Class PhaseBWRSEos

java.lang.Object

neqsim.thermo.phase.Phase

neqsim.thermo.phase.PhaseEos

neqsim.thermo.phase.PhaseSrkEos

neqsim.thermo.phase.PhaseBWRSEos

All Implemented Interfaces:

Serializable, Cloneable, PhaseEosInterface, PhaseInterface, ThermodynamicConstantsInterface

public class PhaseBWRSEos
extends PhaseSrkEos

PhaseBWRSEos class.

Version:

$Id: $Id

Author:

Even Solbraa

See Also:

• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
(package private) static org.apache.logging.log4j.Logger	logger	Logger object for class.
private static final double	MBWR_UNIT_FACTOR	Unit conversion factor for MBWR-32 parameters.
private double[]	mixBE	Mole-fraction-weighted exponential MBWR coefficients for the mixture.
private double[]	mixBEdT	Mole-fraction-weighted exponential temperature derivatives for the mixture.
private double[]	mixBEdTdT	Mole-fraction-weighted exponential second temperature derivatives for the mixture.
private double[]	mixBP	Mole-fraction-weighted polynomial MBWR coefficients for the mixture.
private double[]	mixBPdT	Mole-fraction-weighted polynomial temperature derivatives for the mixture.
private double[]	mixBPdTdT	Mole-fraction-weighted polynomial second temperature derivatives for the mixture.
private double	mixGamma	Mixed gamma parameter = 1/rhoc_mix^2 for one-fluid mixing.
(package private) int	OE
(package private) int	OP
private static final long	serialVersionUID	Serialization version UID.

Fields inherited from class PhaseEos

delta1, delta2, mixRule, mixSelect, uEOS, wEOS

Fields inherited from class Phase

beta, calcMolarVolume, chemSyst, componentArray, diElectricConstant, mixingRuleType, molarVolume, numberOfComponents, numberOfMolesInPhase, phaseVolume, physicalPropertyHandler, pressure, pt, refPhase, temperature, thermoPropertyModelName, useVolumeCorrection, Z

Fields inherited from interface ThermodynamicConstantsInterface

atm, avagadroNumber, boltzmannConstant, electronCharge, faradayConstant, gravity, molarMassAir, normalStateTemperature, pi, planckConstant, R, referencePressure, referenceTemperature, standardStateTemperature, vacumPermittivity

Constructor Summary

Constructors

Constructor	Description
PhaseBWRSEos()	Constructor for PhaseBWRSEos.

