ChemEquil Class Reference

Class ChemEquil implements a chemical equilibrium solver for single-phase solutions. More...

#include <ChemEquil.h>

Collaboration diagram for ChemEquil:

Public Member Functions
	ChemEquil (thermo_t &s)
	Constructor combined with the initialization function. More...
int	equilibrate (thermo_t &s, const char *XY, bool useThermoPhaseElementPotentials=false, int loglevel=0)
int	equilibrate (thermo_t &s, const char *XY, vector_fp &elMoles, bool useThermoPhaseElementPotentials=false, int loglevel=0)
const vector_fp &	elementPotentials () const

Public Attributes
EquilOpt	options
	Options controlling how the calculation is carried out. More...

Protected Member Functions
doublereal	nAtoms (size_t k, size_t m) const
	number of atoms of element m in species k. More...
void	initialize (thermo_t &s)
void	setToEquilState (thermo_t &s, const vector_fp &x, doublereal t)
int	setInitialMoles (thermo_t &s, vector_fp &elMoleGoal, int loglevel=0)
	Estimate the initial mole numbers. More...
int	estimateElementPotentials (thermo_t &s, vector_fp &lambda, vector_fp &elMolesGoal, int loglevel=0)
	Generate a starting estimate for the element potentials. More...
int	estimateEP_Brinkley (thermo_t &s, vector_fp &lambda, vector_fp &elMoles)
int	dampStep (thermo_t &s, vector_fp &oldx, double oldf, vector_fp &grad, vector_fp &step, vector_fp &x, double &f, vector_fp &elmols, double xval, double yval)
	Find an acceptable step size and take it. More...
void	equilResidual (thermo_t &s, const vector_fp &x, const vector_fp &elmtotal, vector_fp &resid, double xval, double yval, int loglevel=0)
	Evaluates the residual vector F, of length m_mm. More...
void	equilJacobian (thermo_t &s, vector_fp &x, const vector_fp &elmols, DenseMatrix &jac, double xval, double yval, int loglevel=0)
void	adjustEloc (thermo_t &s, vector_fp &elMolesGoal)
void	update (const thermo_t &s)
	Update internally stored state information. More...
double	calcEmoles (thermo_t &s, vector_fp &x, const double &n_t, const vector_fp &Xmol_i_calc, vector_fp &eMolesCalc, vector_fp &n_i_calc, double pressureConst)
	Given a vector of dimensionless element abundances, this routine calculates the moles of the elements and the moles of the species. More...

Protected Attributes
thermo_t *	m_phase
	Pointer to the ThermoPhase object used to initialize this object. More...
size_t	m_mm
	number of elements in the phase More...
size_t	m_kk
	number of species in the phase More...
size_t	m_skip
size_t	m_nComponents
	This is equal to the rank of the stoichiometric coefficient matrix when it is computed. More...
std::auto_ptr < PropertyCalculator< thermo_t > >	m_p1
std::auto_ptr < PropertyCalculator< thermo_t > >	m_p2
vector_fp	m_molefractions
	Current value of the mole fractions in the single phase. More...
vector_fp	m_lambda
	Current value of the dimensional element potentials -> length = m_mm. More...
doublereal	m_elementTotalSum
vector_fp	m_elementmolefracs
vector_fp	m_reswork
vector_fp	m_jwork1
vector_fp	m_jwork2
vector_fp	m_comp
doublereal	m_temp
doublereal	m_dens
doublereal	m_p0
size_t	m_eloc
	Index of the element id corresponding to the electric charge of each species. More...
vector_fp	m_startSoln
vector_fp	m_grt
vector_fp	m_mu_RT
vector_fp	m_muSS_RT
	Dimensionless values of the Gibbs free energy for the standard state of each species, at the temperature and pressure of the solution (the star standard state). More...
std::vector< size_t >	m_component
double	m_elemFracCutoff
	element fractional cutoff, below which the element will be zeroed. More...
bool	m_doResPerturb
std::vector< size_t >	m_orderVectorElements
std::vector< size_t >	m_orderVectorSpecies

Detailed Description

Class ChemEquil implements a chemical equilibrium solver for single-phase solutions.

