. More... | |
| void | getPartialMolarEntropies (double *sbar) const override |
| Returns an array of partial molar entropies of the species in the solution. More... | |
| void | getPartialMolarCp (double *cpbar) const override |
| Return an array of partial molar heat capacities for the species in the mixture. More... | |
| void | getPartialMolarVolumes (double *vbar) const override |
| Return an array of partial molar volumes for the species in the mixture. More... | |
 Public Member Functions inherited from MolalityVPSSTP | |
| MolalityVPSSTP () | |
| Default Constructor. More... | |
| void | setState_TPM (double t, double p, const double *const molalities) |
| Set the temperature (K), pressure (Pa), and molalities (gmol kg-1) of the solutes. More... | |
| void | setState_TPM (double t, double p, const Composition &m) |
| Set the temperature (K), pressure (Pa), and molalities. More... | |
| void | setState_TPM (double t, double p, const string &m) |
| Set the temperature (K), pressure (Pa), and molalities. More... | |
| void | setState (const AnyMap &state) override |
| Set the state using an AnyMap containing any combination of properties supported by the thermodynamic model. More... | |
| void | getdlnActCoeffdlnN (const size_t ld, double *const dlnActCoeffdlnN) override |
| Get the array of derivatives of the log activity coefficients with respect to the log of the species mole numbers. More... | |
| string | report (bool show_thermo=true, double threshold=1e-14) const override |
| returns a summary of the state of the phase as a string More... | |
| string | phaseOfMatter () const override |
| String indicating the mechanical phase of the matter in this Phase. 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 | setMoleFSolventMin (double xmolSolventMIN) |
| Sets the minimum mole fraction in the molality formulation. More... | |
| double | 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 (double *const molal) const |
| This function will return the molalities of the species. More... | |
| void | setMolalities (const double *const molal) |
| Set the molalities of the solutes in a phase. More... | |
| void | setMolalitiesByName (const Composition &xMap) |
| Set the molalities of a phase. More... | |
| void | setMolalitiesByName (const string &name) |
| Set the molalities of a phase. More... | |
| int | activityConvention () const override |
| We set the convention to molality here. More... | |
| void | getActivityConcentrations (double *c) const override |
| This method returns an array of generalized concentrations. More... | |
| double | standardConcentration (size_t k=0) const override |
| Return the standard concentration for the kth species. More... | |
| void | getActivities (double *ac) const override |
| Get the array of non-dimensional activities (molality based for this class and classes that derive from it) at the current solution temperature, pressure, and solution concentration. More... | |
| void | getActivityCoefficients (double *ac) const override |
| Get the array of non-dimensional activity coefficients at the current solution temperature, pressure, and solution concentration. More... | |
| virtual double | osmoticCoefficient () const |
| Calculate the osmotic coefficient. More... | |
| bool | addSpecies (shared_ptr< Species > spec) override |
| Add a Species to this Phase. More... | |
| void | initThermo () override |
| Initialize the ThermoPhase object after all species have been set up. More... | |
| Public Member Functions inherited from VPStandardStateTP | |
| void | setTemperature (const double temp) override |
| Set the temperature of the phase. More... | |
| void | setPressure (double p) override |
| Set the internally stored pressure (Pa) at constant temperature and composition. More... | |
| void | setState_TP (double T, double pres) override |
| Set the temperature and pressure at the same time. More... | |
| double | pressure () const override |
| Returns the current pressure of the phase. More... | |
| virtual void | updateStandardStateThermo () const |
| Updates the standard state thermodynamic functions at the current T and P of the solution. More... | |
| double | minTemp (size_t k=npos) const override |
| Minimum temperature for which the thermodynamic data for the species or phase are valid. More... | |
| double | maxTemp (size_t k=npos) const override |
| Maximum temperature for which the thermodynamic data for the species are valid. More... | |
| PDSS * | providePDSS (size_t k) |
| const PDSS * | providePDSS (size_t k) const |
| VPStandardStateTP () | |
| Constructor. More... | |
| ~VPStandardStateTP () override | |
| bool | isCompressible () const override |
| Return whether phase represents a compressible substance. More... | |
| int | standardStateConvention () const override |
| 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... | |
| void | getStandardChemPotentials (double *mu) const override |
| 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... | |
| void | getEnthalpy_RT (double *hrt) const override |
| Get the nondimensional Enthalpy functions for the species at their standard states at the current T and P of the solution. More... | |
| void | getEntropy_R (double *sr) const override |
| Get the array of nondimensional Entropy functions for the standard state species at the current T and P of the solution. More... | |
| void | getGibbs_RT (double *grt) const override |
| Get the nondimensional Gibbs functions for the species in their standard states at the current T and P of the solution. More... | |
| void | getPureGibbs (double *gpure) const override |
| Get the Gibbs functions for the standard state of the species at the current T and P of the solution. More... | |
| void | getIntEnergy_RT (double *urt) const override |
| Returns the vector of nondimensional Internal Energies of the standard state species at the current T and P of the solution. More... | |
| void | getCp_R (double *cpr) const override |
| Get the nondimensional Heat Capacities at constant pressure for the species standard states at the current T and P of the solution. More... | |
| void | getStandardVolumes (double *vol) const override |
| Get the molar volumes of the species standard states at the current T and P of the solution. More... | |
| virtual const vector< double > & | getStandardVolumes () const |
| void | initThermo () override |
| Initialize the ThermoPhase object after all species have been set up. More... | |
| void | getSpeciesParameters (const string &name, AnyMap &speciesNode) const override |
| Get phase-specific parameters of a Species object such that an identical one could be reconstructed and added to this phase. More... | |
| bool | addSpecies (shared_ptr< Species > spec) override |
| Add a Species to this Phase. More... | |
| void | installPDSS (size_t k, unique_ptr< PDSS > &&pdss) |
| Install a PDSS object for species k More... | |
| virtual bool | addSpecies (shared_ptr< Species > spec) |
| Add a Species to this Phase. More... | |
| void | getEnthalpy_RT_ref (double *hrt) const override |
| Returns the vector of nondimensional enthalpies of the reference state at the current temperature of the solution and the reference pressure for the species. More... | |
| void | getGibbs_RT_ref (double *grt) const override |
| 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... | |
| void | getGibbs_ref (double *g) const override |
| 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... | |
| void | getEntropy_R_ref (double *er) const override |
| 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... | |
| void | getCp_R_ref (double *cprt) const override |