Method Summary

Modifier and Type	Method	Description
void	addComponent(String name, double moles, double molesInPhase, int compNumber)	Add component to component array and update moles variables.
double	calcPressure2()	calcPressure2.
void	calcPVT()	calcPVT.
PhaseBWRSEos	clone()	clone.
private void	computeMixedParameters()	Computes mole-fraction-weighted MBWR parameters for the one-fluid mixture.
double	dFdT()	Calculate derivative of F per Temperature, i.e., dF/dT.
double	dFdTdT()	dFdTdT.
double	dFdTdV()	Calculate derivative of F per Temperature and Volume, i.e., dF/dT * 1/dV.
double	dFdV()	Calculate derivative of F per Volume, i.e., dF/dV.
double	dFdVdV()	dFdVdV.
double	dFdVdVdV()	dFdVdVdV.
double	getdFdN(int compNumb)	Numerical dF/dn_i at constant T, V.
double	getdFdNdN(int compI, int compJ)	Numerical d2F/(dn_i dn_j) at constant T, V.
double	getdFdNdT(int compNumb)	Numerical d2F/(dn_i dT) at constant V, n.
double	getdFdNdV(int compNumb)	Numerical d2F/(dn_i dV) at constant T, n.
double	getdRhodV()	getdRhodV.
double	getdRhodVdV()	getdRhodVdV.
double	getdRhodVdVdV()	getdRhodVdVdV.
double	getEL()	getEL.
double	getELdRho()	getELdRho.
double	getELdRhodedRho()	Second derivative of the exponential EL term with respect to molar density.
double	getELdRhodedRhodedRho()	Third derivative of the exponential EL term with respect to molar density.
double	getF()	getF.
double	getFdRho()	Total derivative of F with respect to molar density.
double	getFexp()	getFexp.
private double	getFexpdRho()	First derivative of Fexp with respect to molar density.
private double	getFexpdRhodRho()	Second derivative of Fexp with respect to molar density.
private double	getFexpdRhodRhodRho()	Third derivative of Fexp with respect to molar density.
double	getFexpdT()	getFexpdT.
private double	getFexpdTdRho()	Cross derivative of Fexp with respect to temperature and molar density.
private double	getFexpdTdT()	Second derivative of Fexp with respect to temperature.
private double	getFexpdTdV()	Cross derivative of Fexp with respect to temperature and molar volume.
double	getFexpdV()	First derivative of Fexp with respect to molar volume.
double	getFexpdVdV()	Second derivative of Fexp with respect to molar volume.
double	getFexpdVdVdV()	Third derivative of Fexp with respect to molar volume.
double	getFpol()	getFpol.
double	getFpoldRho()	Derivative of the polynomial F-term with respect to molar density.
double	getFpoldT()	getFpoldT.
private double	getFpoldTdRho()	Cross derivative of the polynomial F-term with respect to temperature and molar density.
private double	getFpoldTdT()	Second derivative of the polynomial F-term with respect to temperature.
private double	getFpoldTdV()	Cross derivative of the polynomial F-term with respect to temperature and molar volume.
double	getFpoldV()	getFpoldV.
double	getFpoldVdV()	getFpoldVdV.
double	getFpoldVdVdV()	getFpoldVdVdV.
double	getGammadRho()	getGammadRho.
double	getJouleThomsonCoefficient()	Get the Joule Thomson Coefficient of a phase.
double	getMolarDensity()	getMolarDensity.
void	init(double totalNumberOfMoles, int numberOfComponents, int initType, PhaseType pt, double beta)	init.
double	molarVolume2(double pressure, double temperature, double A, double B, PhaseType pt)	molarVolume2.
private void	recomputeLight()	Lightweight recomputation for numerical derivatives.

Methods inherited from class PhaseEos

calcA, calcAi, calcAij, calcAiT, calcAT, calcATT, calcB, calcBi, calcBij, calcf, calcg, calcPressure, calcPressuredV, dFdN, dFdNdN, dFdNdT, dFdNdV, dFdxdxMatrix, dFdxdxMatrixSimple, dFdxMatrix, dFdxMatrixSimple, displayInteractionCoefficients, equals, F, fb, FB, fBB, FBB, FBD, FBT, fBV, FBV, FD, FDT, FDV, Fn, FnB, FnV, FT, FTT, FTV, fv, FV, fVV, FVV, fVVV, FVVV, gb, gBB, gBV, geta, geta, getA, getAresTV, getAT, getATT, getb, getb, getB, getCpres, getCvres, getdPdrho, getdPdTVn, getdPdVTn, getdrhodN, getdrhodP, getdrhodT, getdTVndSVnJaobiMatrix, getdUdSdSVn, getdUdSdVn, getdUdSVn, getdUdVdVSn, getdUdVSn, getdVdrho, getEosMixingRule, getf_loc, getg, getGradientVector, getGresTP, getHresdP, getHresTP, getKappa, getMixingRule, getMixingRuleName, getPressureAttractive, getPressureRepulsive, getSoundSpeed, getSresTP, getSresTV, getUSVHessianMatrix, gV, gVV, gVVV, molarVolume, resetMixingRule, setMixingRule, setMixingRuleGEModel

