EquilibriumInverseProblem Class Reference

A class used for defining an inverse equilibrium problem. More...

#include <EquilibriumInverseProblem.hpp>

Public Member Functions
	EquilibriumInverseProblem (const ChemicalSystem &system)
	Construct an EquilibriumInverseProblem instance.
	EquilibriumInverseProblem (const EquilibriumInverseProblem &other)
	Construct a copy of an EquilibriumInverseProblem instance.
virtual	~EquilibriumInverseProblem ()
	Destroy this EquilibriumInverseProblem instance.
auto	operator= (EquilibriumInverseProblem other) -> EquilibriumInverseProblem &
	Assign a copy of an EquilibriumInverseProblem instance.
auto	setPartition (const Partition &partition) -> EquilibriumInverseProblem &
	Set the partition of the chemical system. More...
auto	setTemperature (double val) -> EquilibriumInverseProblem &
	Set the temperature for the equilibrium calculation (in units of K). More...
auto	setTemperature (double val, std::string units) -> EquilibriumInverseProblem &
	Set the temperature for the equilibrium calculation. More...
auto	setPressure (double val) -> EquilibriumInverseProblem &
	Set the pressure for the equilibrium calculation (in units of Pa). More...
auto	setPressure (double val, std::string units) -> EquilibriumInverseProblem &
	Set the pressure for the equilibrium calculation. More...
auto	setElementInitialAmounts (VectorConstRef values) -> EquilibriumInverseProblem &
	Set the initial known molar amounts of the elements in the equilibrium partition. More...
auto	add (std::string name, double amount, std::string units) -> EquilibriumInverseProblem &
	Add a given amount of a compound or species to the initial equilibrium recipe. More...
auto	fixSpeciesAmount (std::string species, double value, std::string units) -> EquilibriumInverseProblem &
	Fix the molar amount of a species at equilibrium. More...
auto	fixSpeciesAmount (std::string species, double value, std::string units, std::string titrant) -> EquilibriumInverseProblem &
	Fix the molar amount of a species at equilibrium with given titrant. More...
auto	fixSpeciesMass (std::string species, double value, std::string units) -> EquilibriumInverseProblem &
	Fix the mass of a species at equilibrium. More...
auto	fixSpeciesMass (std::string species, double value, std::string units, std::string titrant) -> EquilibriumInverseProblem &
	Fix the mass of a species at equilibrium with given titrant. More...
auto	fixSpeciesActivity (std::string species, double value) -> EquilibriumInverseProblem &
	Fix the activity of a species at equilibrium. More...
auto	fixSpeciesActivity (std::string species, double value, std::string titrant) -> EquilibriumInverseProblem &
	Fix the activity of a species at equilibrium with given titrant. More...
auto	fixSpeciesActivity (std::string species, double value, std::string titrant1, std::string titrant2) -> EquilibriumInverseProblem &
	Fix the activity of a species at equilibrium with either one of the two given titrants. More...
auto	fixSpeciesFugacity (std::string species, double value, std::string units) -> EquilibriumInverseProblem &
	Fix the fugacity of a gaseous species. More...
auto	fixSpeciesFugacity (std::string species, double value, std::string units, std::string titrant) -> EquilibriumInverseProblem &
	Fix the fugacity of a gaseous species with given titrant. More...
auto	fixPhaseAmount (std::string phase, double value, std::string units, std::string titrant) -> EquilibriumInverseProblem &
	Fix the total molar amount of a phase at equilibrium with given titrant. More...
auto	fixPhaseMass (std::string phase, double value, std::string units, std::string titrant) -> EquilibriumInverseProblem &
	Fix the total mass of a phase at equilibrium with given titrant. More...
auto	fixPhaseVolume (std::string phase, double value, std::string units, std::string titrant) -> EquilibriumInverseProblem &
	Fix the volume of a phase at equilibrium with given titrant. More...
auto	fixPhaseSetVolume (const std::vector< std::string > &phases, double value, std::string units, std::string titrant) -> EquilibriumInverseProblem &
	Fix the total volume of a set of phases at equilibrium with given titrant. More...
auto	pH (double value) -> EquilibriumInverseProblem &
	Fix the pH of the aqueous solution. More...
auto	pH (double value, std::string titrant) -> EquilibriumInverseProblem &
	Fix the pH of the aqueous solution with given titrant. More...
auto	pH (double value, std::string titrant1, std::string titrant2) -> EquilibriumInverseProblem &
	Fix the pH of the aqueous solution with either one of the two given titrants. More...
auto	pE (double value) -> EquilibriumInverseProblem &
	Fix the pe of the aqueous solution. More...
auto	pE (double value, std::string titrant) -> EquilibriumInverseProblem &
	Fix the pe of the aqueous solution with given half reaction. More...
auto	Eh (double value, std::string units) -> EquilibriumInverseProblem &
	Fix the Eh of the aqueous solution (in units of volts). More...
auto	Eh (double value, std::string units, std::string titrant) -> EquilibriumInverseProblem &
	Fix the Eh of the aqueous solution with given half reaction. More...
auto	alkalinity (double value, std::string units, std::string titrant) -> EquilibriumInverseProblem &
	Fix the total alkalinity of the aqueous solution. More...
auto	system () const -> const ChemicalSystem &
	Return a reference to the ChemicalSystem instance used to create this EquilibriumProblem instance.
auto	partition () const -> const Partition &
	Return a reference to the Partition instance used to create this EquilibriumProblem instance.
auto	temperature () const -> double
	Return the temperature for the equilibrium calculation (in units of K)
auto	pressure () const -> double
	Return the pressure for the equilibrium calculation (in units of Pa)
auto	numConstraints () const -> Index
	Return the number of constraints used in the inverse equilibrium problem.
auto	numTitrants () const -> Index
	Return the number of titrants used in the inverse equilibrium problem.
auto	formulaMatrixTitrants () const -> Matrix
	Return the formula matrix of the titrants. More...
auto	elementInitialAmounts () const -> Vector
	Return the initial amounts of elements in the equilibrium partition. More...
auto	titrantInitialAmounts () const -> Vector
	Return the initial amounts of titrants as initial guess for the inverse equilibrium calculation.
auto	residualEquilibriumConstraints (VectorConstRef x, const ChemicalState &state) const -> ResidualEquilibriumConstraints
	Return the residuals of the equilibrium constraints and their partial derivatives. More...
auto	solve (ChemicalState &state) -> EquilibriumResult
	Solve the inverse equilibrium problem. More...