It is a "non-stoichiometric" solver in the terminology of Smith and Missen, meaning that every intermediate state is a valid chemical equilibrium state, but does not necessarily satisfy the element constraints. In contrast, the solver implemented in class MultiPhaseEquil uses a "stoichiometric" algorithm, in which each intermediate state satisfies the element constraints but is not a state of chemical equilibrium. Non-stoichiometric methods are faster when they converge, but stoichiometric ones tend to be more robust and can be used also for problems with multiple condensed phases. As expected, the ChemEquil solver is faster than MultiPhaseEquil for many single-phase equilibrium problems (particularly if there are only a few elements but very many species), but can be less stable. Problem situations include low temperatures where only a few species have non-zero mole fractions, precisely stoichiometric compositions (e.g. 2 H2 + O2). In general, if speed is important, this solver should be tried first, and if it fails then use MultiPhaseEquil.

Definition at line 92 of file ChemEquil.h.

Constructor & Destructor Documentation

ChemEquil

(

thermo_t &

s

)

Constructor combined with the initialization function.

This constructor initializes the ChemEquil object with everything it needs to start solving equilibrium problems.

Parameters

s	ThermoPhase object that will be used in the equilibrium calls.

Definition at line 53 of file ChemEquil.cpp.

References ChemEquil::initialize().

Member Function Documentation

int equilibrate	(	thermo_t &	s,
		const char *	XY,
		bool	useThermoPhaseElementPotentials = false,
		int	loglevel = 0
	)

Equilibrate a phase, holding the elemental composition fixed at the initial value found within the ThermoPhase object s.

The value of 2 specified properties are obtained by querying the ThermoPhase object. The properties must be already contained within the current thermodynamic state of the system.

Definition at line 336 of file ChemEquil.cpp.

References ChemEquil::initialize(), Phase::nElements(), and ChemEquil::update().

Referenced by Cantera::equilibrate(), ThermoPhase::equilibrate(), and Cantera::vcs_equilibrate().

int equilibrate	(	thermo_t &	s,
		const char *	XY,
		vector_fp &	elMoles,
		bool	useThermoPhaseElementPotentials = false,
		int	loglevel = 0
	)

Compute the equilibrium composition for 2 specified properties and the specified element moles.

The 2 specified properties are obtained by querying the ThermoPhase object. The properties must be already contained within the current thermodynamic state of the system.

Parameters

s	phase object to be equilibrated
XY	property pair to hold constant
elMoles	specified vector of element abundances.
useThermoPhaseElementPotentials	get the initial estimate for the chemical potentials from the ThermoPhase object (true) or create our own estimate (false)
loglevel	Specify amount of debug logging (0 to disable)

Returns

Successful returns are indicated by a return value of 0. Unsuccessful returns are indicated by a return value of -1 for lack of convergence or -3 for a singular Jacobian.

Definition at line 348 of file ChemEquil.cpp.

References Cantera::_equilflag(), EquilOpt::absElemTol, Cantera::clip(), ChemEquil::dampStep(), DATA_PTR, Cantera::dot(), Phase::elementName(), ChemEquil::equilResidual(), ChemEquil::estimateElementPotentials(), ChemEquil::estimateEP_Brinkley(), Cantera::fp2str(), Cantera::GasConstant, ThermoPhase::getElementPotentials(), ChemEquil::initialize(), Cantera::int2str(), EquilOpt::iterations, ChemEquil::m_elemFracCutoff, ChemEquil::m_eloc, ChemEquil::m_kk, ChemEquil::m_lambda, ChemEquil::m_mm, ChemEquil::m_nComponents, EquilOpt::maxIterations, ThermoPhase::maxTemp(), ThermoPhase::minTemp(), Phase::moleFraction(), Phase::nElements(), Cantera::npos, Phase::nSpecies(), ChemEquil::options, EquilOpt::relTolerance, Phase::restoreState(), CanteraError::save(), Phase::saveState(), Cantera::scale(), ThermoPhase::setElementPotentials(), ChemEquil::setInitialMoles(), Phase::setMoleFractions(), Phase::setTemperature(), ChemEquil::setToEquilState(), Cantera::solve(), Phase::temperature(), ChemEquil::update(), Cantera::writelog(), and Cantera::writelogf().

doublereal nAtoms ( size_t  k, size_t  m  ) const

inlineprotected

number of atoms of element m in species k.

