HMWSoln Class Reference

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:

Detailed Description

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

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

Specification of Species Standard State Properties

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

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

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

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

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

The enthalpy function is given by the following relation.

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

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

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

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

The current model assumes that an incompressible molar volume for all solutes. The molar volume for the water solvent, however, is obtained from a pure water equation of state, waterSS. Therefore, the water standard state varies with both T and P. It is an error to request standard state water properties at a T and P where the water phase is not a stable phase, that is, beyond its spinodal curve.

Specification of Solution Thermodynamic Properties

Chemical potentials of the solutes, \( \mu_k \), and the solvent, \( \mu_o \), which are based on the molality form, have the following general format:

\[ \mu_k = \mu^{\triangle}_k(T,P) + R T \ln(\gamma_k^{\triangle} \frac{m_k}{m^\triangle}) \]

\[ \mu_o = \mu^o_o(T,P) + RT \ln(a_o) \]

where \( \gamma_k^{\triangle} \) is the molality based activity coefficient for species \( k \).

Individual activity coefficients of ions can not be independently measured. Instead, only binary pairs forming electroneutral solutions can be measured. This problem leads to a redundancy in the evaluation of species standard state properties. The redundancy issue is resolved by setting the standard state chemical potential enthalpy, entropy, and volume for the hydrogen ion, H+, to zero, for every temperature and pressure. After this convention is applied, all other standard state properties of ionic species contain meaningful information.

Ionic Strength

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

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

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

Specification of the Excess Gibbs Free Energy

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

\[ G = G^{id} + G^{ex} \]

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

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

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

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

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

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

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

\( I \) is the ionic strength of the solution, and is given by:

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

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

The function \( Z \) is given by

\[ Z = \sum_i m_i \left| z_i \right| \]

The value of \( B_{ca} \) is given by the following function

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

where

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

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

The \( \Phi_{c{c'}} \) and \( \Phi_{a{a'}} \) formulations are slightly more complicated. \( b \) is a universal constant defined to be equal to \( 1.2\ kg^{1/2}\ gmol^{-1/2} \). The exponential coefficient \( \alpha^{(1)}_{ca} \) is usually fixed at \( \alpha^{(1)}_{ca} = 2.0\ kg^{1/2} gmol^{-1/2} \) except for 2-2 electrolytes, while other parameters were fit to experimental data. For 2-2 electrolytes, \( \alpha^{(1)}_{ca} = 1.4\ kg^{1/2}\ gmol^{-1/2} \) is used in combination with either \( \alpha^{(2)}_{ca} = 12\ kg^{1/2}\ gmol^{-1/2} \) or \( \alpha^{(2)}_{ca} = k A_\psi \), where k is a constant. For electrolytes other than 2-2 electrolytes the \( \beta^{(2)}_{ca} g(\alpha^{(2)}_{ca} \sqrt{I}) \) term is not used in the fitting procedure; it is only used for divalent metal sulfates 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 Silvester and Pitzer [42], 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 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.

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 [14]. 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 value, specified for pair of cations or a pair of anions.

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.

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 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.

An example phase definition specifying a number of the above species interaction parameters is given in the YAML API Reference.

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

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.

Definition at line 777 of file HMWSoln.h.

