Implements the Benedict-Webb-Rubin-Starling (BWRS) equation of state. More...

#include <bwrs.hpp>

Inheritance diagram for BWRS:

Public Member Functions
	BWRS (const arma::vec &composition=Composition::defaultComposition, const std::string &parameterSet="Calsep")
	Constructor that uses a string to select which mixture parameters \(A_0\) and \(B_0\), binary interaction coefficients \(k_{ij}\), and critical properties \(T_c\) etc. to use. The options are "Calsep", "JFH" and "Starling". More...

virtual arma::vec	evaluate (const double pressure, const double temperature) const override
	Evaluate the BWRS equation of state at the given pressure and temperature. More...

virtual double	calculateCompressibility (const double pressure, const double temperature) const override
	Calculate the compressibility factor (Z) of the gas at a given pressure and temperature. More...

virtual bool	setComposition (const arma::vec &composition, const bool force=true) override
	Set the composition of the EOS. More...

void	loadCriticalProperties (const std::string name)
	loadCriticalProperties Load a set of critical properties. Either "Calsep", "JFH" or "Starling". More...

void	loadParametersAndCriticalProperties (const std::string parameterSet)
	loadParametersAndCriticalProperties Load parameters and critical properties. More...

void	loadStarlingCriticalProperties ()
	Load the critical properties from Starling. More...

void	loadJFHCriticalProperties ()
	Load the critical properties from Helgaker. More...

void	loadCalsepCriticalProperties ()
	Load the critical properties from the Calsep report. More...

void	loadGasscoParameters ()

void	loadCalsepParameters ()

void	loadStarlingParameters ()

void	loadParameterFiles (const std::string &ABparameterFile, const std::string &binaryInteractionTableFile)
	Load mixture parameters \(A_0\) and \(B_0\), and binary interaction coefficients \(k_{ij}\) coefficients from specific files. More...

void	enableConstantHeatCapacities ()
	Enable constant heat capacity \(c_p\) and \(c_v\).

double	findDensity (const double pressure, const double temperature, const double tolerance=1e-4) const
	Find the gas density at a given pressure and temperature. More...

double	getGasConstant () const
	Get the gas constant R.

double	getMixtureCriticalPressure () const
	Get the critical pressure of the gas mixture [Pa].

double	getMixtureCriticalTemperature () const
	Get the critical temperature of the gas mixture [K].

Public Member Functions inherited from EquationOfStateBase
virtual	~EquationOfStateBase ()

	EquationOfStateBase (const arma::vec &composition=Composition::defaultComposition)
	EquationOfStateBase constructor. More...

virtual arma::vec	evaluate (const double pressure, const double temperature, const arma::vec &composition)
	Virtual function for evaluating the EOS at a new composition. More...

virtual double	calculateStandardDensity () const

double	getMolarMassOfMixture () const
	Get the molar mass of the gas.

const arma::vec &	getComposition () const
	Get the current composition stored in the EOS instance.

Static Public Member Functions
static BWRS	fromFilePaths (const arma::vec &composition=Composition::defaultComposition, const std::string &ABparameterFile=std::string(TRANSFLOW_RESOURCE_PATH)+"/equationofstate/bwrs/calsepABparameters.csv", const std::string &binaryInteractionTableFile=std::string(TRANSFLOW_RESOURCE_PATH)+"/equationofstate/bwrs/calsepBinaryInteraction.csv", const std::string &criticalProperties="Starling")
	Explicit BWRS constructor which allows specifying which files to load mixture parameters \(A_0\) and \(B_0\) and binary interaction coefficients \(k_{ij}\) from, and which critical properties to use. More...

Protected Member Functions
void	calculateCoefficients ()
	Calculates all the coefficients used for evaluating BWRS that are independent of pressure and temperature. More...

void	findNonZeroComponents ()
	Set up BWRS::m_indices to reflect which gas fractions are non-zero. More...

double	findMolarDensity (const double pressure, const double temperature, const double tolerance=1e-4) const
	Find the molar density of the gas at a given pressure and temperature. More...