Definition at line 162 of file ChemEquil.h.

References ChemEquil::m_mm.

Referenced by ChemEquil::calcEmoles(), ChemEquil::estimateElementPotentials(), ChemEquil::estimateEP_Brinkley(), ChemEquil::setToEquilState(), and ChemEquil::update().

void initialize ( thermo_t &  s )

protected

Prepare for equilibrium calculations.

Parameters

s	object representing the solution phase.

Definition at line 67 of file ChemEquil.cpp.

References Phase::atomicWeight(), Phase::elementName(), Cantera::fp2str(), ChemEquil::m_eloc, ChemEquil::m_kk, ChemEquil::m_lambda, ChemEquil::m_mm, ChemEquil::m_molefractions, ChemEquil::m_muSS_RT, ChemEquil::m_nComponents, ChemEquil::m_phase, Phase::nAtoms(), Phase::nElements(), Cantera::npos, Phase::nSpecies(), ThermoPhase::refPressure(), Phase::speciesName(), and Cantera::writelog().

Referenced by ChemEquil::ChemEquil(), and ChemEquil::equilibrate().

void setToEquilState ( thermo_t &  s, const vector_fp &  x, doublereal  t  )

protected

Set mixture to an equilibrium state consistent with specified element potentials and temperature.

Parameters

s	mixture to be updated
x	vector of non-dimensional element potentials \[ \lambda_m/RT \] .
t	temperature in K.

Definition at line 142 of file ChemEquil.cpp.

References DATA_PTR, ChemEquil::m_kk, ChemEquil::m_mm, ChemEquil::nAtoms(), Phase::setTemperature(), ThermoPhase::setToEquilState(), and ChemEquil::update().

Referenced by ChemEquil::equilibrate(), and ChemEquil::equilResidual().

int setInitialMoles ( thermo_t &  s, vector_fp &  elMoleGoal, int  loglevel = 0  )

protected

Estimate the initial mole numbers.

This version borrows from the MultiPhaseEquil solver.

Definition at line 192 of file ChemEquil.cpp.

References MultiPhase::addPhase(), Phase::elementName(), MultiPhase::init(), ChemEquil::m_kk, ChemEquil::m_mm, ChemEquil::m_nComponents, Phase::moleFraction(), ThermoPhase::pressure(), CanteraError::save(), Phase::speciesName(), Phase::temperature(), ChemEquil::update(), Cantera::writelog(), and Cantera::writelogf().

Referenced by ChemEquil::equilibrate().

int estimateElementPotentials ( thermo_t &  s, vector_fp &  lambda, vector_fp &  elMolesGoal, int  loglevel = 0  )

protected

Generate a starting estimate for the element potentials.

Definition at line 240 of file ChemEquil.cpp.

References MultiPhase::addPhase(), Cantera::BasisOptimize(), DATA_PTR, Phase::elementName(), Cantera::ElemRearrange(), Cantera::GasConstant, ThermoPhase::getChemPotentials(), Phase::getMoleFractions(), MultiPhase::init(), ChemEquil::m_kk, ChemEquil::m_mm, ChemEquil::m_nComponents, ChemEquil::nAtoms(), Phase::nSpecies(), ThermoPhase::pressure(), Cantera::scale(), Phase::setMoleFractions(), Cantera::solve(), Phase::speciesName(), Phase::temperature(), Cantera::writelog(), and Cantera::writelogf().

Referenced by ChemEquil::equilibrate().

int estimateEP_Brinkley ( thermo_t &  s, vector_fp &  lambda, vector_fp &  elMoles  )

protected

Do a calculation of the element potentials using the Brinkley method, p. 129 Smith and Missen.

We have found that the previous estimate may not be good enough to avoid drastic numerical issues associated with the use of a numerically generated Jacobian used in the main algorithm.