| 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... | |
| void | getStandardVolumes_ref (double *vol) const override |
| 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 ()=default | |
| Constructor. More... | |
| double | RT () const |
| Return the Gas Constant multiplied by the current temperature. More... | |
| double | equivalenceRatio () const |
| Compute the equivalence ratio for the current mixture from available oxygen and required oxygen. More... | |
| string | type () const override |
| String indicating the thermodynamic model implemented. More... | |
| virtual bool | isIdeal () const |
| Boolean indicating whether phase is ideal. More... | |
| virtual double | refPressure () const |
| Returns the reference pressure in Pa. More... | |
| double | 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 double 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... | |
| bool | chargeNeutralityNecessary () const |
| Returns the chargeNeutralityNecessity boolean. More... | |
| virtual double | intEnergy_mole () const |
| Molar internal energy. Units: J/kmol. More... | |
| virtual double | cv_mole () const |
| Molar heat capacity at constant volume. Units: J/kmol/K. More... | |
| virtual double | isothermalCompressibility () const |
| Returns the isothermal compressibility. Units: 1/Pa. More... | |
| virtual double | thermalExpansionCoeff () const |
| Return the volumetric thermal expansion coefficient. Units: 1/K. More... | |
| virtual double | soundSpeed () const |
| Return the speed of sound. Units: m/s. More... | |
| void | setElectricPotential (double v) |
| Set the electric potential of this phase (V). More... | |
| double | electricPotential () const |
| Returns the electric potential of this phase (V). More... | |
| virtual Units | standardConcentrationUnits () const |
| Returns the units of the "standard concentration" for this phase. More... | |
| virtual double | logStandardConc (size_t k=0) const |
| Natural logarithm of the standard concentration of the kth species. More... | |
| virtual void | getLnActivityCoefficients (double *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 (double *mu) const |
| Get the species electrochemical potentials. More... | |
| virtual void | getPartialMolarIntEnergies (double *ubar) const |
| Return an array of partial molar internal energies for the species in the mixture. More... | |
| virtual void | getIntEnergy_RT_ref (double *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... | |
| double | enthalpy_mass () const |
| Specific enthalpy. Units: J/kg. More... | |
| double | intEnergy_mass () const |
| Specific internal energy. Units: J/kg. More... | |
| double | entropy_mass () const |
| Specific entropy. Units: J/kg/K. More... | |
| double | gibbs_mass () const |
| Specific Gibbs function. Units: J/kg. More... | |
| double | cp_mass () const |
| Specific heat at constant pressure. Units: J/kg/K. More... | |
| double | cv_mass () const |
| Specific heat at constant volume. Units: J/kg/K. More... | |
| virtual void | setState_TPX (double t, double p, const double *x) |
| Set the temperature (K), pressure (Pa), and mole fractions. More... | |
| virtual void | setState_TPX (double t, double p, const Composition &x) |
| Set the temperature (K), pressure (Pa), and mole fractions. More... | |
| virtual void | setState_TPX (double t, double p, const string &x) |
| Set the temperature (K), pressure (Pa), and mole fractions. More... | |
| virtual void | setState_TPY (double t, double p, const double *y) |
| Set the internally stored temperature (K), pressure (Pa), and mass fractions of the phase. More... | |
| virtual void | setState_TPY (double t, double p, const Composition &y) |
| Set the internally stored temperature (K), pressure (Pa), and mass fractions of the phase. More... | |
| virtual void | setState_TPY (double t, double p, const string &y) |
| Set the internally stored temperature (K), pressure (Pa), and mass fractions of the phase. 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_DP (double rho, double p) |
| Set the density (kg/m**3) and pressure (Pa) at constant composition. More... | |
| void | setMixtureFraction (double mixFrac, const double *fuelComp, const double *oxComp, ThermoBasis basis=ThermoBasis::molar) |
| Set the mixture composition according to the mixture fraction = kg fuel / (kg oxidizer + kg fuel) More... | |
| void | setMixtureFraction (double mixFrac, const string &fuelComp, const string &oxComp, ThermoBasis basis=ThermoBasis::molar) |
| Set the mixture composition according to the mixture fraction = kg fuel / (kg oxidizer + kg fuel) More... | |
| void | setMixtureFraction (double mixFrac, const Composition &fuelComp, const Composition &oxComp, ThermoBasis basis=ThermoBasis::molar) |
| Set the mixture composition according to the mixture fraction = kg fuel / (kg oxidizer + kg fuel) More... | |
| double | mixtureFraction (const double *fuelComp, const double *oxComp, ThermoBasis basis=ThermoBasis::molar, const string &element="Bilger") const |
| Compute the mixture fraction = kg fuel / (kg oxidizer + kg fuel) for the current mixture given fuel and oxidizer compositions. More... | |
| double | mixtureFraction (const string &fuelComp, const string &oxComp, ThermoBasis basis=ThermoBasis::molar, const string &element="Bilger") const |
| Compute the mixture fraction = kg fuel / (kg oxidizer + kg fuel) for the current mixture given fuel and oxidizer compositions. More... | |
| double | mixtureFraction (const Composition &fuelComp, const Composition &oxComp, ThermoBasis basis=ThermoBasis::molar, const string &element="Bilger") const |
| Compute the mixture fraction = kg fuel / (kg oxidizer + kg fuel) for the current mixture given fuel and oxidizer compositions. More... | |
| void | setEquivalenceRatio (double phi, const double *fuelComp, const double *oxComp, ThermoBasis basis=ThermoBasis::molar) |
| Set the mixture composition according to the equivalence ratio. More... | |
| void | setEquivalenceRatio (double phi, const string &fuelComp, const string &oxComp, ThermoBasis basis=ThermoBasis::molar) |
| Set the mixture composition according to the equivalence ratio. More... | |
| void | setEquivalenceRatio (double phi, const Composition &fuelComp, const Composition &oxComp, ThermoBasis basis=ThermoBasis::molar) |
| Set the mixture composition according to the equivalence ratio. More... | |
| double | equivalenceRatio (const double *fuelComp, const double *oxComp, ThermoBasis basis=ThermoBasis::molar) const |
| Compute the equivalence ratio for the current mixture given the compositions of fuel and oxidizer. More... | |
| double | equivalenceRatio (const string &fuelComp, const string &oxComp, ThermoBasis basis=ThermoBasis::molar) const |
| Compute the equivalence ratio for the current mixture given the compositions of fuel and oxidizer. More... | |
| double | equivalenceRatio (const Composition &fuelComp, const Composition &oxComp, ThermoBasis basis=ThermoBasis::molar) const |
| Compute the equivalence ratio for the current mixture given the compositions of fuel and oxidizer. More... | |
| double | stoichAirFuelRatio (const double *fuelComp, const double *oxComp, ThermoBasis basis=ThermoBasis::molar) const |
| Compute the stoichiometric air to fuel ratio (kg oxidizer / kg fuel) given fuel and oxidizer compositions. More... | |
| double | stoichAirFuelRatio (const string &fuelComp, const string &oxComp, ThermoBasis basis=ThermoBasis::molar) const |
| Compute the stoichiometric air to fuel ratio (kg oxidizer / kg fuel) given fuel and oxidizer compositions. More... | |
| double | stoichAirFuelRatio (const Composition &fuelComp, const Composition &oxComp, ThermoBasis basis=ThermoBasis::molar) const |