Protected Attributes
arma::vec	m_Tc = arma::vec({ 190.69, 305.39, 369.89, 408.13, 425.19, 460.37, 469.49, 507.29, 126.15, 304.15})
	Critical temperature [K].

arma::vec	m_rhoc = arma::vec({ 1.00500e+4, 6.75659e+3, 4.99936e+3, 3.80118e+3, 3.92132e+3, 3.24694e+3, 3.21491e+3, 2.71673e+3, 1.10992e+4, 1.06379e+4})
	Critical density [kg/m3].

arma::vec	m_w = arma::vec({ 0.013, 0.1018, 0.157, 0.183, 0.197, 0.226, 0.252, 0.302, 0.035, 0.21})
	Accentric factor [-].

arma::vec	m_pc = arma::vec({ 45.96, 48.839, 42.5, 36.48, 37.96, 33.81, 33.69, 27.34, 33.99, 73.825})*1e5
	Critical pressure [Pa].

arma::vec	m_molarMass = arma::vec({ 16.042, 30.068, 44.094, 58.12, 58.12, 72.146, 72.146, 86.172, 28.016, 44.01})
	Molar mass of the different gas components [g/mol].

arma::vec	m_expW = exp(-3.8*m_w)
	Exponential of the accentric factor.

double	m_R = 8.3160
	The gas constant [J/(K mol)]. More...

arma::mat	m_binaryInteractionParameterTable
	Binary interaction coefficients \(k_{ij}\). More...

arma::vec	m_Bi
	Pure component parameters Bi. More...

arma::vec	m_Ai
	Pure component parameters Ai. More...

double	m_A0
	A coefficient used when evaluating the BWRS-equation. Independent of pressure and temperature.

double	m_B0
	A coefficient used when evaluating the BWRS-equation. Independent of pressure and temperature.

double	m_C0
	A coefficient used when evaluating the BWRS-equation. Independent of pressure and temperature.

double	m_D0
	A coefficient used when evaluating the BWRS-equation. Independent of pressure and temperature.

double	m_E0
	A coefficient used when evaluating the BWRS-equation. Independent of pressure and temperature.

double	m_a
	A coefficient used when evaluating the BWRS-equation. Independent of pressure and temperature.

double	m_b
	A coefficient used when evaluating the BWRS-equation. Independent of pressure and temperature.

double	m_c
	A coefficient used when evaluating the BWRS-equation. Independent of pressure and temperature.

double	m_d
	A coefficient used when evaluating the BWRS-equation. Independent of pressure and temperature.

double	m_ALPHA
	A coefficient used when evaluating the BWRS-equation. Independent of pressure and temperature.

double	m_GAMMA
	A coefficient used when evaluating the BWRS-equation. Independent of pressure and temperature.

double	m_criticalPressureOfMixture
	Critical pressure of the gas mixture.

double	m_criticalTemperatureOfMixture
	Critical temperature of the gas mixture.

bool	m_useConstantHeatCapacities = false
	Flag to set if we want to use constant heat capacity \(c_p\) and \(c_v\).

arma::uvec	m_indices
	The indices of the non-zero gas fractions (components).

Protected Attributes inherited from EquationOfStateBase
arma::vec	m_molarMass = { 16.04, 30.07, 44.1, 58.12, 58.12, 72.15, 72.15, 86.18, 28.13, 44.01}
	The molar mass [g/mol] of the different gas components, in order C1, C2, C3, iC4, nC4, iC5, nC5, C6, N2, CO2.

arma::vec::fixed< 10 >	m_composition = arma::vec(10)
	The composition of the gas as fractions, in order C1, C2, C3, iC4, nC4, iC5, nC5, C6, N2, CO2.

double	m_molarMassOfMixture
	The molar mass of the gas mixture [g/mol].

double	m_density = 0
	Cache density for optimization [kg/m3].

Detailed Description

Implements the Benedict-Webb-Rubin-Starling (BWRS) equation of state.

