IdealMolalSoln.h

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/**
 *  @file IdealMolalSoln.h
 *   ThermoPhase object for the ideal molal equation of
 * state (see \ref thermoprops
 * and class \link Cantera::IdealMolalSoln IdealMolalSoln\endlink).
 *
 * Header file for a derived class of ThermoPhase that handles
 * variable pressure standard state methods for calculating
 * thermodynamic properties that are further based upon
 * activities on the molality scale. The Ideal molal
 * solution assumes that all molality-based activity
 * coefficients are equal to one. This turns out to be highly
 * nonlinear in the limit of the solvent mole fraction going
 * to zero.
 */
/*
 * Copyright (2006) Sandia Corporation. Under the terms of
 * Contract DE-AC04-94AL85000 with Sandia Corporation, the
 * U.S. Government retains certain rights in this software.
 */
#ifndef CT_IDEALMOLALSOLN_H
#define CT_IDEALMOLALSOLN_H

#include "MolalityVPSSTP.h"

namespace Cantera
{

/**  \addtogroup thermoprops */
/* @{
 */

/**
 * This phase is based upon the mixing-rule assumption that
 * all molality-based activity coefficients are equal
 * to one.
 *
 * This is a full instantiation of a ThermoPhase object.
 * The assumption is that the molality-based activity
 * coefficient is equal to one. This also implies that
 * the osmotic coefficient is equal to one.
 *
 * Note, this does not mean that the solution is an
 * ideal solution. In fact, there is a singularity in
 * the formulation as
 * the solvent concentration goes to zero.
 *
 * The mechanical equation of state is currently assumed to
 * be that of an incompressible solution. This may change
 * in the future. Each species has its own molar volume.
 * The molar volume is a constant.
 *
 * Class IdealMolalSoln represents a condensed phase.
 * The phase and the pure species phases which
 * comprise the standard states of the species are assumed to have
 * zero volume expansivity and zero isothermal compressibility.
 * Each species does, however, have constant but distinct partial
 * molar volumes equal to their pure species molar volumes.
 * The class derives from class ThermoPhase,
 * and overloads the virtual methods defined there with ones that
 * use expressions appropriate for incompressible mixtures.
 *
 * The standard concentrations can have three different forms
 * depending on the value of the member attribute m_formGC, which
 * is supplied in the XML file.
 *
 * <TABLE>
 * <TR><TD> m_formGC </TD><TD> ActivityConc </TD><TD> StandardConc </TD></TR>
 * <TR><TD> 0        </TD><TD> \f$ {m_k}/ { m^{\Delta}}\f$     </TD><TD> \f$ 1.0        \f$ </TD></TR>
 * <TR><TD> 1        </TD><TD> \f$  m_k / (m^{\Delta} V_k)\f$  </TD><TD> \f$ 1.0 / V_k  \f$ </TD></TR>
 * <TR><TD> 2        </TD><TD> \f$  m_k / (m^{\Delta} V^0_0)\f$</TD><TD> \f$ 1.0 / V^0_0\f$ </TD></TR>
 * </TABLE>
 *
 * \f$ V^0_0 \f$ is the solvent standard molar volume. \f$ m^{\Delta} \f$ is a constant equal to a
 * molality of \f$ 1.0 \quad\mbox{gm kmol}^{-1} \f$.
 *
 * The current default is to have mformGC = 2.
 *
 * The value and form of the activity concentration will affect
 * reaction rate constants involving species in this phase.
 *
 *      <thermo model="IdealMolalSoln">
 *         <standardConc model="solvent_volume" />
 *         <solvent> H2O(l) </solvent>
 *         <activityCoefficients model="IdealMolalSoln" >
 *             <idealMolalSolnCutoff model="polyExp">
 *                 <gamma_O_limit> 1.0E-5  </gamma_O_limit>
 *                 <gamma_k_limit> 1.0E-5  <gamma_k_limit>
 *                 <X_o_cutoff>    0.20    </X_o_cutoff>
 *                 <C_0_param>     0.05    </C_0_param>
 *                 <slope_f_limit> 0.6     </slope_f_limit>
 *                 <slope_g_limit> 0.0     </slope_g_limit>
 *             </idealMolalSolnCutoff>
 *          </activityCoefficients>
 *      </thermo>
 */
class IdealMolalSoln : public MolalityVPSSTP
{
public:

    /// Constructor
    IdealMolalSoln();

    //! Copy Constructor
    IdealMolalSoln(const IdealMolalSoln&);

    //! Assignment operator
    IdealMolalSoln& operator=(const IdealMolalSoln&);

    //! Constructor for phase initialization
    /*!
     * This constructor will initialize a phase, by reading the required
     * information from an input file.
     *
     *  @param inputFile   Name of the Input file that contains information about the phase
     *  @param id          id of the phase within the input file
     */
    IdealMolalSoln(const std::string& inputFile, const std::string& id = "");

    //! Constructor for phase initialization
    /*!
     * This constructor will initialize a phase, by reading the required
     * information from XML_Node tree.
     *
     *  @param phaseRef    reference for an XML_Node tree that contains
     *                     the information necessary to initialize the phase.
     *  @param id          id of the phase within the input file
     */
    IdealMolalSoln(XML_Node& phaseRef, const std::string& id = "");

    //! Duplication function
    /*!
     * This virtual function is used to create a duplicate of the
     * current phase. It's used to duplicate the phase when given
     * a ThermoPhase pointer to the phase.
     *
     * @return It returns a ThermoPhase pointer.
     */
    ThermoPhase* duplMyselfAsThermoPhase() const;

    //! @}
    //! @name  Molar Thermodynamic Properties of the Solution
    //! @{

    //! Molar enthalpy of the solution. Units: J/kmol.
    /*!
     * Returns the amount of enthalpy per mole of solution.
     * For an ideal molal solution,
     * \f[
     * \bar{h}(T, P, X_k) = \sum_k X_k \bar{h}_k(T)
     * \f]
     * The formula is written in terms of the partial molar enthalpies.
     * \f$ \bar{h}_k(T, p, m_k) \f$.
     * See the partial molar enthalpy function, getPartialMolarEnthalpies(),
     * for details.
     *
     * Units: J/kmol
     */
    virtual doublereal enthalpy_mole() const;

    //! Molar internal energy of the solution: Units: J/kmol.
    /*!
     * Returns the amount of internal energy per mole of solution.
     * For an ideal molal solution,
     * \f[
     * \bar{u}(T, P, X_k) = \sum_k X_k \bar{u}_k(T)
     * \f]
     * The formula is written in terms of the partial molar internal energy.
     * \f$ \bar{u}_k(T, p, m_k) \f$.
     */
    virtual doublereal intEnergy_mole() const;

    //! Molar entropy of the solution. Units: J/kmol/K.
    /*!
     * Returns the amount of entropy per mole of solution.
     * For an ideal molal solution,
     * \f[
     * \bar{s}(T, P, X_k) = \sum_k X_k \bar{s}_k(T)
     * \f]
     * The formula is written in terms of the partial molar entropies.
     * \f$ \bar{s}_k(T, p, m_k) \f$.
     * See the partial molar entropies function, getPartialMolarEntropies(),
     * for details.
     *
     * Units: J/kmol/K.
     */
    virtual doublereal entropy_mole() const;

    //! Molar Gibbs function for the solution: Units J/kmol.
    /*!
     * Returns the Gibbs free energy of the solution per mole of the solution.
     *
     * \f[
     * \bar{g}(T, P, X_k) = \sum_k X_k \mu_k(T)
     * \f]
     *
     * Units: J/kmol
     */
    virtual doublereal gibbs_mole() const;

    //! Molar heat capacity of the solution at constant pressure. Units: J/kmol/K.
    /*!
     * \f[
     * \bar{c}_p(T, P, X_k) = \sum_k X_k \bar{c}_{p,k}(T)
     * \f]
     *
     * Units: J/kmol/K
     */
    virtual doublereal cp_mole() const;