| Compute the stoichiometric air to fuel ratio (kg oxidizer / kg fuel) given fuel and oxidizer compositions. More... | |
| void | equilibrate (const string &XY, const 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 double *mu_RT) |
| This method is used by the ChemEquil equilibrium solver. More... | |
| virtual bool | compatibleWithMultiPhase () const |
| Indicates whether this phase type can be used with class MultiPhase for equilibrium calculations. More... | |
| virtual double | critTemperature () const |
| Critical temperature (K). More... | |
| virtual double | critPressure () const |
| Critical pressure (Pa). More... | |
| virtual double | critVolume () const |
| Critical volume (m3/kmol). More... | |
| virtual double | critCompressibility () const |
| Critical compressibility (unitless). More... | |
| virtual double | critDensity () const |
| Critical density (kg/m3). More... | |
| virtual double | satTemperature (double p) const |
| Return the saturation temperature given the pressure. More... | |
| virtual double | satPressure (double t) |
| Return the saturation pressure given the temperature. More... | |
| virtual double | vaporFraction () const |
| Return the fraction of vapor at the current conditions. More... | |
| virtual void | setState_Tsat (double t, double x) |
| Set the state to a saturated system at a particular temperature. More... | |
| virtual void | setState_Psat (double p, double x) |
| Set the state to a saturated system at a particular pressure. More... | |
| void | setState_TPQ (double T, double P, double Q) |
| Set the temperature, pressure, and vapor fraction (quality). More... | |
| void | modifySpecies (size_t k, shared_ptr< Species > spec) override |
| Modify the thermodynamic data associated with a species. More... | |
| virtual MultiSpeciesThermo & | speciesThermo (int k=-1) |
| Return a changeable reference to the calculation manager for species reference-state thermodynamic properties. More... | |
| virtual const MultiSpeciesThermo & | speciesThermo (int k=-1) const |
| void | initThermoFile (const string &inputFile, const string &id) |
| Initialize a ThermoPhase object using an input file. More... | |
| virtual void | setParameters (const AnyMap &phaseNode, const AnyMap &rootNode=AnyMap()) |
| Set equation of state parameters from an AnyMap phase description. More... | |
| AnyMap | parameters (bool withInput=true) const |
| Returns the parameters of a ThermoPhase object such that an identical one could be reconstructed using the newThermo(AnyMap&) function. More... | |
| const AnyMap & | input () const |
| Access input data associated with the phase description. More... | |
| AnyMap & | input () |
| virtual void | getdlnActCoeffds (const double dTds, const double *const dXds, double *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 (double *dlnActCoeffdlnX_diag) const |
| Get the array of ln mole fraction derivatives of the log activity coefficients - diagonal component only. More... | |
| virtual void | getdlnActCoeffdlnN_diag (double *dlnActCoeffdlnN_diag) const |
| Get the array of log species mole number derivatives of the log activity coefficients. More... | |
| virtual void | getdlnActCoeffdlnN_numderiv (const size_t ld, double *const dlnActCoeffdlnN) |
| Public Member Functions inherited from Phase | |
| Phase ()=default | |
| Default constructor. More... | |
| Phase (const Phase &)=delete | |
| Phase & | operator= (const Phase &)=delete |
| virtual bool | isPure () const |
| Return whether phase represents a pure (single species) substance. More... | |
| virtual bool | hasPhaseTransition () const |
| Return whether phase represents a substance with phase transitions. More... | |
| virtual map< string, size_t > | nativeState () const |
| Return a map of properties defining the native state of a substance. More... | |
| string | nativeMode () const |
| Return string acronym representing the native state of a Phase. More... | |
| virtual vector< string > | fullStates () const |
| Return a vector containing full states defining a phase. More... | |
| virtual vector< string > | partialStates () const |
| Return a vector of settable partial property sets within a phase. More... | |
| virtual size_t | stateSize () const |
| Return size of vector defining internal state of the phase. More... | |
| void | saveState (vector< double > &state) const |
| Save the current internal state of the phase. More... | |
| virtual void | saveState (size_t lenstate, double *state) const |
| Write to array 'state' the current internal state. More... | |
| void | restoreState (const vector< double > &state) |
| Restore a state saved on a previous call to saveState. More... | |
| virtual void | restoreState (size_t lenstate, const double *state) |
| Restore the state of the phase from a previously saved state vector. More... | |
| double | molecularWeight (size_t k) const |
Molecular weight of species k. More... | |
| void | getMolecularWeights (double *weights) const |
| Copy the vector of molecular weights into array weights. More... | |
| const vector< double > & | molecularWeights () const |
| Return a const reference to the internal vector of molecular weights. More... | |
| const vector< double > & | inverseMolecularWeights () const |
| Return a const reference to the internal vector of molecular weights. More... | |
| void | getCharges (double *charges) const |
| Copy the vector of species charges into array charges. More... | |
| virtual void | setMolesNoTruncate (const double *const N) |
| Set the state of the object with moles in [kmol]. More... | |
| double | elementalMassFraction (const size_t m) const |
| Elemental mass fraction of element m. More... | |
| double | elementalMoleFraction (const size_t m) const |
| Elemental mole fraction of element m. More... | |
| double | 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... | |
| double | chargeDensity () const |
| Charge density [C/m^3]. More... | |
| size_t | nDim () const |
| Returns the number of spatial dimensions (1, 2, or 3) More... | |
| void | setNDim (size_t ndim) |
| Set the number of spatial dimensions (1, 2, or 3). More... | |
| virtual bool | ready () const |
| Returns a bool indicating whether the object is ready for use. More... | |
| int | stateMFNumber () const |
| Return the State Mole Fraction Number. More... | |
| bool | caseSensitiveSpecies () const |
Returns true if case sensitive species names are enforced. More... | |
| void | setCaseSensitiveSpecies (bool cflag=true) |
| Set flag that determines whether case sensitive species are enforced in look-up operations, for example speciesIndex. More... | |
| vector< double > | getCompositionFromMap (const Composition &comp) const |
| Converts a Composition to a vector with entries for each species Species that are not specified are set to zero in the vector. More... | |
| void | massFractionsToMoleFractions (const double *Y, double *X) const |
| Converts a mixture composition from mole fractions to mass fractions. More... | |
| void | moleFractionsToMassFractions (const double *X, double *Y) const |
| Converts a mixture composition from mass fractions to mole fractions. More... | |
| string | name () const |
| Return the name of the phase. More... | |
| void | setName (const string &nm) |
| Sets the string name for the phase. More... | |
| string | elementName (size_t m) const |
| Name of the element with index m. More... | |
| size_t | elementIndex (const string &name) const |
| Return the index of element named 'name'. More... | |
| const vector< string > & | elementNames () const |