This class implements the Benedict-Webb-Rubin-Starling (BWRS) equation of state. BWRS depends on 11 mixture parameters B_0 and A_0, which are calculated from the pure component parameters \(A_{0i}\) and \(B_{0i}\), as well as the binary interaction coefficients \(k_{ij}\).

More information on BWRS can be found in Fluid Properties for Light Petroleum Systems (Kenneth E. Starling, 1973, ISBN 978-0872012936).

Critical properties refer to the critical temperature (m_Tc), critical density (m_rhoc), critical pressure (m_pc), and accentric factor (m_w), which are used in the evaluation of the BWRS equation. These are found in Table 5 at page 223 of Fluid Properties for Light Petroleum Systems.

Constructor & Destructor Documentation

◆ BWRS()

BWRS::BWRS	(	const arma::vec &	composition = `Composition::defaultComposition`,
		const std::string &	parameterSet = `"Calsep"`
	)

Constructor that uses a string to select which mixture parameters \(A_0\) and \(B_0\), binary interaction coefficients \(k_{ij}\), and critical properties \(T_c\) etc. to use. The options are "Calsep", "JFH" and "Starling".

"Calsep" refers to the parameters tuned for Statpipe, see Tuning af parametre i BWRS-tilstandsligningen til brug i STATPIPES termodynamiske programpakke (Jan Munch, 1985) for more info.

"JFH" refer to the parameters found in the original code by Helgaker. These have been shown to give bad results after the solver was rewritten to use molar density (the original form used regular density), so I would recommend not using this.

"Staring" refers to the parameters given by Starling in Fluid Properties for Light Petroleum Systems (Kenneth E. Starling, 1973, ISBN 978-0872012936).

Parameters

composition	Gas composition fraction, in order C1, C2, C3, iC4, nC4, iC5, nC5, C6, N2, CO2.
parameterSet	Which parameter set to use ("Starling", "Calsep" or "JFH").

Returns: An instance of BWRS.

Member Function Documentation

◆ calculateCoefficients()

void BWRS::calculateCoefficients ( )

protected

Calculates all the coefficients used for evaluating BWRS that are independent of pressure and temperature.

A lot of different coefficients are used when evaluating the BWRS equation to find the compressibility and the partial derivatives of Z. Many of these are independent of pressure and temperature, so they can be tabulated for the current gas composition.

This optimization is most effective if we use constant composition, but should also improve the evaluation of the formulas otherwise.

◆ calculateCompressibility()

virtual double BWRS::calculateCompressibility	(	const double	pressure,
		const double	temperature
	)		const

overridevirtual

Calculate the compressibility factor (Z) of the gas at a given pressure and temperature.

This function is useful if we just need the compressibility and not all the other properties we can find from the EOS.

It contains a call to BWRS::findMolarDensity(), which contains some Newton-Raphson root finding, which are among the heaviest part of this whole class, so I don't expect much time-save over a call to evaluate().

Parameters

pressure	Gas pressure [Pa].
temperature	Gas temperature [K].

Returns: Compressibility factor Z [-].

Implements EquationOfStateBase.

◆ evaluate()

virtual arma::vec BWRS::evaluate	(	const double	pressure,
		const double	temperature
	)		const

overridevirtual

Evaluate the BWRS equation of state at the given pressure and temperature.

Parameters

pressure	Gas pressure [Pa]
temperature	Gas temperature [K]

Returns: See EquationOfStateBase::evaluate().

Implements EquationOfStateBase.

◆ findDensity()

double BWRS::findDensity	(	const double	pressure,
		const double	temperature,
		const double	tolerance = `1e-4`
	)		const

Find the gas density at a given pressure and temperature.

This is just a wrapper around findMolarDensity() and a conversion from molar density [mol/m3] to density [kg/m3]

Parameters

pressure	Gas pressure [Pa].
temperature	Gas temperature [K].
tolerance	Newton-Raphson tolerance.

Returns: Gas density [kg/m3].