    //! Molar heat capacity of the solution at constant volume. Units: J/kmol/K.
    /*!
     * NOT IMPLEMENTED.
     */
    virtual doublereal cv_mole() const;

    //@}
    /** @name Mechanical Equation of State Properties
     *
     *   In this equation of state implementation, the density is a
     *   function only of the mole fractions. Therefore, it can't be
     *   an independent variable. Instead, the pressure is used as the
     *   independent variable. Functions which try to set the thermodynamic
     *   state by calling setDensity() may cause an exception to be
     *   thrown.
     */
    //@{

    /**
     * Set the pressure at constant temperature. Units: Pa.
     * This method sets a constant within the object.
     * The mass density is not a function of pressure.
     *
     * @param p   Input Pressure
     */
    virtual void setPressure(doublereal p);

protected:
    /**
     * Calculate the density of the mixture using the partial
     * molar volumes and mole fractions as input
     *
     * The formula for this is
     *
     * \f[
     * \rho = \frac{\sum_k{X_k W_k}}{\sum_k{X_k V_k}}
     * \f]
     *
     * where \f$X_k\f$ are the mole fractions, \f$W_k\f$ are
     * the molecular weights, and \f$V_k\f$ 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.
     */
    void calcDensity();

public:
    /**
     * Overwritten setDensity() function is necessary because the
     * density is not an independent variable.
     *
     * This function will now throw an error condition
     *
     * @internal May have to adjust the strategy here to make
     * the eos for these materials slightly compressible, in order
     * to create a condition where the density is a function of
     * the pressure.
     *
     * This function will now throw an error condition.
     *
     * @param rho   Input Density
     */
    void setDensity(const doublereal rho);

    /**
     * Overwritten setMolarDensity() function is necessary because the
     * density is not an independent variable.
     *
     * This function will now throw an error condition.
     *
     * @param rho   Input Density
     */
    void setMolarDensity(const doublereal rho);

    //! Set the temperature (K) and pressure (Pa)
    /*!
     *  Set the temperature and pressure.
     *
     * @param t    Temperature (K)
     * @param p    Pressure (Pa)
     */
    virtual void setState_TP(doublereal t, doublereal p);

    //! The isothermal compressibility. Units: 1/Pa.
    /*!
     * The isothermal compressibility is defined as
     * \f[
     * \kappa_T = -\frac{1}{v}\left(\frac{\partial v}{\partial P}\right)_T
     * \f]
     *
     *  It's equal to zero for this model, since the molar volume
     *  doesn't change with pressure or temperature.
     */
    virtual doublereal isothermalCompressibility() const;

    //!  The thermal expansion coefficient. Units: 1/K.
    /*!
     * The thermal expansion coefficient is defined as
     *
     * \f[
     * \beta = \frac{1}{v}\left(\frac{\partial v}{\partial T}\right)_P
     * \f]
     *
     *  It's equal to zero for this model, since the molar volume
     *  doesn't change with pressure or temperature.
     */
    virtual doublereal thermalExpansionCoeff() const;

    /**
     * @}
     * @name Activities and Activity Concentrations
     *
     * The activity \f$a_k\f$ of a species in solution is
     * related to the chemical potential by \f[ \mu_k = \mu_k^0(T)
     * + \hat R T \log a_k. \f] The quantity \f$\mu_k^0(T)\f$ is
     * the chemical potential at unit activity, which depends only
     * on temperature and the pressure.
     * @{
     */

    /*!
     * This method returns an array of generalized concentrations
     * \f$ C_k\f$ that are defined such that
     * \f$ a_k = C_k / C^0_k, \f$ where \f$ C^0_k \f$
     * 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.
     *
     * @param c Array of generalized concentrations. The
     *          units depend upon the implementation of the
     *          reaction rate expressions within the phase.
     */
    virtual void getActivityConcentrations(doublereal* c) const;