| Return a read-only reference to the vector of element names. More... | |
| double | atomicWeight (size_t m) const |
| Atomic weight of element m. More... | |
| double | 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< double > & | atomicWeights () const |
| Return a read-only reference to the vector of atomic weights. More... | |
| size_t | nElements () const |
| Number of elements. More... | |
| void | checkElementIndex (size_t m) const |
| Check that the specified element index is in range. More... | |
| void | checkElementArraySize (size_t mm) const |
| Check that an array size is at least nElements(). More... | |
| double | nAtoms (size_t k, size_t m) const |
Number of atoms of element m in species k. More... | |
| size_t | speciesIndex (const string &name) const |
| Returns the index of a species named 'name' within the Phase object. More... | |
| string | speciesName (size_t k) const |
| Name of the species with index k. More... | |
| const vector< 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 Composition &xMap) |
| Set the species mole fractions by name. More... | |
| void | setMoleFractionsByName (const string &x) |
| Set the mole fractions of a group of species by name. More... | |
| void | setMassFractionsByName (const Composition &yMap) |
| Set the species mass fractions by name. More... | |
| void | setMassFractionsByName (const string &x) |
| Set the species mass fractions by name. More... | |
| void | setState_TD (double t, double rho) |
| Set the internally stored temperature (K) and density (kg/m^3) More... | |
| Composition | getMoleFractionsByName (double threshold=0.0) const |
| Get the mole fractions by name. More... | |
| double | moleFraction (size_t k) const |
| Return the mole fraction of a single species. More... | |
| double | moleFraction (const string &name) const |
| Return the mole fraction of a single species. More... | |
| Composition | getMassFractionsByName (double threshold=0.0) const |
| Get the mass fractions by name. More... | |
| double | massFraction (size_t k) const |
| Return the mass fraction of a single species. More... | |
| double | massFraction (const string &name) const |
| Return the mass fraction of a single species. More... | |
| void | getMoleFractions (double *const x) const |
| Get the species mole fraction vector. More... | |
| virtual void | setMoleFractions (const double *const x) |
| Set the mole fractions to the specified values. More... | |
| virtual void | setMoleFractions_NoNorm (const double *const x) |
| Set the mole fractions to the specified values without normalizing. More... | |
| void | getMassFractions (double *const y) const |
| Get the species mass fractions. More... | |
| const double * | massFractions () const |
| Return a const pointer to the mass fraction array. More... | |
| virtual void | setMassFractions (const double *const y) |
| Set the mass fractions to the specified values and normalize them. More... | |
| virtual void | setMassFractions_NoNorm (const double *const y) |
| Set the mass fractions to the specified values without normalizing. More... | |
| virtual void | getConcentrations (double *const c) const |
| Get the species concentrations (kmol/m^3). More... | |
| virtual double | concentration (const size_t k) const |
| Concentration of species k. More... | |
| virtual void | setConcentrations (const double *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... | |
| double | temperature () const |
| Temperature (K). More... | |
| virtual double | electronTemperature () const |
| Electron Temperature (K) More... | |
| virtual double | density () const |
| Density (kg/m^3). More... | |
| virtual double | molarDensity () const |
| Molar density (kmol/m^3). More... | |
| virtual double | molarVolume () const |
| Molar volume (m^3/kmol). More... | |
| virtual void | setDensity (const double density_) |
| Set the internally stored density (kg/m^3) of the phase. More... | |
| virtual void | setElectronTemperature (double etemp) |
| Set the internally stored electron temperature of the phase (K). More... | |
| double | mean_X (const double *const Q) const |
| Evaluate the mole-fraction-weighted mean of an array Q. More... | |
| double | mean_X (const vector< double > &Q) const |
| Evaluate the mole-fraction-weighted mean of an array Q. More... | |
| double | meanMolecularWeight () const |
| The mean molecular weight. Units: (kg/kmol) More... | |
| double | sum_xlogx () const |
| Evaluate \( \sum_k X_k \ln X_k \). More... | |
| size_t | addElement (const string &symbol, double weight=-12345.0, int atomicNumber=0, double entropy298=ENTROPY298_UNKNOWN, int elem_type=CT_ELEM_TYPE_ABSPOS) |
| Add an element. More... | |
| void | addSpeciesAlias (const string &name, const string &alias) |
| Add a species alias (that is, a user-defined alternative species name). More... | |
| virtual vector< string > | findIsomers (const Composition &compMap) const |
| Return a vector with isomers names matching a given composition map. More... | |
| virtual vector< string > | findIsomers (const string &comp) const |
| Return a vector with isomers names matching a given composition string. More... | |
| shared_ptr< Species > | species (const string &name) const |
| Return the Species object for the named species. More... | |
| shared_ptr< Species > | species (size_t k) const |
| Return the Species object for species whose index is k. More... | |
| void | ignoreUndefinedElements () |
| Set behavior when adding a species containing undefined elements to just skip the species. More... | |
| void | addUndefinedElements () |
| Set behavior when adding a species containing undefined elements to add those elements to the phase. More... | |
| void | throwUndefinedElements () |
| Set the behavior when adding a species containing undefined elements to throw an exception. More... | |
Public Attributes | |
| bool | m_useHelgesonFixedForm = false |
| If true, then the fixed for of Helgeson's activity for water is used instead of the rigorous form obtained from Gibbs-Duhem relation. More... | |
| int | m_form_A_Debye = A_DEBYE_CONST |
| Form of the constant outside the Debye-Huckel term called A. More... | |
Protected Member Functions | |
Mechanical Equation of State Properties | |
In this equation of state implementation, the density is a function only of the mole fractions. Therefore, it can't be an independent variable. Instead, the pressure is used as the independent variable. Functions which try to set the thermodynamic state by calling setDensity() will cause an exception to be thrown. | |
| void | calcDensity () override |
| 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 | getUnscaledMolalityActivityCoefficients (double *acMolality) const |
| Get the array of unscaled non-dimensional molality based activity coefficients at the current solution temperature, pressure, and solution concentration. More... | |
| virtual void | applyphScale (double *acMolality) const |
| Apply the current phScale to a set of activity Coefficients or activities. More... | |
| Protected Member Functions inherited from VPStandardStateTP | |
| virtual void | _updateStandardStateThermo () const |
| Updates the standard state thermodynamic functions at the current T and P of the solution. More... | |
| void | invalidateCache () override |
| Invalidate any cached values which are normally updated only when a change in state is detected. More... | |
| const vector< double > & | Gibbs_RT_ref () const |
| Protected Member Functions inherited from Phase | |
| void | assertCompressible (const string &setter) const |
| Ensure that phase is compressible. More... | |
| void | assignDensity (const double density_) |