Public Member Functions
	HMWSoln (const string &inputFile="", const string &id="")
	Construct and initialize an HMWSoln ThermoPhase object directly from an input file.
double	satPressure (double T) override
	Get the saturation pressure for a given temperature.
void	setBinarySalt (const string &sp1, const string &sp2, size_t nParams, double *beta0, double *beta1, double *beta2, double *Cphi, double alpha1, double alpha2)
void	setTheta (const string &sp1, const string &sp2, size_t nParams, double *theta)
void	setPsi (const string &sp1, const string &sp2, const string &sp3, size_t nParams, double *psi)
void	setLambda (const string &sp1, const string &sp2, size_t nParams, double *lambda)
void	setMunnn (const string &sp, size_t nParams, double *munnn)
void	setZeta (const string &sp1, const string &sp2, const string &sp3, size_t nParams, double *psi)
void	setPitzerTempModel (const string &model)
void	setPitzerRefTemperature (double Tref)
void	setA_Debye (double A)
	Set the A_Debye parameter.
void	setMaxIonicStrength (double Imax)
void	setCroppingCoefficients (double ln_gamma_k_min, double ln_gamma_k_max, double ln_gamma_o_min, double ln_gamma_o_max)
void	initThermo () override
	Initialize the ThermoPhase object after all species have been set up.
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.
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.
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.
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.
double	ADebye_L (double temperature=-1.0, double pressure=-1.0) const
	Return Pitzer's definition of A_L.
double	ADebye_J (double temperature=-1.0, double pressure=-1.0) const
	Return Pitzer's definition of A_J.
double	ADebye_V (double temperature=-1.0, double pressure=-1.0) const
	Return Pitzer's definition of A_V.
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.
void	printCoeffs () const
	Print out all of the input Pitzer coefficients.
void	getUnscaledMolalityActivityCoefficients (double *acMolality) const override
	Get the array of unscaled non-dimensional molality based activity coefficients at the current solution temperature, pressure, and solution concentration.
Utilities
string	type () const override
	String indicating the thermodynamic model implemented.
Molar Thermodynamic Properties of the Solution
double	enthalpy_mole () const override
	Molar enthalpy. Units: J/kmol.
virtual double	relative_enthalpy () const
	Excess molar enthalpy of the solution from the mixing process.
virtual double	relative_molal_enthalpy () const
	Excess molar enthalpy of the solution from the mixing process on a molality basis.
double	entropy_mole () const override
	Molar entropy. Units: J/kmol/K.
double	gibbs_mole () const override
	Molar Gibbs function. Units: J/kmol.
double	cp_mole () const override
	Molar heat capacity at constant pressure. Units: J/kmol/K.
double	cv_mole () const override
	Molar heat capacity at constant volume. Units: J/kmol/K.
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 activity concentrations.
double	standardConcentration (size_t k=0) const override
	Return the standard concentration for the kth species.
void	getActivities (double *ac) const override
	Get the array of non-dimensional activities at the current solution temperature, pressure, and solution concentration.
Partial Molar Properties of the Solution
void	getChemPotentials (double *mu) const override
	Get the species chemical potentials. Units: J/kmol.
void	getPartialMolarEnthalpies (double *hbar) const override
	Returns an array of partial molar enthalpies for the species in the mixture.
void	getPartialMolarEntropies (double *sbar) const override
	Returns an array of partial molar entropies of the species in the solution.
void	getPartialMolarVolumes (double *vbar) const override
	Return an array of partial molar volumes for the species in the mixture.
void	getPartialMolarCp (double *cpbar) const override
	Return an array of partial molar heat capacities for the species in the mixture.
Public Member Functions inherited from MolalityVPSSTP
	MolalityVPSSTP ()
	Default Constructor.
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.
void	setState_TPM (double t, double p, const Composition &m)
	Set the temperature (K), pressure (Pa), and molalities.
void	setState_TPM (double t, double p, const string &m)
	Set the temperature (K), pressure (Pa), and molalities.
void	setState (const AnyMap &state) override
	Set the state using an AnyMap containing any combination of properties supported by the thermodynamic model.
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.
string	report (bool show_thermo=true, double threshold=1e-14) const override
	returns a summary of the state of the phase as a string
string	phaseOfMatter () const override
	String indicating the mechanical phase of the matter in this Phase.
void	setpHScale (const int pHscaleType)
	Set the pH scale, which determines the scale for single-ion activity coefficients.
int	pHScale () const
	Reports the pH scale, which determines the scale for single-ion activity coefficients.
void	setMoleFSolventMin (double xmolSolventMIN)
	Sets the minimum mole fraction in the molality formulation.
double	moleFSolventMin () const
	Returns the minimum mole fraction in the molality formulation.
void	calcMolalities () const
	Calculates the molality of all species and stores the result internally.
void	getMolalities (double *const molal) const
	This function will return the molalities of the species.
void	setMolalities (const double *const molal)
	Set the molalities of the solutes in a phase.
void	setMolalitiesByName (const Composition &xMap)
	Set the molalities of a phase.
void	setMolalitiesByName (const string &name)
	Set the molalities of a phase.
int	activityConvention () const override
	We set the convention to molality here.
void	getActivityConcentrations (double *c) const override
	This method returns an array of generalized concentrations.
double	standardConcentration (size_t k=0) const override
	Return the standard concentration for the kth species.
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.
void	getActivityCoefficients (double *ac) const override
	Get the array of non-dimensional activity coefficients at the current solution temperature, pressure, and solution concentration.
virtual void	getMolalityActivityCoefficients (double *acMolality) const
	Get the array of non-dimensional molality based activity coefficients at the current solution temperature, pressure, and solution concentration.
virtual double	osmoticCoefficient () const
	Calculate the osmotic coefficient.
bool	addSpecies (shared_ptr< Species > spec) override
	Add a Species to this Phase.
void	initThermo () override
	Initialize the ThermoPhase object after all species have been set up.
Public Member Functions inherited from VPStandardStateTP
void	setTemperature (const double temp) override
	Set the temperature of the phase.
void	setPressure (double p) override
	Set the internally stored pressure (Pa) at constant temperature and composition.
void	setState_TP (double T, double pres) override
	Set the temperature and pressure at the same time.
double	pressure () const override
	Returns the current pressure of the phase.
virtual void	updateStandardStateThermo () const
	Updates the standard state thermodynamic functions at the current T and P of the solution.
double	minTemp (size_t k=npos) const override
	Minimum temperature for which the thermodynamic data for the species or phase are valid.
double	maxTemp (size_t k=npos) const override
	Maximum temperature for which the thermodynamic data for the species are valid.
PDSS *	providePDSS (size_t k)
const PDSS *	providePDSS (size_t k) const
	VPStandardStateTP ()
	Constructor.
bool	isCompressible () const override
	Return whether phase represents a compressible substance.
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.
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.
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.
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.
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.
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.
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.
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.
void	getStandardVolumes (double *vol) const override
	Get the molar volumes of the species standard states at the current T and P of the solution.
virtual const vector< double > &	getStandardVolumes () const
void	initThermo () override
	Initialize the ThermoPhase object after all species have been set up.
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.
bool	addSpecies (shared_ptr< Species > spec) override
	Add a Species to this Phase.
void	installPDSS (size_t k, unique_ptr< PDSS > &&pdss)
	Install a PDSS object for species k
virtual bool	addSpecies (shared_ptr< Species > spec)
	Add a Species to this Phase.
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.
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.
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.
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.
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.
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.
Public Member Functions inherited from ThermoPhase
	ThermoPhase ()=default
	Constructor.
double	RT () const
	Return the Gas Constant multiplied by the current temperature.
double	equivalenceRatio () const
	Compute the equivalence ratio for the current mixture from available oxygen and required oxygen.
virtual AnyMap	getAuxiliaryData ()
	Return intermediate or model-specific parameters used by particular derived classes.
string	type () const override
	String indicating the thermodynamic model implemented.
virtual bool	isIdeal () const
	Boolean indicating whether phase is ideal.
virtual double	refPressure () const
	Returns the reference pressure in Pa.
double	Hf298SS (const size_t k) const
	Report the 298 K Heat of Formation of the standard state of one species (J kmol-1)
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)
virtual void	resetHf298 (const size_t k=npos)
	Restore the original heat of formation of one or more species.
bool	chargeNeutralityNecessary () const
	Returns the chargeNeutralityNecessity boolean.
virtual double	intEnergy_mole () const
	Molar internal energy. Units: J/kmol.
virtual double	isothermalCompressibility () const
	Returns the isothermal compressibility. Units: 1/Pa.
virtual double	thermalExpansionCoeff () const
	Return the volumetric thermal expansion coefficient. Units: 1/K.
virtual double	soundSpeed () const
	Return the speed of sound. Units: m/s.
void	setElectricPotential (double v)
	Set the electric potential of this phase (V).
double	electricPotential () const
	Returns the electric potential of this phase (V).
virtual Units	standardConcentrationUnits () const
	Returns the units of the "standard concentration" for this phase.
virtual double	logStandardConc (size_t k=0) const
	Natural logarithm of the standard concentration of the kth species.
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.
void	getElectrochemPotentials (double *mu) const
	Get the species electrochemical potentials.
virtual void	getPartialMolarIntEnergies (double *ubar) const
	Return an array of partial molar internal energies for the species in the mixture.
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.
double	enthalpy_mass () const
	Specific enthalpy. Units: J/kg.
double	intEnergy_mass () const
	Specific internal energy. Units: J/kg.
double	entropy_mass () const
	Specific entropy. Units: J/kg/K.
double	gibbs_mass () const
	Specific Gibbs function. Units: J/kg.
double	cp_mass () const
	Specific heat at constant pressure. Units: J/kg/K.
double	cv_mass () const
	Specific heat at constant volume. Units: J/kg/K.
virtual void	setState_TPX (double t, double p, const double *x)
	Set the temperature (K), pressure (Pa), and mole fractions.
virtual void	setState_TPX (double t, double p, const Composition &x)
	Set the temperature (K), pressure (Pa), and mole fractions.
virtual void	setState_TPX (double t, double p, const string &x)
	Set the temperature (K), pressure (Pa), and mole fractions.
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.
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.
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.
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.
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).
virtual void	setState_SP (double s, double p, double tol=1e-9)
	Set the specific entropy (J/kg/K) and pressure (Pa).
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).
virtual void	setState_ST (double s, double t, double tol=1e-9)
	Set the specific entropy (J/kg/K) and temperature (K).
virtual void	setState_TV (double t, double v, double tol=1e-9)
	Set the temperature (K) and specific volume (m^3/kg).
virtual void	setState_PV (double p, double v, double tol=1e-9)
	Set the pressure (Pa) and specific volume (m^3/kg).
virtual void	setState_UP (double u, double p, double tol=1e-9)
	Set the specific internal energy (J/kg) and pressure (Pa).
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)
virtual void	setState_TH (double t, double h, double tol=1e-9)
	Set the temperature (K) and the specific enthalpy (J/kg)
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)