Methods inherited from class Phase

addComponent, addMoles, addMolesChemReac, calcA, calcAT, calcDiElectricConstant, calcDiElectricConstantdT, calcDiElectricConstantdTdT, calcMolarVolume, calcR, getActivityCoefficient, getActivityCoefficient, getActivityCoefficient, getActivityCoefficientSymetric, getActivityCoefficientUnSymetric, getAiT, getAlpha0_EOSCG, getAlpha0_GERG2008, getAlpha0_Leachman, getAlpha0_Leachman, getAlpha0_Vega, getAlphares_EOSCG, getAlphares_GERG2008, getAlphares_Leachman, getAlphares_Leachman, getAlphares_Vega, getAntoineVaporPressure, getBeta, getBi, getComponent, getComponent, getcomponentArray, getComponentNames, getComponents, getComponentWithIndex, getComposition, getCompressibilityX, getCompressibilityY, getCorrectedVolume, getCp, getCp, getCp0, getCv, getCv, getDensity, getDensity, getDensity_AGA8, getDensity_EOSCG, getDensity_GERG2008, getDensity_Leachman, getDensity_Leachman, getDensity_Vega, getDielectricConstant, getEnthalpy, getEnthalpy, getEnthalpydP, getEnthalpydT, getEntropy, getEntropy, getEntropydP, getEntropydT, getExcessGibbsEnergy, getExcessGibbsEnergySymetric, getFlowRate, getFugacity, getFugacity, getGamma, getGibbsEnergy, getHelmholtzEnergy, getHID, getInfiniteDiluteFugacity, getInfiniteDiluteFugacity, getInitType, getInternalEnergy, getInternalEnergy, getIsobaricThermalExpansivity, getIsothermalCompressibility, getJouleThomsonCoefficient, getLogActivityCoefficient, getLogInfiniteDiluteFugacity, getLogInfiniteDiluteFugacity, getLogPureComponentFugacity, getLogPureComponentFugacity, getMass, getMeanIonicActivity, getMixGibbsEnergy, getMixingRuleType, getModelName, getMolalMeanIonicActivity, getMolarComposition, getMolarMass, getMolarMass, getMolarVolume, getMolarVolume, getMoleFraction, getNumberOfComponents, getNumberOfIonicComponents, getNumberOfMolecularComponents, getNumberOfMolesInPhase, getOsmoticCoefficient, getOsmoticCoefficientOfWater, getOsmoticCoefficientOfWaterMolality, getpH, getpH, getPhase, getPhysicalProperties, getPhysicalPropertyModel, getPressure, getPressure, getProperties_EOSCG, getProperties_GERG2008, getProperties_Leachman, getProperties_Leachman, getProperties_Vega, getPseudoCriticalPressure, getPseudoCriticalTemperature, getPureComponentFugacity, getPureComponentFugacity, getRefPhase, getRefPhase, getSoundSpeed, getTemperature, getTemperature, getThermalConductivity, getThermalConductivity, getThermoPropertyModelName, getTotalVolume, getType, getViscosity, getViscosity, getVolume, getVolume, getWaterDensity, getWtFrac, getWtFrac, getWtFraction, getWtFractionOfWaxFormingComponents, getZ, getZvolcorr, groupTBPfractions, hasComponent, hasPlusFraction, hasTBPFraction, initPhysicalProperties, initPhysicalProperties, initRefPhases, initRefPhases, isConstantPhaseVolume, isMixingRuleDefined, normalize, removeComponent, resetPhysicalProperties, setAttractiveTerm, setBeta, setComponentArray, setConstantPhaseVolume, setEmptyFluid, setInitType, setMolarVolume, setMoleFractions, setNumberOfComponents, setParams, setPhysicalProperties, setPhysicalPropertyModel, setPpm, setPressure, setProperties, setRefPhase, setRefPhase, setTemperature, setTotalVolume, setType, useVolumeCorrection, useVolumeCorrection