Detailed Description

A class used for defining an inverse equilibrium problem.

In an inverse equilibrium problem, not all elements have known molar amounts. Their amount constraints are replaced by other equilibrium constraints such as fixed species amount or activity, or the volume or total amount of a phase. Since the amounts of elements are not known a priori, an inverse equilibrium calculation tries to determine amounts of titrants that can control the specified equilibrium constraints. The amount of the titrants are unknown, and its addition or removal is done over the calculation so that the equilibrium state is driven towards a state where all given equilibrium constraints are satisfied.

Member Function Documentation

setPartition()

auto setPartition

(

const Partition &

partition

)

-> EquilibriumInverseProblem&

Set the partition of the chemical system.

Use this method to specify the equilibrium, kinetic, and inert species.

setTemperature() [1/2]

auto setTemperature

(

double

val

)

-> EquilibriumInverseProblem&

Set the temperature for the equilibrium calculation (in units of K).

By default, the temperature is 25 °C.

Parameters

val	The temperature value (in units of K).

setTemperature() [2/2]

auto setTemperature	(	double	val,
		std::string	units
	)		-> EquilibriumInverseProblem&

Set the temperature for the equilibrium calculation.

By default, the temperature is 25 °C.

Parameters

val	The temperature value.
units	The units of the temperature (K, degC, degF, degR, kelvin, celsius, fahrenheit, rankine).

setPressure() [1/2]

auto setPressure

(

double

val

)

-> EquilibriumInverseProblem&

Set the pressure for the equilibrium calculation (in units of Pa).

By default, the pressure is 1 bar.

Parameters

val	The pressure value (in units of Pa).

setPressure() [2/2]

auto setPressure	(	double	val,
		std::string	units
	)		-> EquilibriumInverseProblem&

Set the pressure for the equilibrium calculation.

By default, the pressure is 1 bar.

Parameters

val	The pressure value.
units	The units of the pressure (Pa, kPa, MPa, GPa, atm, mmHg, inHg, psi, kpsi, Mpsi, psf, bar, torr, inH2O, ftH2O, pascal).

setElementInitialAmounts()

auto setElementInitialAmounts

(

VectorConstRef

values

)

-> EquilibriumInverseProblem&

Set the initial known molar amounts of the elements in the equilibrium partition.

These are the amounts of the equilibrium elements before unknown amounts of titrants are added.

add()

auto add	(	std::string	name,
		double	amount,
		std::string	units
	)		-> EquilibriumInverseProblem&

Add a given amount of a compound or species to the initial equilibrium recipe.