virtual void	setState_DP (double rho, double p)
	Set the density (kg/m**3) and pressure (Pa) at constant composition.
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)
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)
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)
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.
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.
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.
void	setEquivalenceRatio (double phi, const double *fuelComp, const double *oxComp, ThermoBasis basis=ThermoBasis::molar)
	Set the mixture composition according to the equivalence ratio.
void	setEquivalenceRatio (double phi, const string &fuelComp, const string &oxComp, ThermoBasis basis=ThermoBasis::molar)
	Set the mixture composition according to the equivalence ratio.
void	setEquivalenceRatio (double phi, const Composition &fuelComp, const Composition &oxComp, ThermoBasis basis=ThermoBasis::molar)
	Set the mixture composition according to the equivalence ratio.
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.
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.
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.
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.
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.
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.
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.
virtual void	setToEquilState (const double *mu_RT)
	This method is used by the ChemEquil equilibrium solver.
virtual bool	compatibleWithMultiPhase () const
	Indicates whether this phase type can be used with class MultiPhase for equilibrium calculations.
virtual double	critTemperature () const
	Critical temperature (K).
virtual double	critPressure () const
	Critical pressure (Pa).
virtual double	critVolume () const
	Critical volume (m3/kmol).
virtual double	critCompressibility () const
	Critical compressibility (unitless).
virtual double	critDensity () const
	Critical density (kg/m3).
virtual double	satTemperature (double p) const
	Return the saturation temperature given the pressure.
virtual double	vaporFraction () const
	Return the fraction of vapor at the current conditions.
virtual void	setState_Tsat (double t, double x)
	Set the state to a saturated system at a particular temperature.
virtual void	setState_Psat (double p, double x)
	Set the state to a saturated system at a particular pressure.
void	setState_TPQ (double T, double P, double Q)
	Set the temperature, pressure, and vapor fraction (quality).
void	modifySpecies (size_t k, shared_ptr< Species > spec) override
	Modify the thermodynamic data associated with a species.
virtual MultiSpeciesThermo &	speciesThermo (int k=-1)
	Return a changeable reference to the calculation manager for species reference-state thermodynamic properties.
virtual const MultiSpeciesThermo &	speciesThermo (int k=-1) const
void	initThermoFile (const string &inputFile, const string &id)
	Initialize a ThermoPhase object using an input file.
virtual void	setParameters (const AnyMap &phaseNode, const AnyMap &rootNode=AnyMap())
	Set equation of state parameters from an AnyMap phase description.
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.
const AnyMap &	input () const
	Access input data associated with the phase description.
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.
virtual void	getdlnActCoeffdlnX_diag (double *dlnActCoeffdlnX_diag) const
	Get the array of ln mole fraction derivatives of the log activity coefficients - diagonal component only.
virtual void	getdlnActCoeffdlnN_diag (double *dlnActCoeffdlnN_diag) const
	Get the array of log species mole number derivatives of the log activity coefficients.
virtual void	getdlnActCoeffdlnN_numderiv (const size_t ld, double *const dlnActCoeffdlnN)
Public Member Functions inherited from Phase
	Phase ()=default
	Default constructor.
	Phase (const Phase &)=delete
Phase &	operator= (const Phase &)=delete
virtual bool	isPure () const
	Return whether phase represents a pure (single species) substance.
virtual bool	hasPhaseTransition () const
	Return whether phase represents a substance with phase transitions.
virtual bool	isCompressible () const
	Return whether phase represents a compressible substance.
virtual map< string, size_t >	nativeState () const
	Return a map of properties defining the native state of a substance.
string	nativeMode () const
	Return string acronym representing the native state of a Phase.
virtual vector< string >	fullStates () const
	Return a vector containing full states defining a phase.
virtual vector< string >	partialStates () const
	Return a vector of settable partial property sets within a phase.
virtual size_t	stateSize () const
	Return size of vector defining internal state of the phase.
void	saveState (vector< double > &state) const
	Save the current internal state of the phase.
virtual void	saveState (size_t lenstate, double *state) const
	Write to array 'state' the current internal state.
void	restoreState (const vector< double > &state)
	Restore a state saved on a previous call to saveState.
virtual void	restoreState (size_t lenstate, const double *state)
	Restore the state of the phase from a previously saved state vector.
double	molecularWeight (size_t k) const
	Molecular weight of species k.
void	getMolecularWeights (double *weights) const
	Copy the vector of molecular weights into array weights.
const vector< double > &	molecularWeights () const
	Return a const reference to the internal vector of molecular weights.
const vector< double > &	inverseMolecularWeights () const
	Return a const reference to the internal vector of molecular weights.
void	getCharges (double *charges) const
	Copy the vector of species charges into array charges.
virtual void	setMolesNoTruncate (const double *const N)
	Set the state of the object with moles in [kmol].
double	elementalMassFraction (const size_t m) const
	Elemental mass fraction of element m.
double	elementalMoleFraction (const size_t m) const
	Elemental mole fraction of element m.
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.
double	chargeDensity () const
	Charge density [C/m^3].
size_t	nDim () const
	Returns the number of spatial dimensions (1, 2, or 3)
void	setNDim (size_t ndim)
	Set the number of spatial dimensions (1, 2, or 3).
virtual bool	ready () const
	Returns a bool indicating whether the object is ready for use.
int	stateMFNumber () const
	Return the State Mole Fraction Number.
virtual void	invalidateCache ()
	Invalidate any cached values which are normally updated only when a change in state is detected.
bool	caseSensitiveSpecies () const
	Returns true if case sensitive species names are enforced.
void	setCaseSensitiveSpecies (bool cflag=true)
	Set flag that determines whether case sensitive species are enforced in look-up operations, for example speciesIndex.
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.
void	massFractionsToMoleFractions (const double *Y, double *X) const
	Converts a mixture composition from mole fractions to mass fractions.
void	moleFractionsToMassFractions (const double *X, double *Y) const
	Converts a mixture composition from mass fractions to mole fractions.
string	name () const
	Return the name of the phase.
void	setName (const string &nm)
	Sets the string name for the phase.
string	elementName (size_t m) const
	Name of the element with index m.
size_t	elementIndex (const string &name) const
	Return the index of element named 'name'.
const vector< string > &	elementNames () const
	Return a read-only reference to the vector of element names.
double	atomicWeight (size_t m) const
	Atomic weight of element m.
double	entropyElement298 (size_t m) const
	Entropy of the element in its standard state at 298 K and 1 bar.
int	atomicNumber (size_t m) const
	Atomic number of element m.
int	elementType (size_t m) const
	Return the element constraint type Possible types include:
int	changeElementType (int m, int elem_type)
	Change the element type of the mth constraint Reassigns an element type.
const vector< double > &	atomicWeights () const
	Return a read-only reference to the vector of atomic weights.
size_t	nElements () const
	Number of elements.
void	checkElementIndex (size_t m) const
	Check that the specified element index is in range.
void	checkElementArraySize (size_t mm) const
	Check that an array size is at least nElements().
double	nAtoms (size_t k, size_t m) const
	Number of atoms of element m in species k.
size_t	speciesIndex (const string &name) const
	Returns the index of a species named 'name' within the Phase object.
string	speciesName (size_t k) const
	Name of the species with index k.
const vector< string > &	speciesNames () const
	Return a const reference to the vector of species names.
size_t	nSpecies () const
	Returns the number of species in the phase.
void	checkSpeciesIndex (size_t k) const
	Check that the specified species index is in range.
void	checkSpeciesArraySize (size_t kk) const
	Check that an array size is at least nSpecies().
void	setMoleFractionsByName (const Composition &xMap)
	Set the species mole fractions by name.
void	setMoleFractionsByName (const string &x)
	Set the mole fractions of a group of species by name.
void	setMassFractionsByName (const Composition &yMap)
	Set the species mass fractions by name.
void	setMassFractionsByName (const string &x)
	Set the species mass fractions by name.
void	setState_TD (double t, double rho)
	Set the internally stored temperature (K) and density (kg/m^3)
Composition	getMoleFractionsByName (double threshold=0.0) const
	Get the mole fractions by name.
double	moleFraction (size_t k) const
	Return the mole fraction of a single species.
double	moleFraction (const string &name) const
	Return the mole fraction of a single species.
Composition	getMassFractionsByName (double threshold=0.0) const
	Get the mass fractions by name.
double	massFraction (size_t k) const
	Return the mass fraction of a single species.
double	massFraction (const string &name) const
	Return the mass fraction of a single species.
void	getMoleFractions (double *const x) const
	Get the species mole fraction vector.
virtual void	setMoleFractions (const double *const x)
	Set the mole fractions to the specified values.
virtual void	setMoleFractions_NoNorm (const double *const x)
	Set the mole fractions to the specified values without normalizing.
void	getMassFractions (double *const y) const
	Get the species mass fractions.
const double *	massFractions () const
	Return a const pointer to the mass fraction array.
virtual void	setMassFractions (const double *const y)
	Set the mass fractions to the specified values and normalize them.
virtual void	setMassFractions_NoNorm (const double *const y)
	Set the mass fractions to the specified values without normalizing.
virtual void	getConcentrations (double *const c) const
	Get the species concentrations (kmol/m^3).
virtual double	concentration (const size_t k) const
	Concentration of species k.
virtual void	setConcentrations (const double *const conc)
	Set the concentrations to the specified values within the phase.
virtual void	setConcentrationsNoNorm (const double *const conc)
	Set the concentrations without ignoring negative concentrations.
double	temperature () const
	Temperature (K).
virtual double	electronTemperature () const
	Electron Temperature (K)
virtual double	density () const
	Density (kg/m^3).
virtual double	molarDensity () const
	Molar density (kmol/m^3).
virtual double	molarVolume () const
	Molar volume (m^3/kmol).
virtual void	setDensity (const double density_)
	Set the internally stored density (kg/m^3) of the phase.
virtual void	setElectronTemperature (double etemp)
	Set the internally stored electron temperature of the phase (K).
double	mean_X (const double *const Q) const
	Evaluate the mole-fraction-weighted mean of an array Q.
double	mean_X (const vector< double > &Q) const
	Evaluate the mole-fraction-weighted mean of an array Q.
double	meanMolecularWeight () const
	The mean molecular weight. Units: (kg/kmol)
double	sum_xlogx () const
	Evaluate \( \sum_k X_k \ln X_k \).
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.
void	addSpeciesAlias (const string &name, const string &alias)
	Add a species alias (that is, a user-defined alternative species name).
void	addSpeciesLock ()
	Lock species list to prevent addition of new species.
void	removeSpeciesLock ()
	Decrement species lock counter.
virtual vector< string >	findIsomers (const Composition &compMap) const
	Return a vector with isomers names matching a given composition map.
virtual vector< string >	findIsomers (const string &comp) const
	Return a vector with isomers names matching a given composition string.
shared_ptr< Species >	species (const string &name) const
	Return the Species object for the named species.
shared_ptr< Species >	species (size_t k) const
	Return the Species object for species whose index is k.
void	ignoreUndefinedElements ()
	Set behavior when adding a species containing undefined elements to just skip the species.
void	addUndefinedElements ()
	Set behavior when adding a species containing undefined elements to add those elements to the phase.
void	throwUndefinedElements ()
	Set the behavior when adding a species containing undefined elements to throw an exception.

