Implementation of a multi-species Peng-Robinson equation of state. More...

#include <PengRobinson.h>

Inheritance diagram for PengRobinson:

Detailed Description

Implementation of a multi-species Peng-Robinson equation of state.

Definition at line 19 of file PengRobinson.h.

Public Member Functions
	PengRobinson (const string &infile="", const string &id="")
	Construct and initialize a PengRobinson object directly from an input file.

string	type () const override
	String indicating the thermodynamic model implemented.

double	standardConcentration (size_t k=0) const override
	Returns the standard concentration \( C^0_k \), which is used to normalize the generalized concentration.

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

double	speciesCritTemperature (double a, double b) const
	Calculate species-specific critical temperature.

double	isothermalCompressibility () const override
	Returns the isothermal compressibility. Units: 1/Pa.

double	thermalExpansionCoeff () const override
	Return the volumetric thermal expansion coefficient. Units: 1/K.

double	soundSpeed () const override
	Return the speed of sound. Units: m/s.

void	calculatePressureDerivatives () const
	Calculate \( dp/dV \) and \( dp/dT \) at the current conditions.

void	updateMixingExpressions () override
	Update the \( a \), \( b \), and \( \alpha \) parameters.

void	calculateAB (double &aCalc, double &bCalc, double &aAlpha) const
	Calculate the \( a \), \( b \), and \( \alpha \) parameters given the temperature.

void	calcCriticalConditions (double &pc, double &tc, double &vc) const override

int	solveCubic (double T, double pres, double a, double b, double aAlpha, double Vroot[3]) const
	Prepare variables and call the function to solve the cubic equation of state.

Molar Thermodynamic properties
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.

Mechanical Properties
double	pressure () const override
	Return the thermodynamic pressure (Pa).

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	getPartialMolarIntEnergies (double *ubar) const override
	Return an array of partial molar internal energies for the species in the mixture.

void	getPartialMolarCp (double *cpbar) const override
	Calculate species-specific molar specific heats.

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

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

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.

void	setSpeciesCoeffs (const string &species, double a, double b, double w)
	Set the pure fluid interaction parameters for a species.

void	setBinaryCoeffs (const string &species_i, const string &species_j, double a)
	Set values for the interaction parameter between two species.

Public Member Functions inherited from MixtureFugacityTP
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.

	MixtureFugacityTP ()=default
	Constructor.

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	setForcedSolutionBranch (int solnBranch)
	Set the solution branch to force the ThermoPhase to exist on one branch or another.

int	forcedSolutionBranch () const
	Report the solution branch which the solution is restricted to.

int	reportSolnBranchActual () const
	Report the solution branch which the solution is actually on.

double	enthalpy_mole () const override
	Molar enthalpy. Units: J/kmol.

double	entropy_mole () const override
	Molar entropy. Units: J/kmol/K.

void	getChemPotentials_RT (double *mu) const override
	Get the array of non-dimensional species chemical potentials These are partial molar Gibbs free energies.

void	getStandardChemPotentials (double *mu) const override
	Get the array of chemical potentials at unit activity.

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 Enthalpy 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 at their standard states of solution at the current T and P of the solution.

void	getPureGibbs (double *gpure) const override
	Get the pure Gibbs free energies of each species.

void	getIntEnergy_RT (double *urt) const override
	Returns the vector of nondimensional internal Energies of the standard state at the current temperature and pressure of the solution for each species.

void	getCp_R (double *cpr) const override
	Get the nondimensional Heat Capacities at constant pressure for the standard state of the species at the current T and P.

void	getStandardVolumes (double *vol) const override
	Get the molar volumes of each species in their standard states at the current T and P of the solution.

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.

int	phaseState (bool checkState=false) const
	Returns the Phase State flag for the current state of the object.

double	calculatePsat (double TKelvin, double &molarVolGas, double &molarVolLiquid)
	Calculate the saturation pressure at the current mixture content for the given temperature.

double	satPressure (double TKelvin) override
	Calculate the saturation pressure at the current mixture content for the given temperature.

void	getActivityConcentrations (double *c) const override
	This method returns an array of generalized concentrations.