Parameters

name	The name of the compound or species
amount	The amount of the compound or species
units	The units of the amount (must be convertible to either mol or kg)

fixSpeciesAmount() [1/2]

auto fixSpeciesAmount	(	std::string	species,
		double	value,
		std::string	units
	)		-> EquilibriumInverseProblem&

Fix the molar amount of a species at equilibrium.

Parameters

species	The name of the species for which its amount is given.
value	The value of the species amount (in units of mol).
units	The units of the species amount (must be convertible to mol)

fixSpeciesAmount() [2/2]

auto fixSpeciesAmount	(	std::string	species,
		double	value,
		std::string	units,
		std::string	titrant
	)		-> EquilibriumInverseProblem&

Fix the molar amount of a species at equilibrium with given titrant.

Parameters

species	The name of the species for which its amount is given.
value	The value of the species amount.
units	The units of the species amount (must be convertible to mol)
titrant	The titrant that controls the species amount.

fixSpeciesMass() [1/2]

auto fixSpeciesMass	(	std::string	species,
		double	value,
		std::string	units
	)		-> EquilibriumInverseProblem&

Fix the mass of a species at equilibrium.

Parameters

species	The name of the species for which its amount is given.
value	The value of the species mass.
units	The units of the species mass (must be convertible to kg)

fixSpeciesMass() [2/2]

auto fixSpeciesMass	(	std::string	species,
		double	value,
		std::string	units,
		std::string	titrant
	)		-> EquilibriumInverseProblem&

Fix the mass of a species at equilibrium with given titrant.

Parameters

species	The name of the species for which its amount is given.
value	The value of the species amount (in units of kg).
units	The units of the species mass (must be convertible to kg)
titrant	The titrant that controls the species mass.

fixSpeciesActivity() [1/3]

auto fixSpeciesActivity	(	std::string	species,
		double	value
	)		-> EquilibriumInverseProblem&

Fix the activity of a species at equilibrium.

Parameters

species	The name of the species for which its activity is given.
value	The value of the species activity.

fixSpeciesActivity() [2/3]

auto fixSpeciesActivity	(	std::string	species,
		double	value,
		std::string	titrant
	)		-> EquilibriumInverseProblem&

Fix the activity of a species at equilibrium with given titrant.

Parameters

species	The name of the species for which its activity is given.
value	The value of the species activity.
titrant	The titrant that controls the species activity.

fixSpeciesActivity() [3/3]

auto fixSpeciesActivity	(	std::string	species,
		double	value,
		std::string	titrant1,
		std::string	titrant2
	)		-> EquilibriumInverseProblem&

Fix the activity of a species at equilibrium with either one of the two given titrants.

Parameters

species	The name of the species for which its activity is given.
value	The value of the species activity.
titrant1	The first titrant that might control the species activity.
titrant2	The second titrant that might control the species activity.

fixSpeciesFugacity() [1/2]

auto fixSpeciesFugacity	(	std::string	species,
		double	value,
		std::string	units
	)		-> EquilibriumInverseProblem&

Fix the fugacity of a gaseous species.

Parameters

species	The name of the gaseous species.
value	The value of the species fugacity.
units	The units of the species fugacity (must be convertible to Pa).

fixSpeciesFugacity() [2/2]

auto fixSpeciesFugacity	(	std::string	species,
		double	value,
		std::string	units,
		std::string	titrant
	)		-> EquilibriumInverseProblem&

Fix the fugacity of a gaseous species with given titrant.

Parameters

species	The name of the gaseous species.
value	The value of the species fugacity.
units	The units of the species fugacity (must be convertible to Pa).
titrant	The titrant that controls the fugacity value.

fixPhaseAmount()

auto fixPhaseAmount	(	std::string	phase,
		double	value,
		std::string	units,
		std::string	titrant
	)		-> EquilibriumInverseProblem&

Fix the total molar amount of a phase at equilibrium with given titrant.

Parameters

phase	The name of the phase for which its total molar amount is given.
value	The value of the phase total amount
units	The units of the amount (must be convertible to mol)
titrant	The titrant that controls the phase amount.

fixPhaseMass()

auto fixPhaseMass	(	std::string	phase,
		double	value,
		std::string	units,
		std::string	titrant
	)		-> EquilibriumInverseProblem&

Fix the total mass of a phase at equilibrium with given titrant.