Public Attributes
int	m_form_A_Debye = A_DEBYE_CONST
	Form of the constant outside the Debye-Huckel term called A.

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.
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.
virtual void	applyphScale (double *acMolality) const
	Apply the current phScale to a set of activity Coefficients or activities.
Protected Member Functions inherited from VPStandardStateTP
virtual void	calcDensity ()
	Calculate the density of the mixture using the partial molar volumes and mole fractions as input.
virtual void	_updateStandardStateThermo () const
	Updates the standard state thermodynamic functions at the current T and P of the solution.
void	invalidateCache () override
	Invalidate any cached values which are normally updated only when a change in state is detected.
const vector< double > &	Gibbs_RT_ref () const
virtual void	getParameters (AnyMap &phaseNode) const
	Store the parameters of a ThermoPhase object such that an identical one could be reconstructed using the newThermo(AnyMap&) function.
Protected Member Functions inherited from Phase
void	assertCompressible (const string &setter) const
	Ensure that phase is compressible.
void	assignDensity (const double density_)
	Set the internally stored constant density (kg/m^3) of the phase.
void	setMolecularWeight (const int k, const double mw)
	Set the molecular weight of a single species to a given value.
virtual void	compositionChanged ()
	Apply changes to the state which are needed after the composition changes.

Private Member Functions
void	s_updateScaling_pHScaling () const
	Apply the current phScale to a set of activity Coefficients.
void	s_updateScaling_pHScaling_dT () const
	Apply the current phScale to a set of derivatives of the activity Coefficients wrt temperature.
void	s_updateScaling_pHScaling_dT2 () const
	Apply the current phScale to a set of 2nd derivatives of the activity Coefficients wrt temperature.
void	s_updateScaling_pHScaling_dP () const
	Apply the current phScale to a set of derivatives of the activity Coefficients wrt pressure.
double	s_NBS_CLM_lnMolalityActCoeff () const
	Calculate the Chlorine activity coefficient on the NBS scale.
double	s_NBS_CLM_dlnMolalityActCoeff_dT () const
	Calculate the temperature derivative of the Chlorine activity coefficient on the NBS scale.
double	s_NBS_CLM_d2lnMolalityActCoeff_dT2 () const
	Calculate the second temperature derivative of the Chlorine activity coefficient on the NBS scale.
double	s_NBS_CLM_dlnMolalityActCoeff_dP () const
	Calculate the pressure derivative of the Chlorine activity coefficient.
void	initLengths ()
	Initialize all of the species-dependent lengths in the object.
void	applyphScale (double *acMolality) const override
	Apply the current phScale to a set of activity Coefficients or activities.
void	s_update_lnMolalityActCoeff () const
	This function will be called to update the internally stored natural logarithm of the molality activity coefficients.
void	s_update_dlnMolalityActCoeff_dT () const
	This function calculates the temperature derivative of the natural logarithm of the molality activity coefficients.
void	s_update_d2lnMolalityActCoeff_dT2 () const
	This function calculates the temperature second derivative of the natural logarithm of the molality activity coefficients.
void	s_update_dlnMolalityActCoeff_dP () const
	This function calculates the pressure derivative of the natural logarithm of the molality activity coefficients.
void	s_updateIMS_lnMolalityActCoeff () const
	This function will be called to update the internally stored natural logarithm of the molality activity coefficients.
void	s_updatePitzer_lnMolalityActCoeff () const
	Calculate the Pitzer portion of the activity coefficients.
void	s_updatePitzer_dlnMolalityActCoeff_dT () const
	Calculates the temperature derivative of the natural logarithm of the molality activity coefficients.
void	s_updatePitzer_d2lnMolalityActCoeff_dT2 () const
	This function calculates the temperature second derivative of the natural logarithm of the molality activity coefficients.
void	s_updatePitzer_dlnMolalityActCoeff_dP () const
	Calculates the Pressure derivative of the natural logarithm of the molality activity coefficients.
void	s_updatePitzer_CoeffWRTemp (int doDerivs=2) const
	Calculates the Pitzer coefficients' dependence on the temperature.
void	calc_lambdas (double is) const
	Calculate the lambda interactions.
void	calc_thetas (int z1, int z2, double *etheta, double *etheta_prime) const
	Calculate etheta and etheta_prime.
void	counterIJ_setup () const
	Set up a counter variable for keeping track of symmetric binary interactions amongst the solute species.
void	calcMolalitiesCropped () const
	Calculate the cropped molalities.
void	calcIMSCutoffParams_ ()
	Precalculate the IMS Cutoff parameters for typeCutoff = 2.
void	calcMCCutoffParams_ ()
	Calculate molality cut-off parameters.

Private Attributes
int	m_formPitzerTemp = PITZER_TEMP_CONSTANT
	This is the form of the temperature dependence of Pitzer parameterization used in the model.
double	m_IionicMolality = 0.0
	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.
double	m_maxIionicStrength
	Maximum value of the ionic strength allowed in the calculation of the activity coefficients.
double	m_TempPitzerRef = 298.15
	Reference Temperature for the Pitzer formulations.
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.
PDSS *	m_waterSS = nullptr
	Water standard state calculator.
unique_ptr< WaterProps >	m_waterProps
	Pointer to the water property calculator.
vector< double >	m_tmpV
	vector of size m_kk, used as a temporary holding area.
vector< double >	m_Beta0MX_ij
	Array of 2D data used in the Pitzer/HMW formulation.
vector< double >	m_Beta0MX_ij_L
	Derivative of Beta0_ij[i][j] wrt T. Vector index is counterIJ.
vector< double >	m_Beta0MX_ij_LL
	Derivative of Beta0_ij[i][j] wrt TT. Vector index is counterIJ.
vector< double >	m_Beta0MX_ij_P
	Derivative of Beta0_ij[i][j] wrt P. Vector index is counterIJ.
Array2D	m_Beta0MX_ij_coeff
	Array of coefficients for Beta0, a variable in Pitzer's papers.
vector< double >	m_Beta1MX_ij
	Array of 2D data used in the Pitzer/HMW formulation.
vector< double >	m_Beta1MX_ij_L
	Derivative of Beta1_ij[i][j] wrt T. Vector index is counterIJ.
vector< double >	m_Beta1MX_ij_LL
	Derivative of Beta1_ij[i][j] wrt TT. Vector index is counterIJ.
vector< double >	m_Beta1MX_ij_P
	Derivative of Beta1_ij[i][j] wrt P. Vector index is counterIJ.
Array2D	m_Beta1MX_ij_coeff
	Array of coefficients for Beta1, a variable in Pitzer's papers.
vector< double >	m_Beta2MX_ij
	Array of 2D data used in the Pitzer/HMW formulation.
vector< double >	m_Beta2MX_ij_L
	Derivative of Beta2_ij[i][j] wrt T. Vector index is counterIJ.
vector< double >	m_Beta2MX_ij_LL
	Derivative of Beta2_ij[i][j] wrt TT. Vector index is counterIJ.
vector< double >	m_Beta2MX_ij_P
	Derivative of Beta2_ij[i][j] wrt P. Vector index is counterIJ.
Array2D	m_Beta2MX_ij_coeff
	Array of coefficients for Beta2, a variable in Pitzer's papers.
vector< double >	m_Alpha1MX_ij
vector< double >	m_Alpha2MX_ij
	Array of 2D data used in the Pitzer/HMW formulation.
vector< double >	m_CphiMX_ij
	Array of 2D data used in the Pitzer/HMW formulation.
vector< double >	m_CphiMX_ij_L
	Derivative of Cphi_ij[i][j] wrt T. Vector index is counterIJ.
vector< double >	m_CphiMX_ij_LL
	Derivative of Cphi_ij[i][j] wrt TT. Vector index is counterIJ.
vector< double >	m_CphiMX_ij_P
	Derivative of Cphi_ij[i][j] wrt P. Vector index is counterIJ.
Array2D	m_CphiMX_ij_coeff
	Array of coefficients for CphiMX, a parameter in the activity coefficient formulation.
vector< double >	m_Theta_ij
	Array of 2D data for Theta_ij[i][j] in the Pitzer/HMW formulation.
vector< double >	m_Theta_ij_L
	Derivative of Theta_ij[i][j] wrt T. Vector index is counterIJ.
vector< double >	m_Theta_ij_LL
	Derivative of Theta_ij[i][j] wrt TT. Vector index is counterIJ.
vector< double >	m_Theta_ij_P
	Derivative of Theta_ij[i][j] wrt P. Vector index is counterIJ.
Array2D	m_Theta_ij_coeff
	Array of coefficients for Theta_ij[i][j] in the Pitzer/HMW formulation.
vector< double >	m_Psi_ijk
	Array of 3D data used in the Pitzer/HMW formulation.
vector< double >	m_Psi_ijk_L
	Derivative of Psi_ijk[n] wrt T.
vector< double >	m_Psi_ijk_LL
	Derivative of Psi_ijk[n] wrt TT.
vector< double >	m_Psi_ijk_P
	Derivative of Psi_ijk[n] wrt P.
Array2D	m_Psi_ijk_coeff
	Array of coefficients for Psi_ijk[n] in the Pitzer/HMW formulation.
Array2D	m_Lambda_nj
	Lambda coefficient for the ij interaction.
Array2D	m_Lambda_nj_L
	Derivative of Lambda_nj[i][j] wrt T. see m_Lambda_ij.
Array2D	m_Lambda_nj_LL
	Derivative of Lambda_nj[i][j] wrt TT.
Array2D	m_Lambda_nj_P
	Derivative of Lambda_nj[i][j] wrt P.
Array2D	m_Lambda_nj_coeff
	Array of coefficients for Lambda_nj[i][j] in the Pitzer/HMW formulation.
vector< double >	m_Mu_nnn
	Mu coefficient for the self-ternary neutral coefficient.
vector< double >	m_Mu_nnn_L
	Mu coefficient temperature derivative for the self-ternary neutral coefficient.
vector< double >	m_Mu_nnn_LL
	Mu coefficient 2nd temperature derivative for the self-ternary neutral coefficient.
vector< double >	m_Mu_nnn_P
	Mu coefficient pressure derivative for the self-ternary neutral coefficient.
Array2D	m_Mu_nnn_coeff
	Array of coefficients form_Mu_nnn term.
vector< double >	m_lnActCoeffMolal_Scaled
	Logarithm of the activity coefficients on the molality scale.
vector< double >	m_lnActCoeffMolal_Unscaled
	Logarithm of the activity coefficients on the molality scale.
vector< double >	m_dlnActCoeffMolaldT_Scaled
	Derivative of the Logarithm of the activity coefficients on the molality scale wrt T.
vector< double >	m_dlnActCoeffMolaldT_Unscaled
	Derivative of the Logarithm of the activity coefficients on the molality scale wrt T.
vector< double >	m_d2lnActCoeffMolaldT2_Scaled
	Derivative of the Logarithm of the activity coefficients on the molality scale wrt TT.
vector< double >	m_d2lnActCoeffMolaldT2_Unscaled
	Derivative of the Logarithm of the activity coefficients on the molality scale wrt TT.
vector< double >	m_dlnActCoeffMolaldP_Scaled
	Derivative of the Logarithm of the activity coefficients on the molality scale wrt P.
vector< double >	m_dlnActCoeffMolaldP_Unscaled
	Derivative of the Logarithm of the activity coefficients on the molality scale wrt P.
vector< double >	m_molalitiesCropped
	Cropped and modified values of the molalities used in activity coefficient calculations.
bool	m_molalitiesAreCropped = false
	Boolean indicating whether the molalities are cropped or are modified.
vector< int >	m_CounterIJ
	a counter variable for keeping track of symmetric binary interactions amongst the solute species.
double	elambda [17]
	This is elambda, MEC.
double	elambda1 [17]
	This is elambda1, MEC.
vector< double >	m_gfunc_IJ
	Various temporary arrays used in the calculation of the Pitzer activity coefficients.
vector< double >	m_g2func_IJ
	This is the value of g2(x2) in Pitzer's papers. Vector index is counterIJ.
vector< double >	m_hfunc_IJ
	hfunc, was called gprime in Pitzer's paper.
vector< double >	m_h2func_IJ
	hfunc2, was called gprime in Pitzer's paper.
vector< double >	m_BMX_IJ
	Intermediate variable called BMX in Pitzer's paper.
vector< double >	m_BMX_IJ_L
	Derivative of BMX_IJ wrt T. Vector index is counterIJ.
vector< double >	m_BMX_IJ_LL
	Derivative of BMX_IJ wrt TT. Vector index is counterIJ.
vector< double >	m_BMX_IJ_P
	Derivative of BMX_IJ wrt P. Vector index is counterIJ.
vector< double >	m_BprimeMX_IJ
	Intermediate variable called BprimeMX in Pitzer's paper.
vector< double >	m_BprimeMX_IJ_L
	Derivative of BprimeMX wrt T. Vector index is counterIJ.
vector< double >	m_BprimeMX_IJ_LL
	Derivative of BprimeMX wrt TT. Vector index is counterIJ.
vector< double >	m_BprimeMX_IJ_P
	Derivative of BprimeMX wrt P. Vector index is counterIJ.
vector< double >	m_BphiMX_IJ
	Intermediate variable called BphiMX in Pitzer's paper.
vector< double >	m_BphiMX_IJ_L
	Derivative of BphiMX_IJ wrt T. Vector index is counterIJ.
vector< double >	m_BphiMX_IJ_LL
	Derivative of BphiMX_IJ wrt TT. Vector index is counterIJ.
vector< double >	m_BphiMX_IJ_P
	Derivative of BphiMX_IJ wrt P. Vector index is counterIJ.
vector< double >	m_Phi_IJ
	Intermediate variable called Phi in Pitzer's paper.
vector< double >	m_Phi_IJ_L
	Derivative of m_Phi_IJ wrt T. Vector index is counterIJ.
vector< double >	m_Phi_IJ_LL
	Derivative of m_Phi_IJ wrt TT. Vector index is counterIJ.
vector< double >	m_Phi_IJ_P
	Derivative of m_Phi_IJ wrt P. Vector index is counterIJ.
vector< double >	m_Phiprime_IJ
	Intermediate variable called Phiprime in Pitzer's paper.
vector< double >	m_PhiPhi_IJ
	Intermediate variable called PhiPhi in Pitzer's paper.
vector< double >	m_PhiPhi_IJ_L
	Derivative of m_PhiPhi_IJ wrt T. Vector index is counterIJ.
vector< double >	m_PhiPhi_IJ_LL
	Derivative of m_PhiPhi_IJ wrt TT. Vector index is counterIJ.
vector< double >	m_PhiPhi_IJ_P
	Derivative of m_PhiPhi_IJ wrt P. Vector index is counterIJ.
vector< double >	m_CMX_IJ
	Intermediate variable called CMX in Pitzer's paper.
vector< double >	m_CMX_IJ_L
	Derivative of m_CMX_IJ wrt T. Vector index is counterIJ.
vector< double >	m_CMX_IJ_LL
	Derivative of m_CMX_IJ wrt TT. Vector index is counterIJ.
vector< double >	m_CMX_IJ_P
	Derivative of m_CMX_IJ wrt P. Vector index is counterIJ.
vector< double >	m_gamma_tmp
	Intermediate storage of the activity coefficient itself.
vector< double >	IMS_lnActCoeffMolal_
	Logarithm of the molal activity coefficients.
double	IMS_X_o_cutoff_ = 0.2
	value of the solute mole fraction that centers the cutoff polynomials for the cutoff =1 process;
double	IMS_cCut_ = 0.05
	Parameter in the polyExp cutoff treatment having to do with rate of exp decay.
double	IMS_slopegCut_ = 0.0
	Parameter in the polyExp cutoff treatment.
double	MC_X_o_cutoff_ = 0.0
	value of the solvent mole fraction that centers the cutoff polynomials for the cutoff =1 process;
double	m_last_is = -1.0
Parameters in the polyExp cutoff treatment having to do with rate of exp decay
double	IMS_dfCut_ = 0.0
double	IMS_efCut_ = 0.0
double	IMS_afCut_ = 0.0
double	IMS_bfCut_ = 0.0
double	IMS_dgCut_ = 0.0
double	IMS_egCut_ = 0.0
double	IMS_agCut_ = 0.0
double	IMS_bgCut_ = 0.0
Parameters in the Molality Exp cutoff treatment
double	MC_dpCut_ = 0.0
double	MC_epCut_ = 0.0
double	MC_apCut_ = 0.0
double	MC_bpCut_ = 0.0
double	MC_cpCut_ = 0.0
double	CROP_ln_gamma_o_min
double	CROP_ln_gamma_o_max
double	CROP_ln_gamma_k_min
double	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.