Methods inherited from class Object

finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface PhaseEosInterface

getMolarVolume

Methods inherited from interface PhaseInterface

addMoles, addMolesChemReac, addMolesChemReac, calcAT, calcMolarVolume, calcR, getActivityCoefficient, getActivityCoefficient, getActivityCoefficient, getActivityCoefficientSymetric, getActivityCoefficientUnSymetric, getAlpha0_EOSCG, getAlpha0_GERG2008, getAlpha0_Leachman, getAlpha0_Leachman, getAlpha0_Vega, getAlphares_EOSCG, getAlphares_GERG2008, getAlphares_Leachman, getAlphares_Leachman, getAlphares_Vega, getAntoineVaporPressure, getBeta, getComponent, getComponent, getcomponentArray, getComponentNames, getComponents, getComponentWithIndex, getComposition, getCompressibilityX, getCompressibilityY, getCorrectedVolume, getCp, getCp, getCp0, getCv, getCv, getDensity, getDensity, getDensity_AGA8, getDensity_EOSCG, getDensity_GERG2008, getDensity_Leachman, getDensity_Leachman, getDensity_Vega, getEnthalpy, getEnthalpy, getEnthalpydP, getEnthalpydT, getEntropy, getEntropy, getEntropydP, getEntropydT, getExcessGibbsEnergy, getExcessGibbsEnergySymetric, getFlowRate, getFugacity, getFugacity, getGamma, getGamma2, getGibbsEnergy, getHelmholtzEnergy, getInfiniteDiluteFugacity, getInitType, getInternalEnergy, getInternalEnergy, getIsobaricThermalExpansivity, getIsothermalCompressibility, getJouleThomsonCoefficient, getLogActivityCoefficient, getLogInfiniteDiluteFugacity, getLogInfiniteDiluteFugacity, getLogPureComponentFugacity, getMass, getMeanIonicActivity, getMixGibbsEnergy, getMixingRuleType, getModelName, getMolalMeanIonicActivity, getMolarComposition, getMolarMass, getMolarMass, getMolarVolume, getMoleFraction, getNumberOfComponents, getNumberOfIonicComponents, getNumberOfMolecularComponents, getNumberOfMolesInPhase, getOsmoticCoefficient, getOsmoticCoefficientOfWater, getOsmoticCoefficientOfWaterMolality, getpH, getpH, getPhase, getPhaseFraction, getPhaseTypeName, getPhysicalProperties, getPhysicalPropertyModel, getPressure, getPressure, getProperties_EOSCG, getProperties_GERG2008, getProperties_Leachman, getProperties_Leachman, getProperties_Vega, getPseudoCriticalPressure, getPseudoCriticalTemperature, getPureComponentFugacity, getPureComponentFugacity, getRefPhase, getRefPhase, getSoundSpeed, getTemperature, getTemperature, getThermalConductivity, getThermalConductivity, getTotalVolume, getType, getViscosity, getViscosity, getVolume, getVolume, getWaterDensity, getWtFrac, getWtFrac, getWtFraction, getWtFractionOfWaxFormingComponents, getZ, getZvolcorr, hasComponent, hasComponent, hasIons, hasPlusFraction, hasTBPFraction, init, init, initPhysicalProperties, initPhysicalProperties, initPhysicalProperties, initRefPhases, isAsphalteneRich, isConstantPhaseVolume, isMixingRuleDefined, normalize, removeComponent, resetPhysicalProperties, setAttractiveTerm, setBeta, setComponentArray, setConstantPhaseVolume, setEmptyFluid, setInitType, setMixingRule, setMolarVolume, setMoleFractions, setNumberOfComponents, setParams, setPhaseTypeName, setPhysicalProperties, setPhysicalProperties, setPhysicalPropertyModel, setPpm, setPressure, setProperties, setRefPhase, setRefPhase, setTemperature, setTotalVolume, setType, useVolumeCorrection, useVolumeCorrection

Field Details

serialVersionUID

private static final long serialVersionUID

Serialization version UID.

See Also:

• Constant Field Values

logger

static org.apache.logging.log4j.Logger logger

Logger object for class.

MBWR_UNIT_FACTOR

private static final double MBWR_UNIT_FACTOR

Unit conversion factor for MBWR-32 parameters. The database coefficients are calibrated in MPa-based units (density in mol/L, pressure in MPa), using R_MPa = 0.008314 L·MPa/(mol·K). The framework uses R_SI = 8.3144621 J/(mol·K). Since getFpol() divides by R_SI·T, the resulting Helmholtz function is 1000× too small (R_SI / R_MPa = 1000). This factor compensates.

See Also:

• Constant Field Values

OP

int OP

OE

int OE

mixBP

private double[] mixBP

Mole-fraction-weighted polynomial MBWR coefficients for the mixture.

mixBE

private double[] mixBE

Mole-fraction-weighted exponential MBWR coefficients for the mixture.

mixBPdT

private double[] mixBPdT

Mole-fraction-weighted polynomial temperature derivatives for the mixture.

mixBEdT

private double[] mixBEdT

Mole-fraction-weighted exponential temperature derivatives for the mixture.

mixBPdTdT

private double[] mixBPdTdT

Mole-fraction-weighted polynomial second temperature derivatives for the mixture.

mixBEdTdT

private double[] mixBEdTdT

Mole-fraction-weighted exponential second temperature derivatives for the mixture.

mixGamma

private double mixGamma

Mixed gamma parameter = 1/rhoc_mix^2 for one-fluid mixing.

Constructor Details

PhaseBWRSEos

public PhaseBWRSEos()

Constructor for PhaseBWRSEos.