Parameters

phase	The name of the phase for which its total mass is given.
value	The value of the phase mass
units	The units of the phase mass (must be convertible to kg)
titrant	The titrant that controls the phase mass.

fixPhaseVolume()

auto fixPhaseVolume	(	std::string	phase,
		double	value,
		std::string	units,
		std::string	titrant
	)		-> EquilibriumInverseProblem&

Fix the volume of a phase at equilibrium with given titrant.

Parameters

phase	The name of the phase for which its volume is given.
value	The value of the phase volume
units	The units of the phase volume (must be convertible to m3)
titrant	The titrant that controls the phase volume.

fixPhaseSetVolume()

auto fixPhaseSetVolume	(	const std::vector< std::string > &	phases,
		double	value,
		std::string	units,
		std::string	titrant
	)		-> EquilibriumInverseProblem&

Fix the total volume of a set of phases at equilibrium with given titrant.

Parameters

phases	The names of the phases composing the phase set.
value	The value of the total volume of the phase set (in units of m3)
units	The units of the total volume of the phase set (must be convertible to m3)
titrant	The titrant that controls the total volume of the phase set.

pH() [1/3]

auto pH

(

double

value

)

-> EquilibriumInverseProblem&

Fix the pH of the aqueous solution.

Parameters

value

The pH value of the aqueous solution.

pH() [2/3]

auto pH	(	double	value,
		std::string	titrant
	)		-> EquilibriumInverseProblem&

Fix the pH of the aqueous solution with given titrant.

Parameters

value	The pH value of the aqueous solution.
titrant	The titrant that control the solution pH.

pH() [3/3]

auto pH	(	double	value,
		std::string	titrant1,
		std::string	titrant2
	)		-> EquilibriumInverseProblem&

Fix the pH of the aqueous solution with either one of the two given titrants.

Parameters

value	The pH value of the aqueous solution.
titrant1	The first titrant that might control the solution pH.
titrant2	The second titrant that might control the solution pH.

pE() [1/2]

auto pE

(

double

value

)

-> EquilibriumInverseProblem&

Fix the pe of the aqueous solution.

Parameters

value

The pe value of the aqueous solution.

pE() [2/2]

auto pE	(	double	value,
		std::string	titrant
	)		-> EquilibriumInverseProblem&

Fix the pe of the aqueous solution with given half reaction.

Parameters

value	The pe value of the aqueous solution.
titrant	The titrant that control the solution pE.

Eh() [1/2]

auto Eh	(	double	value,
		std::string	units
	)		-> EquilibriumInverseProblem&

Fix the Eh of the aqueous solution (in units of volts).

Parameters

value

The Eh value of the aqueous solution.

Eh() [2/2]

auto Eh	(	double	value,
		std::string	units,
		std::string	titrant
	)		-> EquilibriumInverseProblem&

Fix the Eh of the aqueous solution with given half reaction.

Parameters

value	The Eh value of the aqueous solution.
units	The units of the Eh of the aqueous solution (must be convertible to V).
titrant	The titrant that control the solution Eh.

alkalinity()

auto alkalinity	(	double	value,
		std::string	units,
		std::string	titrant
	)		-> EquilibriumInverseProblem&

Fix the total alkalinity of the aqueous solution.

Parameters

value	The value of the total alkalinity of the aqueous solution.
units	The units of the total alkalinity (must be convertible to eq/L).
titrant	The titrant that control the solution alkalinity.

formulaMatrixTitrants()

auto formulaMatrixTitrants

(

)

const -> Matrix

Return the formula matrix of the titrants.

The formula matrix of the titrants is defined as the matrix whose (j,i)th entry contains the stoichiometric coefficient of jth element in the ith titrant. Its dimension is E x T, where T is the number of titrants.

elementInitialAmounts()

auto elementInitialAmounts

(

)

const -> Vector

Return the initial amounts of elements in the equilibrium partition.

These are the values of element amounts in the equilibrium partition before unknown amounts of titrants are added.

residualEquilibriumConstraints()

auto residualEquilibriumConstraints	(	VectorConstRef	x,
		const ChemicalState &	state
	)		const -> ResidualEquilibriumConstraints

Return the residuals of the equilibrium constraints and their partial derivatives.

Parameters

x	The amounts of the titrants (in units of mol)
state	The chemical state of the system

solve()

auto solve

(

ChemicalState &

state

)

-> EquilibriumResult

Solve the inverse equilibrium problem.

Parameters

state

The initial guess for the final chemical state solution.

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

• Reaktoro/Equilibrium/EquilibriumInverseProblem.hpp
• Reaktoro/Equilibrium/EquilibriumInverseProblem.cpp