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.

string	type () const override
	String indicating the thermodynamic model implemented.

virtual bool	isIdeal () const
	Boolean indicating whether phase is ideal.

virtual string	phaseOfMatter () const
	String indicating the mechanical phase of the matter in this Phase.

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

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

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.

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

bool	chargeNeutralityNecessary () const
	Returns the chargeNeutralityNecessity boolean.

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

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

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

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

virtual int	activityConvention () const
	This method returns the convention used in specification of the activities, of which there are currently two, molar- and molality-based conventions.

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	getActivities (double *a) const
	Get the array of non-dimensional activities at the current solution temperature, pressure, and solution concentration.

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	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_TP (double t, double p)
	Set the temperature (K) and pressure (Pa)

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

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

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)

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

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

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

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

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

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

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

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

virtual void	setState (const AnyMap &state)
	Set the state using an AnyMap containing any combination of properties supported by the thermodynamic model.

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	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).

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

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 ()

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

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 (const size_t ld, double *const dlnActCoeffdlnN)
	Get the array of derivatives of the log activity coefficients with respect to the log of the species mole numbers.

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

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

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

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 (vector< double > &weights) const
	Copy the vector of molecular weights into vector weights.

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.

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

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`.

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

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

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_TRX (double t, double dens, const double *x)
	Set the internally stored temperature (K), density, and mole fractions.

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

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

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

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

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

void	setState_TD (double t, double rho)
	Set the internally stored temperature (K) and density (kg/m^3)

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

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

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

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

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	setMolarDensity (const double molarDensity)
	Set the internally stored molar density (kmol/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).

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.

Protected Types
enum class	CoeffSource { EoS , CritProps , Database }

Protected Member Functions
double	sresid () const override
	Calculate the deviation terms for the total entropy of the mixture from the ideal gas mixture.

double	hresid () const override
	Calculate the deviation terms for the total enthalpy of the mixture from the ideal gas mixture.

double	liquidVolEst (double T, double &pres) const override
	Estimate for the molar volume of the liquid.

double	densityCalc (double T, double pressure, int phase, double rhoguess) override
	Calculates the density given the temperature and the pressure and a guess at the density.

double	densSpinodalLiquid () const override
	Return the value of the density at the liquid spinodal point (on the liquid side) for the current temperature.

double	densSpinodalGas () const override
	Return the value of the density at the gas spinodal point (on the gas side) for the current temperature.

double	dpdVCalc (double T, double molarVol, double &presCalc) const override
	Calculate the pressure and the pressure derivative given the temperature and the molar volume.

double	daAlpha_dT () const
	Calculate temperature derivative \( d(a \alpha)/dT \).

double	d2aAlpha_dT2 () const
	Calculate second derivative \( d^2(a \alpha)/dT^2 \).

Protected Member Functions inherited from MixtureFugacityTP
void	compositionChanged () override
	Apply changes to the state which are needed after the composition changes.

virtual void	_updateReferenceStateThermo () const
	Updates the reference state thermodynamic functions at the current T of the solution.

double	critTemperature () const override
	Critical temperature (K).

double	critPressure () const override
	Critical pressure (Pa).

double	critVolume () const override
	Critical volume (m3/kmol).

double	critCompressibility () const override
	Critical compressibility (unitless).

double	critDensity () const override
	Critical density (kg/m3).

int	solveCubic (double T, double pres, double a, double b, double aAlpha, double Vroot[3], double an, double bn, double cn, double dn, double tc, double vc) const
	Solve the cubic equation of state.

const vector< double > &	gibbs_RT_ref () const
	Returns the vector of nondimensional Gibbs free energies of the reference state at the current temperature of the solution and the reference pressure for the species.

double	z () const
	Calculate the value of z.

virtual double	psatEst (double TKelvin) const
	Estimate for the saturation pressure.

int	corr0 (double TKelvin, double pres, double &densLiq, double &densGas, double &liqGRT, double &gasGRT)
	Utility routine in the calculation of the saturation pressure.