Additional Inherited Members
Protected Attributes inherited from MolalityVPSSTP
int	m_pHScalingType = PHSCALE_PITZER
	Scaling to be used for output of single-ion species activity coefficients.
size_t	m_indexCLM = npos
	Index of the phScale species.
double	m_weightSolvent = 18.01528
	Molecular weight of the Solvent.
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.
double	m_Mnaught = 18.01528E-3
	This is the multiplication factor that goes inside log expressions involving the molalities of species.
vector< double >	m_molalities
	Current value of the molalities of the species in the phase.
Protected Attributes inherited from VPStandardStateTP
double	m_Pcurrent = OneAtm
	Current value of the pressure - state variable.
double	m_minTemp = 0.0
	The minimum temperature at which data for all species is valid.
double	m_maxTemp = BigNumber
	The maximum temperature at which data for all species is valid.
double	m_Tlast_ss = -1.0
	The last temperature at which the standard state thermodynamic properties were calculated at.
double	m_Plast_ss = -1.0
	The last pressure at which the Standard State thermodynamic properties were calculated at.
vector< unique_ptr< PDSS > >	m_PDSS_storage
	Storage for the PDSS objects for the species.
vector< double >	m_h0_RT
	Vector containing the species reference enthalpies at T = m_tlast and P = p_ref.
vector< double >	m_cp0_R
	Vector containing the species reference constant pressure heat capacities at T = m_tlast and P = p_ref.
vector< double >	m_g0_RT
	Vector containing the species reference Gibbs functions at T = m_tlast and P = p_ref.
vector< double >	m_s0_R
	Vector containing the species reference entropies at T = m_tlast and P = p_ref.
vector< double >	m_V0
	Vector containing the species reference molar volumes.
vector< double >	m_hss_RT
	Vector containing the species Standard State enthalpies at T = m_tlast and P = m_plast.
vector< double >	m_cpss_R
	Vector containing the species Standard State constant pressure heat capacities at T = m_tlast and P = m_plast.
vector< double >	m_gss_RT
	Vector containing the species Standard State Gibbs functions at T = m_tlast and P = m_plast.
vector< double >	m_sss_R
	Vector containing the species Standard State entropies at T = m_tlast and P = m_plast.
vector< double >	m_Vss
	Vector containing the species standard state volumes at T = m_tlast and P = m_plast.
Protected Attributes inherited from ThermoPhase
MultiSpeciesThermo	m_spthermo
	Pointer to the calculation manager for species reference-state thermodynamic properties.
AnyMap	m_input
	Data supplied via setParameters.
double	m_phi = 0.0
	Stored value of the electric potential for this phase. Units are Volts.
bool	m_chargeNeutralityNecessary = false
	Boolean indicating whether a charge neutrality condition is a necessity.
int	m_ssConvention = cSS_CONVENTION_TEMPERATURE
	Contains the standard state convention.
double	m_tlast = 0.0
	last value of the temperature processed by reference state
Protected Attributes inherited from Phase
ValueCache	m_cache
	Cached for saved calculations within each ThermoPhase.
size_t	m_kk = 0
	Number of species in the phase.
size_t	m_ndim = 3
	Dimensionality of the phase.
vector< double >	m_speciesComp
	Atomic composition of the species.
vector< double >	m_speciesCharge
	Vector of species charges. length m_kk.
map< string, shared_ptr< Species > >	m_species
	Map of Species objects.
size_t	m_nSpeciesLocks = 0
	Reference counter preventing species addition.
UndefElement::behavior	m_undefinedElementBehavior = UndefElement::add
	Flag determining behavior when adding species with an undefined element.
bool	m_caseSensitiveSpecies = false
	Flag determining whether case sensitive species names are enforced.

Constructor & Destructor Documentation

~HMWSoln()

~HMWSoln

(

)

Definition at line 36 of file HMWSoln.cpp.