    /**
     * The standard concentration \f$ C^0_k \f$ used to normalize
     * the generalized concentration. In many cases, this quantity
     * will be the same for all species in a phase - for example,
     * for an ideal gas \f$ C^0_k = P/\hat R T \f$. For this
     * reason, this method returns a single value, instead of an
     * array.  However, for phases in which the standard
     * concentration is species-specific (e.g. surface species of
     * different sizes), this method may be called with an
     * optional parameter indicating the species.
     *
     * @param k  Species index
     */
    virtual doublereal standardConcentration(size_t k=0) const;

    /*!
     * Returns the units of the standard and generalized
     * concentrations Note they have the same units, as their
     * ratio is defined to be equal to the activity of the kth
     * species in the solution, which is unitless.
     *
     * This routine is used in print out applications where the
     * units are needed. Usually, MKS units are assumed throughout
     * the program and in the XML input files.
     *
     * @param uA Output vector containing the units
     *     uA[0] = kmol units - default  = 1
     *     uA[1] = m    units - default  = -nDim(), the number of spatial
     *                                   dimensions in the Phase class.
     *     uA[2] = kg   units - default  = 0;
     *     uA[3] = Pa(pressure) units - default = 0;
     *     uA[4] = Temperature units - default = 0;
     *     uA[5] = time units - default = 0
     * @param k species index. Defaults to 0.
     * @param sizeUA output int containing the size of the vector.
     *        Currently, this is equal to 6.
     * @deprecated To be removed after Cantera 2.2.
     */
    virtual void getUnitsStandardConc(double* uA, int k = 0,
                                      int sizeUA = 6) const;

    /*!
     * Get the array of non-dimensional activities at
     * the current solution temperature, pressure, and
     * solution concentration.
     *
     * (note solvent is on molar scale)
     *
     * @param ac      Output activity coefficients.
     *                Length: m_kk.
     */
    virtual void getActivities(doublereal* ac) const;

    /*!
     * Get the array of non-dimensional molality-based
     * activity coefficients at the current solution temperature,
     * pressure, and solution concentration.
     *
     *
     * (note solvent is on molar scale. The solvent molar
     *  based activity coefficient is returned).
     *
     * @param acMolality      Output Molality-based activity coefficients.
     *                        Length: m_kk.
     */
    virtual void
    getMolalityActivityCoefficients(doublereal* acMolality) const;

    //@}
    /// @name  Partial Molar Properties of the Solution
    //@{

    //!Get the species chemical potentials: Units: J/kmol.
    /*!
     * This function returns a vector of chemical potentials of the
     * species in solution.
     *
     * \f[
     *    \mu_k = \mu^{o}_k(T,P) + R T \ln(\frac{m_k}{m^\Delta})
     * \f]
     * \f[
     *    \mu_w = \mu^{o}_w(T,P) +
     *            R T ((X_w - 1.0) / X_w)
     * \f]
     *
     * \f$ w \f$ refers to the solvent species.
     * \f$ X_w \f$ is the mole fraction of the solvent.
     * \f$ m_k \f$ is the molality of the kth solute.
     * \f$ m^\Delta \f$ is 1 gmol solute per kg solvent.
     *
     * Units: J/kmol.
     *
     * @param mu     Output vector of species chemical potentials.
     *               Length: m_kk.
     */
    virtual void getChemPotentials(doublereal* mu) const;

    //! 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
     * species standard state enthalpies.
     *  \f[
     * \bar h_k(T,P) = \hat h^{ref}_k(T) + (P - P_{ref}) \hat V^0_k
     * \f]
     * The reference-state pure-species enthalpies, \f$ \hat h^{ref}_k(T) \f$,
     * at the reference pressure,\f$ P_{ref} \f$,
     * are computed by the species thermodynamic
     * property manager. They are polynomial functions of temperature.
     * @see SpeciesThermo
     *
     * @param hbar   Output vector of partial molar enthalpies.
     *               Length: m_kk.
     */
    virtual void getPartialMolarEnthalpies(doublereal* hbar) const;