Protected Member Functions inherited from ThermoPhase
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.

virtual void	getCsvReportData (vector< string > &names, vector< vector< double > > &data) const
	Fills `names` and `data` with the column names and species thermo properties to be included in the output of the reportCSV method.

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.

Protected Attributes
double	m_b = 0.0
	Value of \( b \) in the equation of state.

double	m_a = 0.0
	Value of \( a \) in the equation of state.

double	m_aAlpha_mix = 0.0
	Value of \( a \alpha \) in the equation of state.

vector< double >	m_b_coeffs

vector< double >	m_kappa

vector< double >	m_acentric
	acentric factor for each species, length m_kk

vector< double >	m_dalphadT

vector< double >	m_d2alphadT2

vector< double >	m_alpha

Array2D	m_a_coeffs

Array2D	m_aAlpha_binary

map< string, map< string, double > >	m_binaryParameters
	Explicitly-specified binary interaction parameters, to enable serialization.

int	m_NSolns = 0

double	m_Vroot [3] = {0.0, 0.0, 0.0}

vector< double >	m_pp
	Temporary storage - length = m_kk.

vector< double >	m_partialMolarVolumes

double	m_dpdV = 0.0
	The derivative of the pressure with respect to the volume.

double	m_dpdT = 0.0
	The derivative of the pressure with respect to the temperature.

vector< double >	m_dpdni
	Vector of derivatives of pressure with respect to mole number.

vector< CoeffSource >	m_coeffSource
	For each species, specifies the source of the a, b, and omega coefficients.

Protected Attributes inherited from MixtureFugacityTP
vector< double >	m_tmpV
	Temporary storage - length = m_kk.

vector< double >	moleFractions_
	Storage for the current values of the mole fractions of the species.

int	iState_ = FLUID_GAS
	Current state of the fluid.

int	forcedState_ = FLUID_UNDEFINED
	Force the system to be on a particular side of the spinodal curve.

vector< double >	m_h0_RT
	Temporary storage for dimensionless reference state enthalpies.

vector< double >	m_cp0_R
	Temporary storage for dimensionless reference state heat capacities.

vector< double >	m_g0_RT
	Temporary storage for dimensionless reference state Gibbs energies.

vector< double >	m_s0_R
	Temporary storage for dimensionless reference state entropies.

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

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.

Static Private Attributes
static const double	omega_a = 4.5723552892138218E-01
	Omega constant: a0 (= omega_a) used in Peng-Robinson equation of state.

static const double	omega_b = 7.77960739038885E-02
	Omega constant: b0 (= omega_b) used in Peng-Robinson equation of state.

static const double	omega_vc = 3.07401308698703833E-01
	Omega constant for the critical molar volume.

Member Enumeration Documentation

◆ CoeffSource

enum class CoeffSource

strongprotected

Definition at line 305 of file PengRobinson.h.

Constructor & Destructor Documentation

◆ PengRobinson()

PengRobinson	(	const string &	infile = `""`,
		const string &	id = `""`
	)

explicit

Construct and initialize a PengRobinson object directly from an input file.

Parameters

infile	Name of the input file containing the phase YAML data. If blank, an empty phase will be created.
id	ID of the phase in the input file. If empty, the first phase definition in the input file will be used.

Definition at line 24 of file PengRobinson.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 MixtureFugacityTP.

Definition at line 33 of file PengRobinson.h.

◆ cp_mole()

double cp_mole ( ) const

overridevirtual

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

Reimplemented from ThermoPhase.

Definition at line 98 of file PengRobinson.cpp.

◆ cv_mole()

double cv_mole ( ) const

overridevirtual

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

Reimplemented from ThermoPhase.

Definition at line 112 of file PengRobinson.cpp.

◆ pressure()

double pressure ( ) const

overridevirtual

Return the thermodynamic pressure (Pa).