HMWSoln()

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

explicit

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

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

Parameters

inputFile	Name of the input file containing the phase definition to set up the object. If blank, an empty phase will be created.
id	ID of the phase in the input file. Defaults to the empty string.

Definition at line 41 of file HMWSoln.cpp.

Member Function Documentation

type()

string type ( ) const

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.

Since

Starting in Cantera 3.0, the name returned by this method corresponds to the canonical name used in the YAML input format.

Reimplemented from Phase.

Definition at line 799 of file HMWSoln.h.

enthalpy_mole()

double enthalpy_mole ( ) const

overridevirtual

Molar enthalpy. Units: J/kmol.

Reimplemented from ThermoPhase.

Definition at line 54 of file HMWSoln.cpp.

relative_enthalpy()

double 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 60 of file HMWSoln.cpp.

relative_molal_enthalpy()

double relative_molal_enthalpy ( ) const

virtual

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

Units: J/ (kmol add salt).

Note this is kmol of the guessed at salt composition

Definition at line 72 of file HMWSoln.cpp.

entropy_mole()

double entropy_mole ( ) const

overridevirtual

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:

\[ \hat s(T, P, X_k) = \sum_k X_k \hat s^0_k(T) - \hat R \sum_k X_k \ln(X_k) \]

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.

See also

MultiSpeciesThermo

 (HKM -> Bump up to Parent object)

Reimplemented from ThermoPhase.

Definition at line 112 of file HMWSoln.cpp.

gibbs_mole()

double gibbs_mole ( ) const

overridevirtual

Molar Gibbs function. Units: J/kmol.

Reimplemented from ThermoPhase.

Definition at line 118 of file HMWSoln.cpp.

cp_mole()

double cp_mole ( ) const

overridevirtual

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

Reimplemented from ThermoPhase.

Definition at line 124 of file HMWSoln.cpp.

cv_mole()

double cv_mole ( ) const

overridevirtual

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

Reimplemented from ThermoPhase.

Definition at line 130 of file HMWSoln.cpp.

calcDensity()

void calcDensity ( )

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 142 of file HMWSoln.cpp.

getActivityConcentrations()

void getActivityConcentrations ( double *  c ) const

overridevirtual

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 ThermoPhase.

Definition at line 159 of file HMWSoln.cpp.

standardConcentration()

double standardConcentration ( size_t  k = 0 ) const

overridevirtual

Return the standard concentration for the kth species.

The standard concentration \( C^0_k \) used to normalize the activity (that is, 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.

Reimplemented from ThermoPhase.

Definition at line 172 of file HMWSoln.cpp.

getActivities()

void getActivities ( double *  ac ) const

overridevirtual

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 ThermoPhase.

Definition at line 182 of file HMWSoln.cpp.

getChemPotentials()

void getChemPotentials ( double *  mu ) const

overridevirtual

Get the species chemical potentials. Units: J/kmol.

This function returns a vector of chemical potentials of the species in solution.

\[ \mu_k = \mu^{\triangle}_k(T,P) + R T \ln(\gamma_k^{\triangle} m_k) \]

Parameters

mu	Output vector of species chemical potentials. Length: m_kk. Units: J/kmol

Reimplemented from ThermoPhase.

Definition at line 211 of file HMWSoln.cpp.

getPartialMolarEnthalpies()

void getPartialMolarEnthalpies ( double *  hbar ) const

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

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

Parameters

hbar	Output vector of species partial molar enthalpies. Length: m_kk. units are J/kmol.

Reimplemented from ThermoPhase.

Definition at line 231 of file HMWSoln.cpp.

getPartialMolarEntropies()

void getPartialMolarEntropies ( double *  sbar ) const

overridevirtual

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 250 of file HMWSoln.cpp.

getPartialMolarVolumes()

void getPartialMolarVolumes ( double *  vbar ) const

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 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 285 of file HMWSoln.cpp.

getPartialMolarCp()

void getPartialMolarCp ( double *  cpbar ) const

overridevirtual

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 298 of file HMWSoln.cpp.

satPressure()

double satPressure ( double  T )

overridevirtual

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 318 of file HMWSoln.cpp.

setBinarySalt()

void setBinarySalt	(	const string &	sp1,
		const string &	sp2,
		size_t	nParams,
		double *	beta0,
		double *	beta1,
		double *	beta2,
		double *	Cphi,
		double	alpha1,
		double	alpha2
	)

Definition at line 343 of file HMWSoln.cpp.

setTheta()

void setTheta	(	const string &	sp1,
		const string &	sp2,
		size_t	nParams,
		double *	theta
	)

Definition at line 378 of file HMWSoln.cpp.

setPsi()

void setPsi	(	const string &	sp1,
		const string &	sp2,
		const string &	sp3,
		size_t	nParams,
		double *	psi
	)

Definition at line 401 of file HMWSoln.cpp.

setLambda()

void setLambda	(	const string &	sp1,
		const string &	sp2,
		size_t	nParams,
		double *	lambda
	)

Definition at line 437 of file HMWSoln.cpp.

setMunnn()

void setMunnn	(	const string &	sp,
		size_t	nParams,
		double *	munnn
	)

Definition at line 464 of file HMWSoln.cpp.

setZeta()

void setZeta	(	const string &	sp1,
		const string &	sp2,
		const string &	sp3,
		size_t	nParams,
		double *	psi
	)

Definition at line 482 of file HMWSoln.cpp.

setPitzerTempModel()

void setPitzerTempModel

(

const string &

model

)

Definition at line 525 of file HMWSoln.cpp.

setPitzerRefTemperature()

void setPitzerRefTemperature ( double  Tref )

inline

Definition at line 1143 of file HMWSoln.h.

setA_Debye()

void setA_Debye

(

double

A

)

Set the A_Debye parameter.

If a negative value is provided, enables calculation of A_Debye using the detailed water equation of state.

Definition at line 539 of file HMWSoln.cpp.

setMaxIonicStrength()

void setMaxIonicStrength ( double  Imax )

inline

Definition at line 1151 of file HMWSoln.h.

setCroppingCoefficients()

void setCroppingCoefficients	(	double	ln_gamma_k_min,
		double	ln_gamma_k_max,
		double	ln_gamma_o_min,
		double	ln_gamma_o_max
	)

Definition at line 549 of file HMWSoln.cpp.

initThermo()

void initThermo ( )

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 576 of file HMWSoln.cpp.

getParameters()

void getParameters ( AnyMap &  phaseNode ) const

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 752 of file HMWSoln.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 982 of file HMWSoln.cpp.

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 1014 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 1038 of file HMWSoln.cpp.

ADebye_L()

double ADebye_L	(	double	temperature = -1.0,
		double	pressure = -1.0
	)		const

Return Pitzer's definition of A_L.

This is basically the derivative of the A_phi multiplied by 4 R T**2

       A_Debye = (F e B_Debye) / (8 Pi epsilon R T)
       dA_phidT = d(A_Debye)/dT / 3.0
       A_L = dA_phidT * (4 * R * T * T)

       Units = sqrt(kg/gmol) (RT)

Parameters

temperature	Temperature of the derivative calculation or -1 to indicate the current temperature
pressure	Pressure of the derivative calculation or -1 to indicate the current pressure

Definition at line 1070 of file HMWSoln.cpp.

ADebye_J()

double ADebye_J	(	double	temperature = -1.0,
		double	pressure = -1.0
	)		const

Return Pitzer's definition of A_J.

This is basically the temperature derivative of A_L, and the second derivative of A_phi

       A_Debye = (F e B_Debye) / (8 Pi epsilon R T)
       dA_phidT = d(A_Debye)/dT / 3.0
       A_J = 2 A_L/T + 4 * R * T * T * d2(A_phi)/dT2

       Units = sqrt(kg/gmol) (R)

Parameters

temperature	Temperature of the derivative calculation or -1 to indicate the current temperature
pressure	Pressure of the derivative calculation or -1 to indicate the current pressure

Definition at line 1092 of file HMWSoln.cpp.

ADebye_V()

double ADebye_V	(	double	temperature = -1.0,
		double	pressure = -1.0
	)		const

Return Pitzer's definition of A_V.

This is the derivative wrt pressure of A_phi multiplied by - 4 R T

       A_Debye = (F e B_Debye) / (8 Pi epsilon R T)
       dA_phidT = d(A_Debye)/dP / 3.0
       A_V = - dA_phidP * (4 * R * T)

       Units = sqrt(kg/gmol) (RT) / Pascal

Parameters

temperature	Temperature of the derivative calculation or -1 to indicate the current temperature
pressure	Pressure of the derivative calculation or -1 to indicate the current pressure

Definition at line 1081 of file HMWSoln.cpp.

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 1104 of file HMWSoln.cpp.

printCoeffs()

void printCoeffs

(

)

const

Print out all of the input Pitzer coefficients.

Definition at line 3963 of file HMWSoln.cpp.

getUnscaledMolalityActivityCoefficients()

void getUnscaledMolalityActivityCoefficients ( double *  acMolality ) const

overridevirtual

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

See Denbigh p. 278 [5] for a thorough discussion. This method 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 198 of file HMWSoln.cpp.

s_updateScaling_pHScaling()

void s_updateScaling_pHScaling ( ) const

private

Apply the current phScale to a set of activity Coefficients.