    //! Returns an array of partial molar entropies of the species in the solution. Units: J/kmol.
    /*!
     *
     * Maxwell's equations provide an insight in how to calculate this
     * (p.215 Smith and Van Ness)
     * \f[
     *      \frac{d(\mu_k)}{dT} = -\bar{s}_i
     * \f]
     * For this phase, the partial molar entropies are equal to the
     * standard state species entropies plus the ideal molal solution contribution.
     *
     * \f[
     *   \bar{s}_k(T,P) =  s^0_k(T) - R \ln( \frac{m_k}{m^{\triangle}} )
     * \f]
     * \f[
     *   \bar{s}_w(T,P) =  s^0_w(T) - R ((X_w - 1.0) / X_w)
     * \f]
     *
     * The subscript, w, refers to the solvent species. \f$ X_w \f$ is
     * the mole fraction of solvent.
     * The reference-state pure-species entropies,\f$ s^0_k(T) \f$,
     * at the reference pressure, \f$ P_{ref} \f$, are computed by the
     * species thermodynamic
     * property manager. They are polynomial functions of temperature.
     * @see SpeciesThermo
     *
     * @param sbar Output vector of partial molar entropies.
     *             Length: m_kk.
     */
    virtual void getPartialMolarEntropies(doublereal* sbar) const;

    // partial molar volumes of the species Units: m^3 kmol-1.
    /*!
     * For this solution, the partial molar volumes are equal to the
     * constant species molar volumes.
     *
     * Units: m^3 kmol-1.
     *  @param vbar Output vector of partial molar volumes.
     */
    virtual void getPartialMolarVolumes(doublereal* vbar) const;


    //! Partial molar heat capacity of the solution:. UnitsL J/kmol/K
    /*!
     *   The kth partial molar heat capacity is  equal to
     *   the temperature derivative of the partial molar
     *   enthalpy of the kth species in the solution at constant
     *   P and composition (p. 220 Smith and Van Ness).
     *    \f[
     *    \bar{Cp}_k(T,P) =  {Cp}^0_k(T)
     *    \f]
     *
     *   For this solution, this is equal to the reference state
     *   heat capacities.
     *
     *  Units: J/kmol/K
     *
     * @param cpbar  Output vector of partial molar heat capacities.
     *               Length: m_kk.
     */
    virtual void getPartialMolarCp(doublereal* cpbar) const;

    //!@}
    //! @name Chemical Equilibrium
    //! @{

    /**
     * This method is used by the ChemEquil equilibrium solver.
     * It sets the state such that the chemical potentials satisfy
     * \f[ \frac{\mu_k}{\hat R T} = \sum_m A_{k,m}
     * \left(\frac{\lambda_m} {\hat R T}\right) \f] where
     * \f$ \lambda_m \f$ is the element potential of element m. The
     * temperature is unchanged.  Any phase (ideal or not) that
     * implements this method can be equilibrated by ChemEquil.
     *
     * Not implemented.
     *
     * @param lambda_RT vector of Nondimensional element potentials.
     */
    virtual void setToEquilState(const doublereal* lambda_RT) {
        throw NotImplementedError("IdealMolalSoln::setToEquilState");
    }

    //@}

    /*
     *  -------------- Utilities -------------------------------
     */

    //! Initialization routine for an IdealMolalSoln phase.
    /*!
     *  This internal routine is responsible for setting up
     *  the internal storage. This is reimplemented from the ThermoPhase
     *  class.
     */
    virtual void initThermo();

    //!  Import and initialize an IdealMolalSoln phase
    //!  specification in an XML tree into the current object.
    /*!
     *   This routine is called from importPhase() to finish
     *   up the initialization of the thermo object. It reads in the
     *   species molar volumes.
     *
     * @param phaseNode This object must be the phase node of a
     *             complete XML tree
     *             description of the phase, including all of the
     *             species data. In other words while "phase" must
     *             point to an XML phase object, it must have
     *             sibling nodes "speciesData" that describe
     *             the species in the phase.
     * @param id   ID of the phase. If nonnull, a check is done
     *             to see if phaseNode is pointing to the phase
     *             with the correct id.
     */
    virtual void initThermoXML(XML_Node& phaseNode, const std::string& id="");