Method Details

clone

public PhaseBWRSEos clone()

clone.

Specified by:

clone in interface PhaseInterface

Overrides:

clone in class PhaseSrkEos

Returns:

a PhaseInterface object

computeMixedParameters

private void computeMixedParameters()

Computes mole-fraction-weighted MBWR parameters for the one-fluid mixture. Linear mixing: mixBP[i] = sum_j x_j * BP_j[i], similarly for BE, BPdT, BEdT. For gamma (critical density), rhoc_mix = sum_j x_j * rhoc_j, then mixGamma = 1/rhoc_mix^2.

recomputeLight

private void recomputeLight()

Lightweight recomputation for numerical derivatives. Updates mole fractions and mixed BWRS parameters without triggering a full init/Finit cycle.

addComponent

public void addComponent(String name,
 double moles,
 double molesInPhase,
 int compNumber)

Add component to component array and update moles variables.

Specified by:

addComponent in interface PhaseInterface

Overrides:

addComponent in class PhaseSrkEos

Parameters:

name - Name of component.

moles - Total number of moles of component.

molesInPhase - Number of moles in phase.

compNumber - Index number of component in phase object component array.

init

public void init(double totalNumberOfMoles,
 int numberOfComponents,
 int initType,
 PhaseType pt,
 double beta)

init.

initType used in component.init()

Calls component.init(initType)

Specified by:

init in interface PhaseInterface

Overrides:

init in class PhaseEos

Parameters:

totalNumberOfMoles - Total number of moles in all phases of Stream.

numberOfComponents - Number of components in system.

initType - a int. Use 0 to init, and 1 to reset.

pt - Type of phase.

beta - Mole fraction of this phase in system.

getMolarDensity

public double getMolarDensity()

getMolarDensity.

Returns:

a double

getdRhodV

public double getdRhodV()

getdRhodV.

Returns:

a double

getdRhodVdV

public double getdRhodVdV()

getdRhodVdV.

Returns:

a double

getdRhodVdVdV

public double getdRhodVdVdV()

getdRhodVdVdV.

Returns:

a double

getGammadRho

public double getGammadRho()

getGammadRho.

Returns:

a double

getFpol

public double getFpol()

getFpol.

Returns:

a double

getFpoldV

public double getFpoldV()

getFpoldV.

Returns:

a double

getFpoldRho

public double getFpoldRho()

Derivative of the polynomial F-term with respect to molar density.

Returns:

dF_pol/dρ

getFpoldVdV

public double getFpoldVdV()

getFpoldVdV.

Returns:

a double

getFpoldVdVdV

public double getFpoldVdVdV()

getFpoldVdVdV.

Returns:

a double

getFpoldT

public double getFpoldT()

getFpoldT.

Returns:

a double

getFpoldTdRho

private double getFpoldTdRho()

Cross derivative of the polynomial F-term with respect to temperature and molar density.

Returns:

d²F_pol/dT dρ

getFpoldTdV

private double getFpoldTdV()

Cross derivative of the polynomial F-term with respect to temperature and molar volume.

Returns:

d²F_pol/dT dV

getFpoldTdT

private double getFpoldTdT()

Second derivative of the polynomial F-term with respect to temperature.

Returns:

d²F_pol/dT²

getFdRho

public double getFdRho()

Total derivative of F with respect to molar density.

Returns:

dF/dρ

getEL

public double getEL()

getEL.

Returns:

a double

getELdRho

public double getELdRho()

getELdRho.

Returns:

a double

getELdRhodedRho

public double getELdRhodedRho()

Second derivative of the exponential EL term with respect to molar density.

Returns:

d²EL/dρ²

getELdRhodedRhodedRho

public double getELdRhodedRhodedRho()

Third derivative of the exponential EL term with respect to molar density.

Returns:

d³EL/dρ³

getFexp

public double getFexp()

getFexp.

Returns:

a double

getFexpdRho

private double getFexpdRho()

First derivative of Fexp with respect to molar density.

Returns:

dFexp/dρ

getFexpdRhodRho

private double getFexpdRhodRho()

Second derivative of Fexp with respect to molar density.

Returns:

d²Fexp/dρ²

getFexpdRhodRhodRho

private double getFexpdRhodRhodRho()

Third derivative of Fexp with respect to molar density.