| Set the internally stored constant density (kg/m^3) of the phase. More... | |
| 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 | |
| int | m_formDH = DHFORM_DILUTE_LIMIT |
| form of the Debye-Huckel parameterization used in the model. More... | |
| vector< int > | m_electrolyteSpeciesType |
| Vector containing the electrolyte species type. More... | |
| vector< double > | m_Aionic |
| a_k = Size of the ionic species in the DH formulation. units = meters More... | |
| double | m_Aionic_default = NAN |
| Default ionic radius for species where it is not specified. More... | |
| double | m_IionicMolality = 0.0 |
| Current value of the ionic strength on the molality scale. More... | |
| double | m_maxIionicStrength |
| Maximum value of the ionic strength allowed in the calculation of the activity coefficients. More... | |
| double | m_IionicMolalityStoich = 0.0 |
| Stoichiometric ionic strength on the molality scale. More... | |
| double | m_A_Debye |
| Current value of the Debye Constant, A_Debye. More... | |
| double | m_B_Debye |
| Current value of the constant that appears in the denominator. More... | |
| vector< double > | m_B_Dot |
| Array of B_Dot values. More... | |
| PDSS_Water * | m_waterSS = nullptr |
| Pointer to the Water standard state object. More... | |
| double | m_densWaterSS = 1000.0 |
| Storage for the density of water's standard state. More... | |
| unique_ptr< WaterProps > | m_waterProps |
| Pointer to the water property calculator. More... | |
| vector< double > | m_tmpV |
| vector of size m_kk, used as a temporary holding area. More... | |
| vector< double > | m_speciesCharge_Stoich |
| Stoichiometric species charge -> This is for calculations of the ionic strength which ignore ion-ion pairing into neutral molecules. More... | |
| Array2D | m_Beta_ij |
| Array of 2D data used in the DHFORM_BETAIJ formulation Beta_ij.value(i,j) is the coefficient of the jth species for the specification of the chemical potential of the ith species. More... | |
| vector< double > | m_lnActCoeffMolal |
| Logarithm of the activity coefficients on the molality scale. More... | |
| vector< double > | m_dlnActCoeffMolaldT |
| Derivative of log act coeff wrt T. More... | |
| vector< double > | m_d2lnActCoeffMolaldT2 |
| 2nd Derivative of log act coeff wrt T More... | |
| vector< double > | m_dlnActCoeffMolaldP |
| Derivative of log act coeff wrt P. More... | |
| Protected Attributes inherited from MolalityVPSSTP | |
| int | m_pHScalingType = PHSCALE_PITZER |
| Scaling to be used for output of single-ion species activity coefficients. More... | |
| size_t | m_indexCLM = npos |
| Index of the phScale species. More... | |
| double | m_weightSolvent = 18.01528 |
| Molecular weight of the Solvent. More... | |
| double | m_xmolSolventMIN = 0.01 |
| In any molality implementation, it makes sense to have a minimum solvent mole fraction requirement, since the implementation becomes singular in the xmolSolvent=0 limit. More... | |
| double | m_Mnaught = 18.01528E-3 |
| This is the multiplication factor that goes inside log expressions involving the molalities of species. More... | |
| vector< double > | m_molalities |
| Current value of the molalities of the species in the phase. More... | |
| Protected Attributes inherited from VPStandardStateTP | |
| double | m_Pcurrent = OneAtm |
| Current value of the pressure - state variable. More... | |
| double | m_minTemp = 0.0 |
| The minimum temperature at which data for all species is valid. More... | |
| double | m_maxTemp = BigNumber |
| The maximum temperature at which data for all species is valid. More... | |
| double | m_Tlast_ss = -1.0 |
| The last temperature at which the standard state thermodynamic properties were calculated at. More... | |
| double | m_Plast_ss = -1.0 |
| The last pressure at which the Standard State thermodynamic properties were calculated at. More... | |
| vector< unique_ptr< PDSS > > | m_PDSS_storage |
| Storage for the PDSS objects for the species. More... | |
| vector< double > | m_h0_RT |
| Vector containing the species reference enthalpies at T = m_tlast and P = p_ref. More... | |
| vector< double > | m_cp0_R |
| Vector containing the species reference constant pressure heat capacities at T = m_tlast and P = p_ref. More... | |
| vector< double > | m_g0_RT |
| Vector containing the species reference Gibbs functions at T = m_tlast and P = p_ref. More... | |
| vector< double > | m_s0_R |
| Vector containing the species reference entropies at T = m_tlast and P = p_ref. More... | |
| vector< double > | m_V0 |
| Vector containing the species reference molar volumes. More... | |
| vector< double > | m_hss_RT |
| Vector containing the species Standard State enthalpies at T = m_tlast and P = m_plast. More... | |
| vector< double > | m_cpss_R |
| Vector containing the species Standard State constant pressure heat capacities at T = m_tlast and P = m_plast. More... | |
| vector< double > | m_gss_RT |
| Vector containing the species Standard State Gibbs functions at T = m_tlast and P = m_plast. More... | |
| vector< double > | m_sss_R |
| Vector containing the species Standard State entropies at T = m_tlast and P = m_plast. More... | |
| vector< double > | m_Vss |
| Vector containing the species standard state volumes at T = m_tlast and P = m_plast. More... | |
| Protected Attributes inherited from ThermoPhase | |
| MultiSpeciesThermo | m_spthermo |
| Pointer to the calculation manager for species reference-state thermodynamic properties. More... | |
| AnyMap | m_input |
| Data supplied via setParameters. More... | |
| double | m_phi = 0.0 |
| Stored value of the electric potential for this phase. Units are Volts. More... | |
| bool | m_chargeNeutralityNecessary = false |
| Boolean indicating whether a charge neutrality condition is a necessity. More... | |
| int | m_ssConvention = cSS_CONVENTION_TEMPERATURE |
| Contains the standard state convention. More... | |
| double | m_tlast = 0.0 |
| 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 = 0 |
| Number of species in the phase. More... | |
| size_t | m_ndim = 3 |
| Dimensionality of the phase. More... | |
| vector< double > | m_speciesComp |
| Atomic composition of the species. More... | |
| vector< double > | m_speciesCharge |
| Vector of species charges. length m_kk. More... | |
| map< string, shared_ptr< Species > > | m_species |
| UndefElement::behavior | m_undefinedElementBehavior = UndefElement::add |
| Flag determining behavior when adding species with an undefined element. More... | |
| bool | m_caseSensitiveSpecies = false |
| Flag determining whether case sensitive species names are enforced. More... | |
Private Member Functions | |
| double | _osmoticCoeffHelgesonFixedForm () const |
| Formula for the osmotic coefficient that occurs in the GWB. More... | |
| double | _lnactivityWaterHelgesonFixedForm () const |
| Formula for the log of the water activity that occurs in the GWB. More... | |
| void | s_update_lnMolalityActCoeff () const |
| Calculate the log activity coefficients. More... | |
| void | s_update_dlnMolalityActCoeff_dT () const |
| Calculation of temperature derivative of activity coefficient. More... | |
| void | s_update_d2lnMolalityActCoeff_dT2 () const |
| Calculate the temperature 2nd derivative of the activity coefficient. More... | |
| void | s_update_dlnMolalityActCoeff_dP () const |
| Calculate the pressure derivative of the activity coefficient. More... | |
Static Private Member Functions | |
| static double | _nonpolarActCoeff (double IionicMolality) |
| Static function that implements the non-polar species salt-out modifications. More... | |
|
explicit |
Full constructor for creating the phase.