The Brinkley algorithm, here, assumes a constant T, P system and uses a linearized analytical Jacobian that turns out to be very stable even given bad initial guesses.

The pressure and temperature to be used are in the ThermoPhase object input into the routine.

The initial guess for the element potentials used by this routine is taken from the input vector, x.

elMoles is the input element abundance vector to be matched.

Nonideal phases are handled in principle. This is done by calculating the activity coefficients and adding them into the formula in the correct position. However, these are treated as a RHS contribution only. Therefore, convergence might be a problem. This has not been tested. Also molality based unit systems aren't handled.

On return, int return value contains the success code:

• 0 - successful
• 1 - unsuccessful, max num iterations exceeded
• -3 - unsuccessful, singular Jacobian

NOTE: update for activity coefficients.

Definition at line 972 of file ChemEquil.cpp.

References EquilOpt::absElemTol, ChemEquil::calcEmoles(), Cantera::clip(), DATA_PTR, Phase::elementName(), ThermoPhase::getActivityCoefficients(), ThermoPhase::getGibbs_RT(), Phase::getMoleFractions(), ChemEquil::m_eloc, ChemEquil::m_kk, ChemEquil::m_mm, ChemEquil::m_muSS_RT, ChemEquil::m_nComponents, EquilOpt::maxIterations, ChemEquil::nAtoms(), Cantera::npos, ChemEquil::options, ThermoPhase::pressure(), EquilOpt::relTolerance, Phase::restoreState(), CanteraError::save(), Phase::saveState(), Phase::setMoleFractions(), ThermoPhase::setPressure(), Cantera::solve(), Phase::speciesName(), Phase::temperature(), Cantera::writelog(), and Cantera::writelogf().

Referenced by ChemEquil::equilibrate().

int dampStep ( thermo_t &  s, vector_fp &  oldx, double  oldf, vector_fp &  grad, vector_fp &  step, vector_fp &  x, double &  f, vector_fp &  elmols, double  xval, double  yval  )

protected

Find an acceptable step size and take it.

The original implementation employed a line search technique that enforced a reduction in the norm of the residual at every successful step. Unfortunately, this method created false convergence errors near the end of a significant number of steps, usually special conditions where there were stoichiometric constraints.

This new method just does a delta damping approach, based on limiting the jump in the dimensionless element potentials. Mole fractions are limited to a factor of 2 jump in the values from this method. Near convergence, the delta damping gets out of the way.

Definition at line 802 of file ChemEquil.cpp.

References ChemEquil::m_eloc, ChemEquil::m_mm, Cantera::writelog(), and Cantera::writelogf().

Referenced by ChemEquil::equilibrate().

void equilResidual ( thermo_t &  s, const vector_fp &  x, const vector_fp &  elmtotal, vector_fp &  resid, double  xval, double  yval, int  loglevel = 0  )

protected

Evaluates the residual vector F, of length m_mm.

Definition at line 846 of file ChemEquil.cpp.

References ChemEquil::m_elemFracCutoff, ChemEquil::m_eloc, ChemEquil::m_mm, ChemEquil::m_nComponents, ChemEquil::setToEquilState(), Cantera::writelog(), and Cantera::writelogf().

Referenced by ChemEquil::equilibrate().

void update ( const thermo_t &  s )

protected

Update internally stored state information.

Definition at line 162 of file ChemEquil.cpp.

References DATA_PTR, Phase::density(), Cantera::fp2str(), Phase::getMoleFractions(), ChemEquil::m_kk, ChemEquil::m_mm, ChemEquil::m_molefractions, ChemEquil::nAtoms(), Phase::speciesName(), and Phase::temperature().

Referenced by ChemEquil::equilibrate(), ChemEquil::setInitialMoles(), and ChemEquil::setToEquilState().

double calcEmoles ( thermo_t &  s, vector_fp &  x, const double &  n_t, const vector_fp &  Xmol_i_calc, vector_fp &  eMolesCalc, vector_fp &  n_i_calc, double  pressureConst  )

protected

Given a vector of dimensionless element abundances, this routine calculates the moles of the elements and the moles of the species.