See the Eq3/6 Manual for a thorough discussion.

Definition at line 4021 of file HMWSoln.cpp.

s_updateScaling_pHScaling_dT()

void s_updateScaling_pHScaling_dT ( ) const

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 4036 of file HMWSoln.cpp.

s_updateScaling_pHScaling_dT2()

void s_updateScaling_pHScaling_dT2 ( ) const

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 4051 of file HMWSoln.cpp.

s_updateScaling_pHScaling_dP()

void s_updateScaling_pHScaling_dP ( ) const

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 4066 of file HMWSoln.cpp.

s_NBS_CLM_lnMolalityActCoeff()

double 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 4081 of file HMWSoln.cpp.

s_NBS_CLM_dlnMolalityActCoeff_dT()

double 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 4089 of file HMWSoln.cpp.

s_NBS_CLM_d2lnMolalityActCoeff_dT2()

double 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 4096 of file HMWSoln.cpp.

s_NBS_CLM_dlnMolalityActCoeff_dP()

double 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 4103 of file HMWSoln.cpp.

initLengths()

void initLengths ( )

private

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

Definition at line 1132 of file HMWSoln.cpp.

applyphScale()

void applyphScale ( double *  acMolality ) const

overrideprivatevirtual

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 4007 of file HMWSoln.cpp.

s_update_lnMolalityActCoeff()

void s_update_lnMolalityActCoeff ( ) const

private

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

Definition at line 1245 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 2311 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 2830 of file HMWSoln.cpp.

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 3341 of file HMWSoln.cpp.

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.

Normally they are all one. However, sometimes they are not, due to stability schemes

gamma_k_molar = gamma_k_molal / Xmol_solvent

gamma_o_molar = gamma_o_molal

Definition at line 3920 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 1808 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 2339 of file HMWSoln.cpp.

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 2858 of file HMWSoln.cpp.

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 3365 of file HMWSoln.cpp.

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 1562 of file HMWSoln.cpp.

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 [35]. This implementation is based on Bethke, Appendix 2.

Parameters

is	Ionic strength

Definition at line 3850 of file HMWSoln.cpp.

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 3894 of file HMWSoln.cpp.

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 1450 of file HMWSoln.cpp.

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 1309 of file HMWSoln.cpp.

calcIMSCutoffParams_()

void calcIMSCutoffParams_ ( )

private

Precalculate the IMS Cutoff parameters for typeCutoff = 2.

Definition at line 1473 of file HMWSoln.cpp.

calcMCCutoffParams_()

void calcMCCutoffParams_ ( )

private

Calculate molality cut-off parameters.

Definition at line 1526 of file HMWSoln.cpp.

Member Data Documentation

m_formPitzerTemp

int m_formPitzerTemp = PITZER_TEMP_CONSTANT

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 1353 of file HMWSoln.h.

m_IionicMolality

double m_IionicMolality = 0.0

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 1358 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 1362 of file HMWSoln.h.

m_TempPitzerRef

double m_TempPitzerRef = 298.15

private

Reference Temperature for the Pitzer formulations.

Definition at line 1365 of file HMWSoln.h.

m_form_A_Debye

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 1382 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 1414 of file HMWSoln.h.

m_waterSS

PDSS* m_waterSS = nullptr

private

Water standard state calculator.

derived from the equation of state for water.

Definition at line 1420 of file HMWSoln.h.

m_waterProps

unique_ptr<WaterProps> m_waterProps

private

Pointer to the water property calculator.

Definition at line 1423 of file HMWSoln.h.

m_tmpV

vector<double> m_tmpV

mutableprivate

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

Definition at line 1426 of file HMWSoln.h.

m_Beta0MX_ij

vector<double> 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 1435 of file HMWSoln.h.

m_Beta0MX_ij_L

vector<double> m_Beta0MX_ij_L

mutableprivate

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

Definition at line 1438 of file HMWSoln.h.

m_Beta0MX_ij_LL

vector<double> m_Beta0MX_ij_LL

mutableprivate

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

Definition at line 1441 of file HMWSoln.h.

m_Beta0MX_ij_P

vector<double> m_Beta0MX_ij_P

mutableprivate

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

Definition at line 1444 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 1452 of file HMWSoln.h.

m_Beta1MX_ij

vector<double> 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 1459 of file HMWSoln.h.

m_Beta1MX_ij_L

vector<double> m_Beta1MX_ij_L

mutableprivate

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

Definition at line 1462 of file HMWSoln.h.

m_Beta1MX_ij_LL

vector<double> m_Beta1MX_ij_LL

mutableprivate

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

Definition at line 1465 of file HMWSoln.h.

m_Beta1MX_ij_P

vector<double> m_Beta1MX_ij_P

mutableprivate

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

Definition at line 1468 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 1476 of file HMWSoln.h.

m_Beta2MX_ij

vector<double> 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 1483 of file HMWSoln.h.

m_Beta2MX_ij_L

vector<double> m_Beta2MX_ij_L

mutableprivate

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

Definition at line 1486 of file HMWSoln.h.

m_Beta2MX_ij_LL

vector<double> m_Beta2MX_ij_LL

mutableprivate

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

Definition at line 1489 of file HMWSoln.h.

m_Beta2MX_ij_P

vector<double> m_Beta2MX_ij_P

mutableprivate

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

Definition at line 1492 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 1502 of file HMWSoln.h.

m_Alpha1MX_ij

vector<double> m_Alpha1MX_ij

private

Definition at line 1509 of file HMWSoln.h.

m_Alpha2MX_ij

vector<double> 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 1517 of file HMWSoln.h.

m_CphiMX_ij

vector<double> 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 1524 of file HMWSoln.h.

m_CphiMX_ij_L

vector<double> m_CphiMX_ij_L

mutableprivate

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

Definition at line 1527 of file HMWSoln.h.

m_CphiMX_ij_LL

vector<double> m_CphiMX_ij_LL

mutableprivate

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

Definition at line 1530 of file HMWSoln.h.

m_CphiMX_ij_P

vector<double> m_CphiMX_ij_P

mutableprivate

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

Definition at line 1533 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 1542 of file HMWSoln.h.

m_Theta_ij

vector<double> 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 1554 of file HMWSoln.h.

m_Theta_ij_L

vector<double> m_Theta_ij_L

mutableprivate

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

Definition at line 1557 of file HMWSoln.h.

m_Theta_ij_LL

vector<double> m_Theta_ij_LL

mutableprivate

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

Definition at line 1560 of file HMWSoln.h.

m_Theta_ij_P

vector<double> m_Theta_ij_P

mutableprivate

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

Definition at line 1563 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 1575 of file HMWSoln.h.

m_Psi_ijk

vector<double> 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 1588 of file HMWSoln.h.

m_Psi_ijk_L

vector<double> 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 1592 of file HMWSoln.h.

m_Psi_ijk_LL

vector<double> 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 1596 of file HMWSoln.h.

m_Psi_ijk_P

vector<double> 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 1600 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 1616 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, that is, n. The charged species occupy the j coordinate. neutral, neutral interactions are also included here.

Definition at line 1626 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 1629 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 1632 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 1635 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, that is, 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 1650 of file HMWSoln.h.

m_Mu_nnn

vector<double> 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 1658 of file HMWSoln.h.

m_Mu_nnn_L

vector<double> 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 1668 of file HMWSoln.h.

m_Mu_nnn_LL

vector<double> 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 1678 of file HMWSoln.h.

m_Mu_nnn_P

vector<double> 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 1688 of file HMWSoln.h.

m_Mu_nnn_coeff

Array2D m_Mu_nnn_coeff

private

Array of coefficients form_Mu_nnn term.

Definition at line 1691 of file HMWSoln.h.

m_lnActCoeffMolal_Scaled

vector<double> 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 1698 of file HMWSoln.h.

m_lnActCoeffMolal_Unscaled

vector<double> 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 1705 of file HMWSoln.h.

m_dlnActCoeffMolaldT_Scaled

vector<double> 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 1709 of file HMWSoln.h.

m_dlnActCoeffMolaldT_Unscaled

vector<double> 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 1713 of file HMWSoln.h.

m_d2lnActCoeffMolaldT2_Scaled

vector<double> 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 1717 of file HMWSoln.h.

m_d2lnActCoeffMolaldT2_Unscaled

vector<double> 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 1721 of file HMWSoln.h.

m_dlnActCoeffMolaldP_Scaled

vector<double> 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 1725 of file HMWSoln.h.

m_dlnActCoeffMolaldP_Unscaled

vector<double> 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 1729 of file HMWSoln.h.

m_molalitiesCropped

vector<double> m_molalitiesCropped

mutableprivate

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

Definition at line 1735 of file HMWSoln.h.

m_molalitiesAreCropped

bool m_molalitiesAreCropped = false

mutableprivate

Boolean indicating whether the molalities are cropped or are modified.

Definition at line 1738 of file HMWSoln.h.

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 1746 of file HMWSoln.h.

elambda

double elambda[17]

mutableprivate

This is elambda, MEC.

Definition at line 1749 of file HMWSoln.h.

elambda1

double elambda1[17]

mutableprivate

This is elambda1, MEC.