    //! Report the molar volume of species k
    /*!
     * units - \f$ m^3 kmol^{-1} \f$
     *
     * @param k Species index.
     */
    double speciesMolarVolume(int k) const;

    /*!
     * Fill in a return vector containing the species molar volumes
     * units - \f$ m^3 kmol^{-1} \f$
     *
     * @param smv Output vector of species molar volumes.
     */
    void   getSpeciesMolarVolumes(double* smv) const;
    //@}

protected:
    /**
     * Species molar volume \f$ m^3 kmol^{-1} \f$
     */
    vector_fp   m_speciesMolarVolume;

    /**
     * The standard concentrations can have three different forms
     * depending on the value of the member attribute m_formGC, which
     * is supplied in the XML file.
     *
     *  <TABLE>
     *  <TR><TD> m_formGC </TD><TD> ActivityConc </TD><TD> StandardConc </TD></TR>
     *  <TR><TD> 0        </TD><TD> \f$ {m_k}/ { m^{\Delta}}\f$     </TD><TD> \f$ 1.0        \f$ </TD></TR>
     *  <TR><TD> 1        </TD><TD> \f$  m_k / (m^{\Delta} V_k)\f$  </TD><TD> \f$ 1.0 / V_k  \f$ </TD></TR>
     *  <TR><TD> 2        </TD><TD> \f$  m_k / (m^{\Delta} V^0_0)\f$</TD><TD> \f$ 1.0 / V^0_0\f$ </TD></TR>
     *  </TABLE>
     */
    int m_formGC;

public:
    //! Cutoff type
    int IMS_typeCutoff_;

private:
    /**
     * Temporary array used in equilibrium calculations
     */
    mutable vector_fp      m_pp;

    /**
     * vector of size m_kk, used as a temporary holding area.
     */
    mutable vector_fp      m_tmpV;

    //! Logarithm of the molal activity coefficients
    /*!
     *   Normally these are all one. However, stability schemes will change that
     */
    mutable vector_fp      IMS_lnActCoeffMolal_;
public:
    //! value of the solute mole fraction that centers the cutoff polynomials
    //! for the cutoff =1 process;
    doublereal IMS_X_o_cutoff_;

    //! gamma_o value for the cutoff process at the zero solvent point
    doublereal IMS_gamma_o_min_;

    //! gamma_k minimum for the cutoff process at the zero solvent point
    doublereal IMS_gamma_k_min_;

    //! Parameter in the polyExp cutoff treatment
    /*!
     *  This is the slope of the f function at the zero solvent point
     *  Default value is 0.6
     */
    doublereal IMS_slopefCut_;

    //! Parameter in the polyExp cutoff treatment
    /*!
     *  This is the slope of the g function at the zero solvent point
     *  Default value is 0.0
     */
    doublereal IMS_slopegCut_;

    //! @name Parameters in the polyExp cutoff treatment having to do with rate of exp decay
    //! @{
    doublereal IMS_cCut_;
    doublereal IMS_dfCut_;
    doublereal IMS_efCut_;
    doublereal IMS_afCut_;
    doublereal IMS_bfCut_;
    doublereal IMS_dgCut_;
    doublereal IMS_egCut_;
    doublereal IMS_agCut_;
    doublereal IMS_bgCut_;
    //! @}

private:
    //! This function will be called to update the internally stored
    //! natural logarithm of the molality activity coefficients
    /*!
     * Normally the solutes are all zero. However, sometimes they are not,
     * due to stability schemes.
     *
     *    gamma_k_molar =  gamma_k_molal / Xmol_solvent
     *
     *    gamma_o_molar = gamma_o_molal
     */
    void s_updateIMS_lnMolalityActCoeff() const;

    //! This internal function adjusts the lengths of arrays.
    /*!
     * This function is not virtual nor is it inherited
     */
    void initLengths();

    //! Calculate parameters for cutoff treatments of activity coefficients
    /*!
     * Some cutoff treatments for the activity coefficients
     * actually require some calculations to create a consistent treatment.
     *
     * This routine is called during the setup to calculate these parameters
     */
    void calcIMSCutoffParams_();
};

/* @} */
}

#endif