Parameters

[in]

x

= current dimensionless element potentials..

Definition at line 934 of file ChemEquil.cpp.

References DATA_PTR, ThermoPhase::getActivityCoefficients(), ChemEquil::m_kk, ChemEquil::m_mm, ChemEquil::m_muSS_RT, ChemEquil::nAtoms(), Phase::setMoleFractions(), and ThermoPhase::setPressure().

Referenced by ChemEquil::estimateEP_Brinkley().

Member Data Documentation

EquilOpt options

Options controlling how the calculation is carried out.

See Also

EquilOptions

Definition at line 147 of file ChemEquil.h.

Referenced by Cantera::equilibrate(), ChemEquil::equilibrate(), ThermoPhase::equilibrate(), ChemEquil::estimateEP_Brinkley(), and Cantera::vcs_equilibrate().

thermo_t* m_phase

protected

Pointer to the ThermoPhase object used to initialize this object.

This ThermoPhase object must be compatible with the ThermoPhase objects input from the equilibrate function. Currently, this means that the 2 ThermoPhases have to have consist of the same species and elements.

Definition at line 159 of file ChemEquil.h.

Referenced by ChemEquil::initialize().

size_t m_mm

protected

number of elements in the phase

Definition at line 271 of file ChemEquil.h.

Referenced by ChemEquil::calcEmoles(), ChemEquil::dampStep(), ChemEquil::equilibrate(), ChemEquil::equilResidual(), ChemEquil::estimateElementPotentials(), ChemEquil::estimateEP_Brinkley(), ChemEquil::initialize(), ChemEquil::nAtoms(), ChemEquil::setInitialMoles(), ChemEquil::setToEquilState(), and ChemEquil::update().

size_t m_kk

protected

number of species in the phase

Definition at line 272 of file ChemEquil.h.

Referenced by ChemEquil::calcEmoles(), ChemEquil::equilibrate(), ChemEquil::estimateElementPotentials(), ChemEquil::estimateEP_Brinkley(), ChemEquil::initialize(), ChemEquil::setInitialMoles(), ChemEquil::setToEquilState(), and ChemEquil::update().

size_t m_nComponents

protected

This is equal to the rank of the stoichiometric coefficient matrix when it is computed.

It's initialized to m_mm.

Definition at line 279 of file ChemEquil.h.

Referenced by ChemEquil::equilibrate(), ChemEquil::equilResidual(), ChemEquil::estimateElementPotentials(), ChemEquil::estimateEP_Brinkley(), ChemEquil::initialize(), and ChemEquil::setInitialMoles().

vector_fp m_molefractions

protected

Current value of the mole fractions in the single phase.

-> length = m_kk.

Definition at line 287 of file ChemEquil.h.

Referenced by ChemEquil::initialize(), and ChemEquil::update().

vector_fp m_lambda

protected

Current value of the dimensional element potentials -> length = m_mm.

Definition at line 292 of file ChemEquil.h.

Referenced by ChemEquil::equilibrate(), and ChemEquil::initialize().

size_t m_eloc

protected

Index of the element id corresponding to the electric charge of each species.

Equal to -1 if there is no such element id.

Definition at line 320 of file ChemEquil.h.

Referenced by ChemEquil::dampStep(), ChemEquil::equilibrate(), ChemEquil::equilResidual(), ChemEquil::estimateEP_Brinkley(), and ChemEquil::initialize().

vector_fp m_muSS_RT

protected

Dimensionless values of the Gibbs free energy for the standard state of each species, at the temperature and pressure of the solution (the star standard state).

Definition at line 332 of file ChemEquil.h.

Referenced by ChemEquil::calcEmoles(), ChemEquil::estimateEP_Brinkley(), and ChemEquil::initialize().

double m_elemFracCutoff

protected

element fractional cutoff, below which the element will be zeroed.

Definition at line 336 of file ChemEquil.h.

Referenced by ChemEquil::equilibrate(), and ChemEquil::equilResidual().

---

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

• ChemEquil.h
• ChemEquil.cpp