Returns:

d³Fexp/dρ³

getFexpdV

public double getFexpdV()

First derivative of Fexp with respect to molar volume.

Returns:

dFexp/dV

getFexpdVdV

public double getFexpdVdV()

Second derivative of Fexp with respect to molar volume.

Returns:

d²Fexp/dV²

getFexpdVdVdV

public double getFexpdVdVdV()

Third derivative of Fexp with respect to molar volume.

Returns:

d³Fexp/dV³

getFexpdTdRho

private double getFexpdTdRho()

Cross derivative of Fexp with respect to temperature and molar density.

Returns:

d²Fexp/dT dρ

getFexpdTdV

private double getFexpdTdV()

Cross derivative of Fexp with respect to temperature and molar volume.

Returns:

d²Fexp/dT dV

getFexpdT

public double getFexpdT()

getFexpdT.

Returns:

a double

getFexpdTdT

private double getFexpdTdT()

Second derivative of Fexp with respect to temperature.

Returns:

d²Fexp/dT²

calcPressure2

public double calcPressure2()

calcPressure2.

Returns:

a double

calcPVT

public void calcPVT()

calcPVT.

getF

public double getF()

getF.

Overrides:

getF in class PhaseEos

Returns:

a double

getdFdN

public double getdFdN(int compNumb)

Numerical dF/dn_i at constant T, V. Perturbs component moles, adjusts molar volume to keep total volume constant, recomputes mix parameters, and evaluates F.

Parameters:

compNumb - component index to perturb

Returns:

numerical dF/dn_i

getdFdNdV

public double getdFdNdV(int compNumb)

Numerical d2F/(dn_i dV) at constant T, n.

Parameters:

compNumb - component index

Returns:

numerical d2F/(dn_i dV)

getdFdNdT

public double getdFdNdT(int compNumb)

Numerical d2F/(dn_i dT) at constant V, n.

Parameters:

compNumb - component index

Returns:

numerical d2F/(dn_i dT)

getdFdNdN

public double getdFdNdN(int compI,
 int compJ)

Numerical d2F/(dn_i dn_j) at constant T, V.

Parameters:

compI - component i index

compJ - component j index

Returns:

numerical d2F/(dn_i dn_j)

dFdT

public double dFdT()

Calculate derivative of F per Temperature, i.e., dF/dT.

Specified by:

dFdT in interface PhaseInterface

Overrides:

dFdT in class PhaseEos

Returns:

a double

dFdTdT

public double dFdTdT()

dFdTdT.

Specified by:

dFdTdT in interface PhaseInterface

Overrides:

dFdTdT in class PhaseEos

Returns:

a double

dFdTdV

public double dFdTdV()

Calculate derivative of F per Temperature and Volume, i.e., dF/dT * 1/dV.

Specified by:

dFdTdV in interface PhaseInterface

Overrides:

dFdTdV in class PhaseEos

Returns:

a double

dFdV

public double dFdV()

Calculate derivative of F per Volume, i.e., dF/dV.

Specified by:

dFdV in interface PhaseInterface

Overrides:

dFdV in class PhaseEos

Returns:

a double

dFdVdV

public double dFdVdV()

dFdVdV.

Specified by:

dFdVdV in interface PhaseInterface

Overrides:

dFdVdV in class PhaseEos

Returns:

a double

dFdVdVdV

public double dFdVdVdV()

dFdVdVdV.

Overrides:

dFdVdVdV in class PhaseEos

Returns:

a double

getJouleThomsonCoefficient

public double getJouleThomsonCoefficient()

Get the Joule Thomson Coefficient of a phase.

Specified by:

getJouleThomsonCoefficient in interface PhaseInterface

Overrides:

getJouleThomsonCoefficient in class PhaseEos

Returns:

Joule Thomson coefficient in K/bar

molarVolume2

public double molarVolume2(double pressure,
 double temperature,
 double A,
 double B,
 PhaseType pt)
                    throws IsNaNException,
TooManyIterationsException

molarVolume2.

Overrides:

molarVolume2 in class PhaseEos

Parameters:

pressure - a double

temperature - a double

A - a double

B - a double

pt - the PhaseType of the phase

Returns:

a double

Throws:

IsNaNException - if any.

TooManyIterationsException - if any.