Since the mass density, temperature, and mass fractions are stored, this method uses these values to implement the mechanical equation of state \( P(T, \rho, Y_1, \dots, Y_K) \).

\[ P = \frac{RT}{v-b_{mix}} - \frac{\left(\alpha a\right)_{mix}}{v^2 + 2b_{mix}v - b_{mix}^2} \]

where:

\[ \alpha = \left[ 1 + \kappa \left(1-T_r^{0.5}\right)\right]^2 \]

and

\[ \kappa = \left(0.37464 + 1.54226\omega - 0.26992\omega^2\right), \qquad \qquad \text{For } \omega <= 0.491 \\ \kappa = \left(0.379642 + 1.487503\omega - 0.164423\omega^2 + 0.016667\omega^3 \right), \qquad \text{For } \omega > 0.491 \]

Coefficients \( a_{mix}, b_{mix} \) and \( (a \alpha)_{mix} \) are calculated as

\[ a_{mix} = \sum_i \sum_j X_i X_j a_{i, j} = \sum_i \sum_j X_i X_j \sqrt{a_i a_j} \]

\[ b_{mix} = \sum_i X_i b_i \]

\[ {a \alpha}_{mix} = \sum_i \sum_j X_i X_j {a \alpha}_{i, j} = \sum_i \sum_j X_i X_j \sqrt{a_i a_j} \sqrt{\alpha_i \alpha_j} \]

Reimplemented from Phase.

Definition at line 120 of file PengRobinson.cpp.

◆ standardConcentration()

double standardConcentration ( size_t k = 0 ) const

overridevirtual

Returns the standard concentration \( C^0_k \), which is used to normalize the generalized concentration.

This is defined as the concentration by which the generalized concentration is normalized to produce the activity. The ideal gas mixture is considered as the standard or reference state here. Since the activity for an ideal gas mixture is simply the mole fraction, for an ideal gas, \( C^0_k = P/\hat R T \).

Parameters

k	Optional parameter indicating the species. The default is to assume this refers to species 0.

Returns: Returns the standard Concentration in units of m^3 / kmol.

Reimplemented from ThermoPhase.

Definition at line 130 of file PengRobinson.cpp.

◆ getActivityCoefficients()

void getActivityCoefficients ( double * ac ) const

overridevirtual

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

For all objects with the Mixture Fugacity approximation, we define the standard state as an ideal gas at the current temperature and pressure of the solution. The activities are based on this standard state.

Parameters

ac	Output vector of activity coefficients. Length: m_kk.

Reimplemented from ThermoPhase.

Definition at line 136 of file PengRobinson.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 at the current temperature, pressure and mole fraction of the solution.

Parameters

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

Reimplemented from ThermoPhase.

Definition at line 169 of file PengRobinson.cpp.

◆ getPartialMolarEnthalpies()

void getPartialMolarEnthalpies ( double * hbar ) const

overridevirtual

Returns an array of partial molar enthalpies for the species in the mixture.

Units (J/kmol)

Parameters

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

Reimplemented from ThermoPhase.

Definition at line 204 of file PengRobinson.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.

Parameters

sbar	Output vector of species partial molar entropies. Length = m_kk. units are J/kmol/K.

Reimplemented from ThermoPhase.

Definition at line 254 of file PengRobinson.cpp.

◆ getPartialMolarIntEnergies()

void getPartialMolarIntEnergies ( double * ubar ) const

overridevirtual

Return an array of partial molar internal energies for the species in the mixture.

Units: J/kmol.

Parameters

ubar	Output vector of species partial molar internal energies. Length = m_kk. units are J/kmol.

Reimplemented from ThermoPhase.

Definition at line 265 of file PengRobinson.cpp.

◆ getPartialMolarCp()

void getPartialMolarCp ( double * cpbar ) const

overridevirtual

Calculate species-specific molar specific heats.

This function is currently not implemented for Peng-Robinson phase.

Reimplemented from ThermoPhase.