◆ findMolarDensity()

double BWRS::findMolarDensity	(	const double	pressure,
		const double	temperature,
		const double	tolerance = `1e-4`
	)		const

protected

Find the molar density of the gas at a given pressure and temperature.

This is most likely the most computationally heavy function in this class, since it contains a Newton-Raphson root finding, meaning that the BWRS equation will be evaluated multiple times until it reaches convergence.

The convergence criterion is implemented as

if (std::abs(change/previous) < tolerance) break;

Parameters

pressure	Gas pressure [Pa].
temperature	Gas temperature [K].
tolerance	Convergence criterion for the Newton-Raphson method.

Returns: Molar density [mol/m3]

◆ findNonZeroComponents()

void BWRS::findNonZeroComponents ( )

protected

Set up BWRS::m_indices to reflect which gas fractions are non-zero.

The BWRS equation has some issues if it is evaluated with gas fractions of zero, so to avoid this we store the indices of the non-zero fractions and only loop over those when evaluating the equation.

Call this function to find the non-zero indices and store them in BWRS::m_indices.

◆ fromFilePaths()

static BWRS BWRS::fromFilePaths	(	const arma::vec &	composition = `Composition::defaultComposition`,
		const std::string &	ABparameterFile = `std::string(TRANSFLOW_RESOURCE_PATH)+"/equationofstate/bwrs/calsepABparameters.csv"`,
		const std::string &	binaryInteractionTableFile = `std::string(TRANSFLOW_RESOURCE_PATH)+"/equationofstate/bwrs/calsepBinaryInteraction.csv"`,
		const std::string &	criticalProperties = `"Starling"`
	)

static

Explicit BWRS constructor which allows specifying which files to load mixture parameters \(A_0\) and \(B_0\) and binary interaction coefficients \(k_{ij}\) from, and which critical properties to use.

See also: loadJFHCriticalProperties(); loadCalsepCriticalProperties(); loadStarlingCriticalProperties()

Parameters

composition	Gas composition fractions, in order C1, C2, C3, iC4, nC4, iC5, nC5, C6, N2, CO2.
ABparameterFile	Path to file which contains the pure component parameters \(A_{0i}\) and \(B_{0i}\)
binaryInteractionTableFile	Path to file which contains the interaction parameters \(k_{ij}\)
criticalProperties	Which set of critical gas properties should be used.

◆ loadCalsepCriticalProperties()

void BWRS::loadCalsepCriticalProperties ( )

Load the critical properties from the Calsep report.

This function sets the values of m_Tc, m_rhoc, m_w, m_pc, m_molarMass, m_expW, and m_R according to the values found in the original Helgaker Matlab code.

Warning: The values set by this function have been found to produce bad results. This is likely due to the rewrite to a molar density based solver, as the equations are originally given by Starling. Use loadStarlingCriticalProperties() instead.

◆ loadCalsepParameters()

void BWRS::loadCalsepParameters ( )

Load the mixture parameters \(A_0\) and \(B_0\), and binary interaction coefficients \(k_{ij}\) from the Calsep report.

◆ loadCriticalProperties()

void BWRS::loadCriticalProperties ( const std::string name )

loadCriticalProperties Load a set of critical properties. Either "Calsep", "JFH" or "Starling".

Parameters

name	Name of critical properties. Either "Calsep", "JFH" or "Starling".

◆ loadGasscoParameters()

void BWRS::loadGasscoParameters ( )

Load the mixture parameters \(A_0\) and \(B_0\), and binary interaction coefficients \(k_{ij}\) from Gassco.

◆ loadJFHCriticalProperties()

void BWRS::loadJFHCriticalProperties ( )

Load the critical properties from Helgaker.

This function sets the values of m_Tc, m_rhoc, m_w, m_pc, m_molarMass, m_expW, and m_R according to the values found in the original Helgaker Matlab code.

Warning: The values set by this function have been found to produce bad results. This is likely due to the rewrite to a molar density based solver, as the equations are originally given by Starling. Use loadStarlingCriticalProperties() instead.