| inputFile | File name containing the definition of the phase. If blank, an empty phase will be created. |
| id | id attribute containing the name of the phase. |
Definition at line 33 of file DebyeHuckel.cpp.
|
inlineoverridevirtual |
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 Phase.
Definition at line 430 of file DebyeHuckel.h.
|
overridevirtual |
Molar enthalpy. Units: J/kmol.
Reimplemented from ThermoPhase.
Definition at line 48 of file DebyeHuckel.cpp.
|
overridevirtual |
Molar entropy. Units: J/kmol/K.
For an ideal, constant partial molar volume solution mixture with pure species phases which exhibit zero volume expansivity:
\[ \hat s(T, P, X_k) = \sum_k X_k \hat s^0_k(T) - \hat R \sum_k X_k \ln(X_k) \]
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.
Reimplemented from ThermoPhase.
Definition at line 54 of file DebyeHuckel.cpp.
|
overridevirtual |
Molar Gibbs function. Units: J/kmol.
Reimplemented from ThermoPhase.
Definition at line 60 of file DebyeHuckel.cpp.
|
overridevirtual |
Molar heat capacity at constant pressure. Units: J/kmol/K.
Reimplemented from ThermoPhase.
Definition at line 66 of file DebyeHuckel.cpp.
|
overrideprotectedvirtual |
Calculate the density of the mixture using the partial molar volumes and mole fractions as input.
The formula for this is
\[ \rho = \frac{\sum_k{X_k W_k}}{\sum_k{X_k V_k}} \]
where \( X_k \) are the mole fractions, \( W_k \) are the molecular weights, and \( V_k \) are the pure species molar volumes.
Note, the basis behind this formula is that in an ideal solution the partial molar volumes are equal to the pure species molar volumes. We have additionally specified in this class that the pure species molar volumes are independent of temperature and pressure.
NOTE: This function is not a member of the ThermoPhase base class.
Reimplemented from VPStandardStateTP.
Definition at line 74 of file DebyeHuckel.cpp.
|
overridevirtual |
This method returns an array of generalized concentrations.
\( C^a_k \) are defined such that \( a_k = C^a_k / C^0_k, \) where \( C^0_k \) is a standard concentration defined below and \( a_k \) are activities used in the thermodynamic functions. These activity (or generalized) concentrations are used by kinetics manager classes to compute the forward and reverse rates of elementary reactions. Note that they may or may not have units of concentration — they might be partial pressures, mole fractions, or surface coverages, for example.
| c | Output array of generalized concentrations. The units depend upon the implementation of the reaction rate expressions within the phase. |
Reimplemented from ThermoPhase.
Definition at line 88 of file DebyeHuckel.cpp.
|
overridevirtual |
Return the standard concentration for the kth species.
The standard concentration \( C^0_k \) used to normalize the activity (that is, generalized) concentration in kinetics calculations.
For the time being, we will use the concentration of pure solvent for the the standard concentration of all species. This has the effect of making reaction rates based on the molality of species proportional to the molality of the species.
| k | Optional parameter indicating the species. The default is to assume this refers to species 0. |
Reimplemented from ThermoPhase.
Definition at line 97 of file DebyeHuckel.cpp.
|
overridevirtual |
Get the array of non-dimensional activities at the current solution temperature, pressure, and solution concentration.
(note solvent activity coefficient is on molar scale).
| ac | Output vector of activities. Length: m_kk. |
Reimplemented from ThermoPhase.
Definition at line 103 of file DebyeHuckel.cpp.
|
overridevirtual |
Get the array of non-dimensional molality-based activity coefficients at the current solution temperature, pressure, and solution concentration.
note solvent is on molar scale. The solvent molar based activity coefficient is returned.
Note, most of the work is done in an internal private routine
| acMolality | Vector of Molality-based activity coefficients Length: m_kk |
Reimplemented from MolalityVPSSTP.
Definition at line 117 of file DebyeHuckel.cpp.
|
overridevirtual |
Get the species chemical potentials. Units: J/kmol.
This function returns a vector of chemical potentials of the species in solution.
\[ \mu_k = \mu^{\triangle}_k(T,P) + R T \ln(\gamma_k^{\triangle} m_k) \]
| mu | Output vector of species chemical potentials. Length: m_kk. Units: J/kmol |
Reimplemented from ThermoPhase.
Definition at line 130 of file DebyeHuckel.cpp.
|
overridevirtual |
Returns an array of partial molar enthalpies for the species in the mixture.
Units (J/kmol)
For this phase, the partial molar enthalpies are equal to the standard state enthalpies modified by the derivative of the molality-based activity coefficient wrt temperature
\[ \bar h_k(T,P) = h^{\triangle}_k(T,P) - R T^2 \frac{d \ln(\gamma_k^\triangle)}{dT} \]
The solvent partial molar enthalpy is equal to
\[ \bar h_o(T,P) = h^{o}_o(T,P) - R T^2 \frac{d \ln(a_o}{dT} \]
The temperature dependence of the activity coefficients currently only occurs through the temperature dependence of the Debye constant.
| hbar | Output vector of species partial molar enthalpies. Length: m_kk. units are J/kmol. |
Reimplemented from ThermoPhase.
Definition at line 150 of file DebyeHuckel.cpp.
|
overridevirtual |
Returns an array of partial molar entropies of the species in the solution.
Units: J/kmol/K. Maxwell's equations provide an insight in how to calculate this (p.215 Smith and Van Ness)
\[ \frac{d\mu_i}{dT} = -\bar{s}_i \]
For this phase, the partial molar entropies are equal to the SS species entropies plus the ideal solution contribution:
\[ \bar s_k(T,P) = \hat s^0_k(T) - R \ln(M0 * molality[k]) \]
\[ \bar s_{solvent}(T,P) = \hat s^0_{solvent}(T) - R ((xmolSolvent - 1.0) / xmolSolvent) \]
The reference-state pure-species entropies, \( \hat s^0_k(T) \), at the reference pressure, \( P_{ref} \), are computed by the species thermodynamic property manager. They are polynomial functions of temperature.
| sbar | Output vector of species partial molar entropies. Length = m_kk. units are J/kmol/K. |
Reimplemented from ThermoPhase.