Definition at line 276 of file PengRobinson.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.

Parameters

vbar	Output vector of species partial molar volumes. Length = m_kk. units are m^3/kmol.

Reimplemented from ThermoPhase.

Definition at line 281 of file PengRobinson.cpp.

◆ speciesCritTemperature()

double speciesCritTemperature	(	double	a,
		double	b
	)		const

Calculate species-specific critical temperature.

The temperature dependent parameter in P-R EoS is calculated as

\[ T_{crit} = (0.0778 a)/(0.4572 b R) \]

Units: Kelvin

Parameters

a	species-specific coefficients used in P-R EoS
b	species-specific coefficients used in P-R EoS

Definition at line 307 of file PengRobinson.cpp.

◆ addSpecies()

bool addSpecies ( shared_ptr< Species > spec )

overridevirtual

Add a Species to this Phase.

Returns true if the species was successfully added, or false if the species was ignored.

Derived classes which need to size arrays according to the number of species should overload this method. The derived class implementation should call the base class method, and, if this returns true (indicating that the species has been added), adjust their array sizes accordingly.

See also: ignoreUndefinedElements addUndefinedElements throwUndefinedElements

Reimplemented from MixtureFugacityTP.

Definition at line 318 of file PengRobinson.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 338 of file PengRobinson.cpp.

◆ getSpeciesParameters()

void getSpeciesParameters	(	const string &	name,
		AnyMap &	speciesNode
	)		const

overridevirtual

Get phase-specific parameters of a Species object such that an identical one could be reconstructed and added to this phase.

Parameters

name	Name of the species
speciesNode	Mapping to be populated with parameters

Reimplemented from ThermoPhase.

Definition at line 423 of file PengRobinson.cpp.

◆ setSpeciesCoeffs()

void setSpeciesCoeffs	(	const string &	species,
		double	a,
		double	b,
		double	w
	)

Set the pure fluid interaction parameters for a species.

Parameters

species	Name of the species
a	\( a \) parameter in the Peng-Robinson model [Pa-m^6/kmol^2]
b	\( a \) parameter in the Peng-Robinson model [m^3/kmol]
w	acentric factor

Definition at line 29 of file PengRobinson.cpp.

◆ setBinaryCoeffs()

void setBinaryCoeffs	(	const string &	species_i,
		const string &	species_j,
		double	a
	)

Set values for the interaction parameter between two species.

Parameters

species_i	Name of one species
species_j	Name of the other species
a	\( a \) parameter in the Peng-Robinson model [Pa-m^6/kmol^2]

Definition at line 74 of file PengRobinson.cpp.

◆ sresid()

double sresid ( ) const

overrideprotectedvirtual

Calculate the deviation terms for the total entropy of the mixture from the ideal gas mixture.

Here we use the current state conditions

Returns: the change in entropy in units of J kmol-1 K-1.

Reimplemented from MixtureFugacityTP.

Definition at line 459 of file PengRobinson.cpp.

◆ hresid()

double hresid ( ) const

overrideprotectedvirtual

Calculate the deviation terms for the total enthalpy of the mixture from the ideal gas mixture.

Here we use the current state conditions

Returns: the change in entropy in units of J kmol-1.

Reimplemented from MixtureFugacityTP.

Definition at line 472 of file PengRobinson.cpp.

◆ liquidVolEst()

double liquidVolEst	(	double	TKelvin,
		double &	pres
	)		const

overrideprotectedvirtual

Estimate for the molar volume of the liquid.

Note: this is only used as a starting guess for later routines that actually calculate an accurate value for the liquid molar volume. This routine doesn't change the state of the system.

Parameters

TKelvin	temperature in kelvin
pres	Pressure in Pa. This is used as an initial guess. If the routine needs to change the pressure to find a stable liquid state, the new pressure is returned in this variable.

Returns: the estimate of the liquid volume. If the liquid can't be found, this routine returns -1.

Reimplemented from MixtureFugacityTP.