◆ loadParameterFiles()

void BWRS::loadParameterFiles	(	const std::string &	ABparameterFile,
		const std::string &	binaryInteractionTableFile
	)

Load mixture parameters \(A_0\) and \(B_0\), and binary interaction coefficients \(k_{ij}\) coefficients from specific files.

Parameters

ABparameterFile	Path to AB parameter file.
binaryInteractionTableFile	Path to binary interaction coefficients file.

◆ loadParametersAndCriticalProperties()

void BWRS::loadParametersAndCriticalProperties ( const std::string parameterSet )

loadParametersAndCriticalProperties Load parameters and critical properties.

Parameters

parameterSet Name of parameter set. Either "Calsep", "JFH" or "Starling".

◆ loadStarlingCriticalProperties()

void BWRS::loadStarlingCriticalProperties ( )

Load the critical properties from Starling.

This function sets the values of m_Tc, m_rhoc, m_w, m_pc, m_molarMass, m_expW, and m_R according to the values found in Fluid Properties for Light Petroleum Systems (Kenneth E. Starling, 1973, ISBN 978-0872012936).

The values set by this function have been found to produce the best results.

◆ loadStarlingParameters()

void BWRS::loadStarlingParameters ( )

Load the mixture parameters \(A_0\) and \(B_0\), and binary interaction coefficients \(k_{ij}\) from the Starling BWRS book.

◆ setComposition()

virtual bool BWRS::setComposition	(	const arma::vec &	composition,
		const bool	force = `true`
	)

overridevirtual

Set the composition of the EOS.

This calls EquationOfStateBase::setComposition(), then updates the non-zero component indices BWRS::m_indices, calculates the new critical pressure and temperature of the gas mixture, before finally updating all the coefficients m_A0, m_B0, through m_GAMMA.

Parameters

composition	New gas composition.
force	If the composition should be changed even if it's within machine precision of the previous composition.

Returns: True if composition was changed, else false.

Reimplemented from EquationOfStateBase.

Member Data Documentation

◆ m_Ai

arma::vec BWRS::m_Ai

protected

Pure component parameters Ai.

From Table 1 at page 221 of Fluid Properties for Light Petroleum Systems.

◆ m_Bi

arma::vec BWRS::m_Bi

protected

Pure component parameters Bi.

From Table 1 at page 221 of Fluid Properties for Light Petroleum Systems.

◆ m_binaryInteractionParameterTable

arma::mat BWRS::m_binaryInteractionParameterTable

protected

Binary interaction coefficients \(k_{ij}\).

The binary interaction coefficients are stored in matrix of size 10x10, where the binary interactions between component i and j are stored at location \((i, j)\) in the matrix. The matrix is symmetric, so \(k(i, j) == k(j, i)\). The components are in the usual order (C1, C2, C3, iC4, nC4, iC5, nC5, C6, N2, CO2).

These can be found in Table 1 at page 227 of Fluid Properties for Light Petroleum Systems.

◆ m_R

double BWRS::m_R = 8.3160

protected

The gas constant [J/(K mol)].

The exact value of the gas constant is approx 8.3145 J/Kmol, but if we are using the critical properties and other parameters from Starling, these have been determined using an older definition of the gas constant, which is 8.3160 J/Kmol.

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

D:/Code/transient-pipeline-flow-gh-pages/src/equationofstate/bwrs.hpp

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ BWRS()

Member Function Documentation

◆ calculateCoefficients()

◆ calculateCompressibility()

◆ evaluate()

◆ findDensity()

◆ findMolarDensity()

◆ findNonZeroComponents()

◆ fromFilePaths()

◆ loadCalsepCriticalProperties()

◆ loadCalsepParameters()

◆ loadCriticalProperties()

◆ loadGasscoParameters()

◆ loadJFHCriticalProperties()

◆ loadParameterFiles()

◆ loadParametersAndCriticalProperties()

◆ loadStarlingCriticalProperties()

◆ loadStarlingParameters()

◆ setComposition()

Member Data Documentation

◆ m_Ai

◆ m_Bi

◆ m_binaryInteractionParameterTable

◆ m_R