Definition at line 1752 of file HMWSoln.h.

m_gfunc_IJ

vector<double> 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 temperature This is the value of g(x) in Pitzer's papers. Vector index is counterIJ

Definition at line 1761 of file HMWSoln.h.

m_g2func_IJ

vector<double> m_g2func_IJ

mutableprivate

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

Definition at line 1764 of file HMWSoln.h.

m_hfunc_IJ

vector<double> 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 1768 of file HMWSoln.h.

m_h2func_IJ

vector<double> 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 1772 of file HMWSoln.h.

m_BMX_IJ

vector<double> 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 1776 of file HMWSoln.h.

m_BMX_IJ_L

vector<double> m_BMX_IJ_L

mutableprivate

Derivative of BMX_IJ wrt T. Vector index is counterIJ.

Definition at line 1779 of file HMWSoln.h.

m_BMX_IJ_LL

vector<double> m_BMX_IJ_LL

mutableprivate

Derivative of BMX_IJ wrt TT. Vector index is counterIJ.

Definition at line 1782 of file HMWSoln.h.

m_BMX_IJ_P

vector<double> m_BMX_IJ_P

mutableprivate

Derivative of BMX_IJ wrt P. Vector index is counterIJ.

Definition at line 1785 of file HMWSoln.h.

m_BprimeMX_IJ

vector<double> m_BprimeMX_IJ

mutableprivate

Intermediate variable called BprimeMX in Pitzer's paper.

Vector index is counterIJ

Definition at line 1789 of file HMWSoln.h.

m_BprimeMX_IJ_L

vector<double> m_BprimeMX_IJ_L

mutableprivate

Derivative of BprimeMX wrt T. Vector index is counterIJ.

Definition at line 1792 of file HMWSoln.h.

m_BprimeMX_IJ_LL

vector<double> m_BprimeMX_IJ_LL

mutableprivate

Derivative of BprimeMX wrt TT. Vector index is counterIJ.

Definition at line 1795 of file HMWSoln.h.

m_BprimeMX_IJ_P

vector<double> m_BprimeMX_IJ_P

mutableprivate

Derivative of BprimeMX wrt P. Vector index is counterIJ.

Definition at line 1798 of file HMWSoln.h.

m_BphiMX_IJ

vector<double> m_BphiMX_IJ

mutableprivate

Intermediate variable called BphiMX in Pitzer's paper.

Vector index is counterIJ

Definition at line 1802 of file HMWSoln.h.

m_BphiMX_IJ_L

vector<double> m_BphiMX_IJ_L

mutableprivate

Derivative of BphiMX_IJ wrt T. Vector index is counterIJ.

Definition at line 1805 of file HMWSoln.h.

m_BphiMX_IJ_LL

vector<double> m_BphiMX_IJ_LL

mutableprivate

Derivative of BphiMX_IJ wrt TT. Vector index is counterIJ.

Definition at line 1808 of file HMWSoln.h.

m_BphiMX_IJ_P

vector<double> m_BphiMX_IJ_P

mutableprivate

Derivative of BphiMX_IJ wrt P. Vector index is counterIJ.

Definition at line 1811 of file HMWSoln.h.

m_Phi_IJ

vector<double> m_Phi_IJ

mutableprivate

Intermediate variable called Phi in Pitzer's paper.

Vector index is counterIJ

Definition at line 1815 of file HMWSoln.h.

m_Phi_IJ_L

vector<double> m_Phi_IJ_L

mutableprivate

Derivative of m_Phi_IJ wrt T. Vector index is counterIJ.

Definition at line 1818 of file HMWSoln.h.

m_Phi_IJ_LL

vector<double> m_Phi_IJ_LL

mutableprivate

Derivative of m_Phi_IJ wrt TT. Vector index is counterIJ.

Definition at line 1821 of file HMWSoln.h.

m_Phi_IJ_P

vector<double> m_Phi_IJ_P

mutableprivate

Derivative of m_Phi_IJ wrt P. Vector index is counterIJ.

Definition at line 1824 of file HMWSoln.h.

m_Phiprime_IJ

vector<double> m_Phiprime_IJ

mutableprivate

Intermediate variable called Phiprime in Pitzer's paper.

Vector index is counterIJ

Definition at line 1828 of file HMWSoln.h.

m_PhiPhi_IJ

vector<double> m_PhiPhi_IJ

mutableprivate

Intermediate variable called PhiPhi in Pitzer's paper.

Vector index is counterIJ

Definition at line 1832 of file HMWSoln.h.

m_PhiPhi_IJ_L

vector<double> m_PhiPhi_IJ_L

mutableprivate

Derivative of m_PhiPhi_IJ wrt T. Vector index is counterIJ.

Definition at line 1835 of file HMWSoln.h.

m_PhiPhi_IJ_LL

vector<double> m_PhiPhi_IJ_LL

mutableprivate

Derivative of m_PhiPhi_IJ wrt TT. Vector index is counterIJ.

Definition at line 1838 of file HMWSoln.h.

m_PhiPhi_IJ_P

vector<double> m_PhiPhi_IJ_P

mutableprivate

Derivative of m_PhiPhi_IJ wrt P. Vector index is counterIJ.

Definition at line 1841 of file HMWSoln.h.

m_CMX_IJ

vector<double> m_CMX_IJ

mutableprivate

Intermediate variable called CMX in Pitzer's paper.

Vector index is counterIJ

Definition at line 1845 of file HMWSoln.h.

m_CMX_IJ_L

vector<double> m_CMX_IJ_L

mutableprivate

Derivative of m_CMX_IJ wrt T. Vector index is counterIJ.

Definition at line 1848 of file HMWSoln.h.

m_CMX_IJ_LL

vector<double> m_CMX_IJ_LL

mutableprivate

Derivative of m_CMX_IJ wrt TT. Vector index is counterIJ.

Definition at line 1851 of file HMWSoln.h.

m_CMX_IJ_P

vector<double> m_CMX_IJ_P

mutableprivate

Derivative of m_CMX_IJ wrt P. Vector index is counterIJ.

Definition at line 1854 of file HMWSoln.h.

m_gamma_tmp

vector<double> m_gamma_tmp

mutableprivate

Intermediate storage of the activity coefficient itself.

Vector index is the species index

Definition at line 1858 of file HMWSoln.h.

IMS_lnActCoeffMolal_

vector<double> IMS_lnActCoeffMolal_

mutableprivate

Logarithm of the molal activity coefficients.

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

Definition at line 1862 of file HMWSoln.h.

IMS_X_o_cutoff_

double IMS_X_o_cutoff_ = 0.2

private

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

Definition at line 1866 of file HMWSoln.h.

IMS_cCut_

double IMS_cCut_ = 0.05

private

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

Definition at line 1869 of file HMWSoln.h.

IMS_slopegCut_

double IMS_slopegCut_ = 0.0

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 1876 of file HMWSoln.h.

IMS_dfCut_

double IMS_dfCut_ = 0.0

private

Definition at line 1880 of file HMWSoln.h.

IMS_efCut_

double IMS_efCut_ = 0.0

private

Definition at line 1881 of file HMWSoln.h.

IMS_afCut_

double IMS_afCut_ = 0.0

private

Definition at line 1882 of file HMWSoln.h.

IMS_bfCut_

double IMS_bfCut_ = 0.0

private

Definition at line 1883 of file HMWSoln.h.

IMS_dgCut_

double IMS_dgCut_ = 0.0

private

Definition at line 1884 of file HMWSoln.h.

IMS_egCut_

double IMS_egCut_ = 0.0

private

Definition at line 1885 of file HMWSoln.h.

IMS_agCut_

double IMS_agCut_ = 0.0

private

Definition at line 1886 of file HMWSoln.h.

IMS_bgCut_

double IMS_bgCut_ = 0.0

private

Definition at line 1887 of file HMWSoln.h.

MC_X_o_cutoff_

double MC_X_o_cutoff_ = 0.0

private

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

Definition at line 1892 of file HMWSoln.h.

MC_dpCut_

double MC_dpCut_ = 0.0

private

Definition at line 1896 of file HMWSoln.h.

MC_epCut_

double MC_epCut_ = 0.0

private

Definition at line 1897 of file HMWSoln.h.

MC_apCut_

double MC_apCut_ = 0.0

private

Definition at line 1898 of file HMWSoln.h.

MC_bpCut_

double MC_bpCut_ = 0.0

private

Definition at line 1899 of file HMWSoln.h.

MC_cpCut_

double MC_cpCut_ = 0.0

private

Definition at line 1900 of file HMWSoln.h.

CROP_ln_gamma_o_min

double CROP_ln_gamma_o_min

private

Definition at line 1901 of file HMWSoln.h.

CROP_ln_gamma_o_max

double CROP_ln_gamma_o_max

private

Definition at line 1902 of file HMWSoln.h.

CROP_ln_gamma_k_min

double CROP_ln_gamma_k_min

private

Definition at line 1903 of file HMWSoln.h.

CROP_ln_gamma_k_max

double CROP_ln_gamma_k_max

private

Definition at line 1904 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 1915 of file HMWSoln.h.

m_last_is

double m_last_is = -1.0

mutableprivate

Definition at line 2026 of file HMWSoln.h.

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

• HMWSoln.h
• HMWSoln.cpp