Definition at line 485 of file PengRobinson.cpp.

◆ densityCalc()

double densityCalc	(	double	TKelvin,
		double	pressure,
		int	phaseRequested,
		double	rhoguess
	)

overrideprotectedvirtual

Calculates the density given the temperature and the pressure and a guess at the density.

Note, below T_c, this is a multivalued function. We do not cross the vapor dome in this. This is protected because it is called during setState_TP() routines. Infinite loops would result if it were not protected.

Parameters

TKelvin	Temperature in Kelvin
pressure	Pressure in Pascals (Newton/m**2)
phaseRequested	int representing the phase whose density we are requesting. If we put a gas or liquid phase here, we will attempt to find a volume in that part of the volume space, only, in this routine. A value of FLUID_UNDEFINED means that we will accept anything.
rhoguess	Guessed density of the fluid. A value of -1.0 indicates that there is no guessed density

Returns: We return the density of the fluid at the requested phase. If we have not found any acceptable density we return a -1. If we have found an acceptable density at a different phase, we return a -2.

Reimplemented from MixtureFugacityTP.

Definition at line 516 of file PengRobinson.cpp.

◆ densSpinodalLiquid()

double densSpinodalLiquid ( ) const

overrideprotectedvirtual

Return the value of the density at the liquid spinodal point (on the liquid side) for the current temperature.

Returns: the density with units of kg m-3

Reimplemented from MixtureFugacityTP.

Definition at line 574 of file PengRobinson.cpp.

◆ densSpinodalGas()

double densSpinodalGas ( ) const

overrideprotectedvirtual

Return the value of the density at the gas spinodal point (on the gas side) for the current temperature.

Returns: the density with units of kg m-3

Reimplemented from MixtureFugacityTP.

Definition at line 596 of file PengRobinson.cpp.

◆ dpdVCalc()

double dpdVCalc	(	double	TKelvin,
		double	molarVol,
		double &	presCalc
	)		const

overrideprotectedvirtual

Calculate the pressure and the pressure derivative given the temperature and the molar volume.

Temperature and mole number are held constant

Parameters

TKelvin	temperature in kelvin
molarVol	molar volume ( m3/kmol)
presCalc	Returns the pressure.

Returns: the derivative of the pressure wrt the molar volume

Reimplemented from MixtureFugacityTP.

Definition at line 618 of file PengRobinson.cpp.

◆ daAlpha_dT()

double daAlpha_dT ( ) const

protected

Calculate temperature derivative \( d(a \alpha)/dT \).

These are stored internally.

Definition at line 690 of file PengRobinson.cpp.

◆ d2aAlpha_dT2()

double d2aAlpha_dT2 ( ) const

protected

Calculate second derivative \( d^2(a \alpha)/dT^2 \).

These are stored internally.

Definition at line 713 of file PengRobinson.cpp.

◆ isothermalCompressibility()

double isothermalCompressibility ( ) const

overridevirtual

Returns the isothermal compressibility. Units: 1/Pa.

The isothermal compressibility is defined as

\[ \kappa_T = -\frac{1}{v}\left(\frac{\partial v}{\partial P}\right)_T \]

or

\[ \kappa_T = \frac{1}{\rho}\left(\frac{\partial \rho}{\partial P}\right)_T \]

Reimplemented from ThermoPhase.

Definition at line 626 of file PengRobinson.cpp.

◆ thermalExpansionCoeff()

double thermalExpansionCoeff ( ) const

overridevirtual

Return the volumetric thermal expansion coefficient. Units: 1/K.

The thermal expansion coefficient is defined as

\[ \beta = \frac{1}{v}\left(\frac{\partial v}{\partial T}\right)_P \]

Reimplemented from ThermoPhase.

Definition at line 632 of file PengRobinson.cpp.

◆ soundSpeed()

double soundSpeed ( ) const

overridevirtual

Return the speed of sound. Units: m/s.