Definition at line 175 of file DebyeHuckel.cpp.
|
overridevirtual |
Return an array of partial molar heat capacities for the species in the mixture.
Units: J/kmol/K
| 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 225 of file DebyeHuckel.cpp.
|
overridevirtual |
Return an array of partial molar volumes for the species in the mixture.
Units: m^3/kmol.
For this solution, the partial molar volumes are normally equal to the constant species molar volumes, except when the activity coefficients depend on pressure.
The general relation is
vbar_i = d(chemPot_i)/dP at const T, n
= V0_i + d(Gex)/dP)_T,M
= V0_i + RT d(lnActCoeffi)dP _T,M
| vbar | Output vector of species partial molar volumes. Length = m_kk. units are m^3/kmol. |
Reimplemented from ThermoPhase.
Definition at line 213 of file DebyeHuckel.cpp.
|
overridevirtual |
Returns true if the species was successfully added, or false if the species was ignored.
Derived classes which need to size arrays according to the number of species should overload this method. The derived class implementation should call the base class method, and, if this returns true (indicating that the species has been added), adjust their array sizes accordingly.
Reimplemented from Phase.
Definition at line 643 of file DebyeHuckel.cpp.
|
overridevirtual |
Initialize the ThermoPhase object after all species have been set up.
This method is provided to allow subclasses to perform any initialization required after all species have been added. For example, it might be used to resize internal work arrays that must have an entry for each species. The base class implementation does nothing, and subclasses that do not require initialization do not need to overload this method. Derived classes which do override this function should call their parent class's implementation of this function as their last action.
When importing from an AnyMap phase description (or from a YAML file), setupPhase() adds all the species, stores the input data in m_input, and then calls this method to set model parameters from the data stored in m_input.
Reimplemented from ThermoPhase.
Definition at line 356 of file DebyeHuckel.cpp.
|
overridevirtual |
Store the parameters of a ThermoPhase object such that an identical one could be reconstructed using the newThermo(AnyMap&) function.
This does not include user-defined fields available in input().
Reimplemented from ThermoPhase.
Definition at line 414 of file DebyeHuckel.cpp.
|
overridevirtual |
Get phase-specific parameters of a Species object such that an identical one could be reconstructed and added to this phase.
| name | Name of the species |
| speciesNode | Mapping to be populated with parameters |
Reimplemented from ThermoPhase.
Definition at line 479 of file DebyeHuckel.cpp.
|
virtual |
Return the Debye Huckel constant as a function of temperature and pressure (Units = sqrt(kg/gmol))
The default is to assume that it is constant, given in the initialization process, and stored in the member double, m_A_Debye. Optionally, a full water treatment may be employed that makes \( A_{Debye} \) a full function of T and P.
\[ A_{Debye} = \frac{F e B_{Debye}}{8 \pi \epsilon R T} {\left( C_o \tilde{M}_o \right)}^{1/2} \]
where
\[ B_{Debye} = \frac{F} {{(\frac{\epsilon R T}{2})}^{1/2}} \]
Therefore:
\[ A_{Debye} = \frac{1}{8 \pi} {\left(\frac{2 N_a \rho_o}{1000}\right)}^{1/2} {\left(\frac{N_a e^2}{\epsilon R T }\right)}^{3/2} \]
where
Nominal value at 298 K and 1 atm = 1.172576 (kg/gmol)^(1/2) based on:
| temperature | Temperature in kelvin. Defaults to -1, in which case the temperature of the phase is assumed. |
| pressure | Pressure (Pa). Defaults to -1, in which case the pressure of the phase is assumed. |
Definition at line 536 of file DebyeHuckel.cpp.
|
virtual |
Value of the derivative of the Debye Huckel constant with respect to temperature.
This is a function of temperature and pressure. See A_Debye_TP() for a definition of \( A_{Debye} \).
Units = sqrt(kg/gmol) K-1
| temperature | Temperature in kelvin. Defaults to -1, in which case the temperature of the phase is assumed. |
| pressure | Pressure (Pa). Defaults to -1, in which case the pressure of the phase is assumed. |
Definition at line 562 of file DebyeHuckel.cpp.
|
virtual |
Value of the 2nd derivative of the Debye Huckel constant with respect to temperature as a function of temperature and pressure.
This is a function of temperature and pressure. See A_Debye_TP() for a definition of \( A_{Debye} \).
Units = sqrt(kg/gmol) K-2
| temperature | Temperature in kelvin. Defaults to -1, in which case the temperature of the phase is assumed. |
| pressure | Pressure (Pa). Defaults to -1, in which case the pressure of the phase is assumed. |
Definition at line 586 of file DebyeHuckel.cpp.
|
virtual |
Value of the derivative of the Debye Huckel constant with respect to pressure, as a function of temperature and pressure.
This is a function of temperature and pressure. See A_Debye_TP() for a definition of \( A_{Debye} \).
Units = sqrt(kg/gmol) Pa-1
| temperature | Temperature in kelvin. Defaults to -1, in which case the temperature of the phase is assumed. |
| pressure | Pressure (Pa). Defaults to -1, in which case the pressure of the phase is assumed. |
Definition at line 610 of file DebyeHuckel.cpp.
| double AionicRadius | ( | int | k = 0 | ) | const |
Reports the ionic radius of the kth species.
| k | species index. |
Definition at line 636 of file DebyeHuckel.cpp.
| void setDebyeHuckelModel | ( | const string & | form | ) |
Set the DebyeHuckel parameterization form.
Must be one of 'dilute-limit', 'B-dot-with-variable-a', 'B-dot-with-common-a', 'beta_ij', or 'Pitzer-with-beta_ij'.
Definition at line 281 of file DebyeHuckel.cpp.
|
inline |
Returns the form of the Debye-Huckel parameterization used.
Definition at line 733 of file DebyeHuckel.h.
| void setA_Debye | ( | double | A | ) |
Set the A_Debye parameter.
If a negative value is provided, enables calculation of A_Debye using the detailed water equation of state.
Definition at line 305 of file DebyeHuckel.cpp.
| void setDefaultIonicRadius | ( | double | value | ) |
Set the default ionic radius [m] for each species.
Definition at line 332 of file DebyeHuckel.cpp.
| void setBeta | ( | const string & | sp1, |
| const string & | sp2, | ||
| double | value | ||
| ) |
Set the value for the beta interaction between species sp1 and sp2.
Definition at line 342 of file DebyeHuckel.cpp.
|
inline |
Returns a reference to M_Beta_ij.
Definition at line 753 of file DebyeHuckel.h.
|
staticprivate |
Static function that implements the non-polar species salt-out modifications.
Returns the calculated activity coefficients.
| IionicMolality | Value of the ionic molality (sqrt(gmol/kg)) |
Definition at line 690 of file DebyeHuckel.cpp.
|
private |
Formula for the osmotic coefficient that occurs in the GWB.
It is originally from Helgeson for a variable NaCl brine. It's to be used with extreme caution.
Definition at line 704 of file DebyeHuckel.cpp.
|
private |
Formula for the log of the water activity that occurs in the GWB.
It is originally from Helgeson for a variable NaCl brine. It's to be used with extreme caution.
Definition at line 723 of file DebyeHuckel.cpp.
|
private |
Calculate the log activity coefficients.
This function updates the internally stored natural logarithm of the molality activity coefficients. This is the main routine for implementing the activity coefficient formulation.
Definition at line 738 of file DebyeHuckel.cpp.
|
private |
Calculation of temperature derivative of activity coefficient.
Using internally stored values, this function calculates the temperature derivative of the logarithm of the activity coefficient for all species in the mechanism.
We assume that the activity coefficients are current in this routine. The solvent activity coefficient is on the molality scale. Its derivative is too.
Definition at line 961 of file DebyeHuckel.cpp.
|
private |
Calculate the temperature 2nd derivative of the activity coefficient.
Using internally stored values, this function calculates the temperature 2nd derivative of the logarithm of the activity coefficient for all species in the mechanism.
We assume that the activity coefficients are current in this routine. Solvent activity coefficient is on the molality scale. Its derivatives are too.
Definition at line 1071 of file DebyeHuckel.cpp.
|
private |
Calculate the pressure derivative of the activity coefficient.
Using internally stored values, this function calculates the pressure derivative of the logarithm of the activity coefficient for all species in the mechanism.
We assume that the activity coefficients, molalities, and A_Debye are current. Solvent activity coefficient is on the molality scale. Its derivatives are too.
Definition at line 1177 of file DebyeHuckel.cpp.
|
protected |
form of the Debye-Huckel parameterization used in the model.
The options are described at the top of this document, and in the general documentation. The list is repeated here:
DHFORM_DILUTE_LIMIT = 0 (default) DHFORM_BDOT_AK = 1 DHFORM_BDOT_AUNIFORM = 2 DHFORM_BETAIJ = 3 DHFORM_PITZER_BETAIJ = 4
Definition at line 794 of file DebyeHuckel.h.
|
protected |
Vector containing the electrolyte species type.
The possible types are:
Definition at line 807 of file DebyeHuckel.h.
|
protected |
a_k = Size of the ionic species in the DH formulation. units = meters
Definition at line 810 of file DebyeHuckel.h.
|
protected |
Default ionic radius for species where it is not specified.
Definition at line 813 of file DebyeHuckel.h.
|
mutableprotected |
Current value of the ionic strength on the molality scale.
Definition at line 816 of file DebyeHuckel.h.
|
protected |
Maximum value of the ionic strength allowed in the calculation of the activity coefficients.
Definition at line 820 of file DebyeHuckel.h.
| bool m_useHelgesonFixedForm = false |
If true, then the fixed for of Helgeson's activity for water is used instead of the rigorous form obtained from Gibbs-Duhem relation.
This should be used with caution, and is really only included as a validation exercise.
Definition at line 827 of file DebyeHuckel.h.
|
mutableprotected |
Stoichiometric ionic strength on the molality scale.
Definition at line 830 of file DebyeHuckel.h.
| int m_form_A_Debye = A_DEBYE_CONST |
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 849 of file DebyeHuckel.h.
|
mutableprotected |
Current value of the Debye Constant, A_Debye.
A_Debye -> this expression appears on the top of the ln actCoeff term in the general Debye-Huckel expression It depends on temperature and pressure.
A_Debye = (F e B_Debye) / (8 Pi epsilon R T)
Units = sqrt(kg/gmol)
Nominal value(298K, atm) = 1.172576 sqrt(kg/gmol) based on: epsilon/epsilon_0 = 78.54 (water at 25C) T = 298.15 K B_Debye = 3.28640E9 sqrt(kg/gmol)/m
note in Pitzer's nomenclature, A_phi = A_Debye/3.0
Definition at line 871 of file DebyeHuckel.h.
|
protected |
Current value of the constant that appears in the denominator.
B_Debye -> this expression appears on the bottom of the ln actCoeff term in the general Debye-Huckel expression It depends on temperature
B_Bebye = F / sqrt( epsilon R T / 2 )
Units = sqrt(kg/gmol) / m
Nominal value = 3.28640E9 sqrt(kg/gmol) / m based on: epsilon/epsilon_0 = 78.54 (water at 25C) T = 298.15 K
Definition at line 889 of file DebyeHuckel.h.
|
protected |
Array of B_Dot values.
This expression is an extension of the Debye-Huckel expression used in some formulations to extend DH to higher molalities. B_dot is specific to the major ionic pair.
Definition at line 897 of file DebyeHuckel.h.
|
protected |
Pointer to the Water standard state object.
derived from the equation of state for water.
Definition at line 903 of file DebyeHuckel.h.
|
protected |
Storage for the density of water's standard state.
Density depends on temperature and pressure.
Definition at line 909 of file DebyeHuckel.h.
|
protected |
Pointer to the water property calculator.
Definition at line 912 of file DebyeHuckel.h.
|
mutableprotected |
vector of size m_kk, used as a temporary holding area.
Definition at line 915 of file DebyeHuckel.h.
|
protected |
Stoichiometric species charge -> This is for calculations of the ionic strength which ignore ion-ion pairing into neutral molecules.
The Stoichiometric species charge is the charge of one of the ion that would occur if the species broke into two charged ion pairs. NaCl -> m_speciesCharge_Stoich = -1; HSO4- -> H+ + SO42- = -2 -> The other charge is calculated. For species that aren't ion pairs, it's equal to the m_speciesCharge[] value.
Definition at line 929 of file DebyeHuckel.h.
|
protected |
Array of 2D data used in the DHFORM_BETAIJ formulation Beta_ij.value(i,j) is the coefficient of the jth species for the specification of the chemical potential of the ith species.
Definition at line 937 of file DebyeHuckel.h.
|
mutableprotected |
Logarithm of the activity coefficients on the molality scale.
mutable because we change this if the composition or temperature or pressure changes.
Definition at line 944 of file DebyeHuckel.h.
|
mutableprotected |
Derivative of log act coeff wrt T.
Definition at line 947 of file DebyeHuckel.h.
|
mutableprotected |
2nd Derivative of log act coeff wrt T
Definition at line 950 of file DebyeHuckel.h.
|
mutableprotected |
Derivative of log act coeff wrt P.
Definition at line 953 of file DebyeHuckel.h.
1.9.1