The speed of sound is defined as

\[ c = \sqrt{\left(\frac{\partial P}{\partial\rho}\right)_s} \]

Reimplemented from ThermoPhase.

Definition at line 638 of file PengRobinson.cpp.

◆ calculatePressureDerivatives()

void calculatePressureDerivatives ( ) const

Calculate \( dp/dV \) and \( dp/dT \) at the current conditions.

These are stored internally.

Definition at line 644 of file PengRobinson.cpp.

◆ updateMixingExpressions()

void updateMixingExpressions ( )

overridevirtual

Update the \( a \), \( b \), and \( \alpha \) parameters.

The \( a \) and the \( b \) parameters depend on the mole fraction and the parameter \( \alpha \) depends on the temperature. This function updates the internal numbers based on the state of the object.

Reimplemented from MixtureFugacityTP.

Definition at line 656 of file PengRobinson.cpp.

◆ calculateAB()

void calculateAB	(	double &	aCalc,
		double &	bCalc,
		double &	aAlpha
	)		const

Calculate the \( a \), \( b \), and \( \alpha \) parameters given the temperature.

This function doesn't change the internal state of the object, so it is a const function. It does use the stored mole fractions in the object.

Parameters

aCalc	(output) Returns the a value
bCalc	(output) Returns the b value.
aAlpha	(output) Returns the (a*alpha) value.

Definition at line 676 of file PengRobinson.cpp.

◆ calcCriticalConditions()

void calcCriticalConditions	(	double &	pc,
		double &	tc,
		double &	vc
	)		const

overridevirtual

Reimplemented from MixtureFugacityTP.

Definition at line 744 of file PengRobinson.cpp.

◆ solveCubic()

int solveCubic	(	double	T,
		double	pres,
		double	a,
		double	b,
		double	aAlpha,
		double	Vroot[3]
	)		const

Prepare variables and call the function to solve the cubic equation of state.

Definition at line 763 of file PengRobinson.cpp.

Member Data Documentation

◆ m_b

double m_b = 0.0

protected

Value of \( b \) in the equation of state.

m_b is a function of the mole fractions and species-specific b values.

Definition at line 243 of file PengRobinson.h.

◆ m_a

double m_a = 0.0

protected

Value of \( a \) in the equation of state.

m_a depends only on the mole fractions.

Definition at line 249 of file PengRobinson.h.

◆ m_aAlpha_mix

double m_aAlpha_mix = 0.0

protected

Value of \( a \alpha \) in the equation of state.

m_aAlpha_mix is a function of the temperature and the mole fractions.

Definition at line 255 of file PengRobinson.h.

◆ m_b_coeffs

vector<double> m_b_coeffs

protected

Definition at line 259 of file PengRobinson.h.

◆ m_kappa

vector<double> m_kappa

protected

Definition at line 260 of file PengRobinson.h.

◆ m_acentric

vector<double> m_acentric

protected

acentric factor for each species, length m_kk

Definition at line 261 of file PengRobinson.h.

◆ m_dalphadT

vector<double> m_dalphadT

mutableprotected

Definition at line 262 of file PengRobinson.h.

◆ m_d2alphadT2

vector<double> m_d2alphadT2

mutableprotected

Definition at line 263 of file PengRobinson.h.

◆ m_alpha

vector<double> m_alpha

protected

Definition at line 264 of file PengRobinson.h.

◆ m_a_coeffs

Array2D m_a_coeffs

protected

Definition at line 268 of file PengRobinson.h.

◆ m_aAlpha_binary

Array2D m_aAlpha_binary

protected

Definition at line 269 of file PengRobinson.h.

◆ m_binaryParameters

map<string, map<string, double> > m_binaryParameters

protected

Explicitly-specified binary interaction parameters, to enable serialization.

Definition at line 272 of file PengRobinson.h.

◆ m_NSolns

int m_NSolns = 0

protected

Definition at line 274 of file PengRobinson.h.

◆ m_Vroot

double m_Vroot[3] = {0.0, 0.0, 0.0}

protected

Definition at line 276 of file PengRobinson.h.

◆ m_pp

vector<double> m_pp

mutableprotected

Temporary storage - length = m_kk.

Definition at line 279 of file PengRobinson.h.

◆ m_partialMolarVolumes

vector<double> m_partialMolarVolumes

mutableprotected

Definition at line 282 of file PengRobinson.h.

◆ m_dpdV

double m_dpdV = 0.0

mutableprotected

The derivative of the pressure with respect to the volume.

Calculated at the current conditions. temperature and mole number kept constant

Definition at line 289 of file PengRobinson.h.

◆ m_dpdT

double m_dpdT = 0.0

mutableprotected

The derivative of the pressure with respect to the temperature.

Calculated at the current conditions. Total volume and mole number kept constant

Definition at line 296 of file PengRobinson.h.

◆ m_dpdni

vector<double> m_dpdni

mutableprotected

Vector of derivatives of pressure with respect to mole number.

Calculated at the current conditions. Total volume, temperature and other mole number kept constant

Definition at line 303 of file PengRobinson.h.

◆ m_coeffSource

vector<CoeffSource> m_coeffSource

protected

For each species, specifies the source of the a, b, and omega coefficients.

Definition at line 307 of file PengRobinson.h.

◆ omega_a

const double omega_a = 4.5723552892138218E-01

staticprivate

Omega constant: a0 (= omega_a) used in Peng-Robinson equation of state.

This value is calculated by solving P-R cubic equation at the critical point.

Definition at line 314 of file PengRobinson.h.

◆ omega_b

const double omega_b = 7.77960739038885E-02

staticprivate

Omega constant: b0 (= omega_b) used in Peng-Robinson equation of state.

This value is calculated by solving P-R cubic equation at the critical point.

Definition at line 320 of file PengRobinson.h.

◆ omega_vc

const double omega_vc = 3.07401308698703833E-01

staticprivate

Omega constant for the critical molar volume.

Definition at line 323 of file PengRobinson.h.

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

Detailed Description

Public Member Functions

Protected Types

Protected Member Functions

Protected Attributes

Static Private Attributes

Member Enumeration Documentation

◆ CoeffSource

Constructor & Destructor Documentation

◆ PengRobinson()

Member Function Documentation

◆ type()

◆ cp_mole()

◆ cv_mole()

◆ pressure()

◆ standardConcentration()

◆ getActivityCoefficients()

◆ getChemPotentials()

◆ getPartialMolarEnthalpies()

◆ getPartialMolarEntropies()

◆ getPartialMolarIntEnergies()

◆ getPartialMolarCp()

◆ getPartialMolarVolumes()

◆ speciesCritTemperature()

◆ addSpecies()

◆ initThermo()

◆ getSpeciesParameters()

◆ setSpeciesCoeffs()

◆ setBinaryCoeffs()

◆ sresid()

◆ hresid()

◆ liquidVolEst()

◆ densityCalc()

◆ densSpinodalLiquid()

◆ densSpinodalGas()

◆ dpdVCalc()

◆ daAlpha_dT()

◆ d2aAlpha_dT2()

◆ isothermalCompressibility()

◆ thermalExpansionCoeff()

◆ soundSpeed()

◆ calculatePressureDerivatives()

◆ updateMixingExpressions()

◆ calculateAB()

◆ calcCriticalConditions()

◆ solveCubic()

Member Data Documentation

◆ m_b

◆ m_a

◆ m_aAlpha_mix

◆ m_b_coeffs

◆ m_kappa

◆ m_acentric

◆ m_dalphadT

◆ m_d2alphadT2

◆ m_alpha

◆ m_a_coeffs

◆ m_aAlpha_binary

◆ m_binaryParameters

◆ m_NSolns

◆ m_Vroot

◆ m_pp

◆ m_partialMolarVolumes

◆ m_dpdV

◆ m_dpdT

◆ m_dpdni

◆ m_coeffSource

◆ omega_a

◆ omega_b

◆ omega_vc