CO2 Transport (Span-Wagner / PR)

DWSIM Plus

Available with a DWSIM Plus (Patreon) subscription.

Property package for CO2-rich streams in pipelines, compression and shipping: the Span-Wagner reference equation of state for pure CO2, and Peng-Robinson with binary parameters for the usual pipeline impurities for CO2 with impurities.

DWSIM.Extensions.PropertyPackages.CCUS.Transport.CO2TransportPropertyPackage
Assembly DWSIM.Extensions.PropertyPackages.CCUS.dll · Object ← PropertyPackage ← CO2TransportPropertyPackage
Name in the flowsheet CO2 Transport (Span-Wagner/PR) · FluentAPI PropertyPackages.Plus.CO2Transport

Scope

The package is for CO₂-rich streams in pipeline transport, compression trains and ship transport: dense-phase and gas-phase properties, phase envelopes of CO₂ with impurities, and the detection of two-phase flow. It switches between two equations of state on the CO₂ content of the stream:

• Pure CO₂ (mole fraction above 0.9999): the Span-Wagner (1996) reference equation of state, a 42-term Helmholtz energy formulation (7 polynomial, 27 exponential and 8 Gaussian terms) with T_c = 304.1282 K, P_c = 73.773 bar and ρ_c = 467.6 kg/m³. Density, fugacity, enthalpy and entropy come from the Helmholtz energy and its derivatives.
• CO₂ with impurities: Peng-Robinson with binary parameters for the usual pipeline impurities, which the package editor lists with their sources.

Pair	kij	Pair	kij
CO2-N2	0.0070	CO2-CH4	0.0919
CO2-O2	0.1140	CO2-H2	0.0920
CO2-Ar	0.1150	CO2-CO	0.0490
CO2-H2S	0.0974	CO2-NO2	0.0500
CO2-H2O	0.1896	N2-O2	-0.0119
CO2-SO2	0.0440	N2-Ar	-0.0060
		N2-H2	-0.0200

The CO₂-H₂O value comes from Spycher, Pruess and Ennis-King (2003). Pairs not in the table have k_ij = 0. The package also offers IsTwoPhase(T, P) and MinimumOperatingPressure(T, safetyFactor) for pipeline checks on the stream composition.

Recommended envelope. Temperature 216 to 1100 K and pressure up to 800 MPa (the range of Span-Wagner); CO₂ purity above 90 mol% for pipeline work; impurities N₂, O₂, Ar, H₂S, H₂O, SO₂, CH₄, H₂, CO and NO₂.

Validation. The pure CO₂ density from Span-Wagner matches the NIST WebBook data: 228.8 kg/m³ at 350 K and 100 bar (supercritical, +0.003 %) and 938.2 kg/m³ at 280 K and 100 bar (liquid, +0.001 %). The validation cases also cover the saturated liquid and vapor densities from 220 to 300 K, the region near the critical point, a CO₂/N₂/O₂ pipeline mixture and a compression from 10 to 100 bar.

Limitations

• A stream with more than 0.01 mol% of impurities leaves Span-Wagner for Peng-Robinson; the mixture properties carry the accuracy of a cubic equation of state and of the general methods listed under the property methods below.
• The viscosity and thermal conductivity of the streams come from the general correlations of DWSIM listed there.

Example

This code runs on every build of this site, and the output below is what it printed.

Python

fs = (Flowsheet.Create("CO2TransportExample")
      .WithCompounds("Carbon dioxide", "Nitrogen", "Argon", "Methane")
      .WithPropertyPackage(PropertyPackages.Plus.CO2Transport))

def pure(name):                           # pure CO2: Span-Wagner
    return fs.AddMaterialStream(name).SetCompoundMolarFlow("Carbon dioxide", 100.0)

def mixture(name):                        # 96 % CO2 with N2, Ar and CH4: Peng-Robinson
    return (fs.AddMaterialStream(name)
            .SetCompoundMolarFlow("Carbon dioxide", 96.0).SetCompoundMolarFlow("Nitrogen", 2.0)
            .SetCompoundMolarFlow("Argon", 1.0).SetCompoundMolarFlow("Methane", 1.0))

dense = pure("CO2, 110 bar").At(Q.Celsius(25.0), Q.Bar(110.0))
gas = pure("CO2, 30 bar").At(Q.Celsius(25.0), Q.Bar(30.0))
pipeline = mixture("Mixture, 110 bar").At(Q.Celsius(25.0), Q.Bar(110.0))
dew25 = mixture("Mixture, dew point at 25 C").WithTemperature(Q.Celsius(25.0)).WithVaporFraction(1.0)
bubble60 = mixture("Mixture, bubble point at 60 bar").WithPressure(Q.Bar(60.0)).WithVaporFraction(0.0)
dew60 = mixture("Mixture, dew point at 60 bar").WithPressure(Q.Bar(60.0)).WithVaporFraction(1.0)
fs.Solve()

for b in (dense, gas, pipeline):
    s = b.Object
    i = 2 if s.Phases[2].Properties.molarfraction else 3     # vapor or liquid
    p = s.Phases[i].Properties
    print(f"{s.GraphicObject.Tag:16}: {'vapor' if i == 2 else 'liquid'}, density {p.density:.1f} kg/m3, "
          f"viscosity {p.viscosity * 1e6:.1f} uPa s")
print(f"Mixture dew pressure at 25 C = {dew25.Object.Phases[0].Properties.pressure / 1e5:.1f} bar")
print(f"Mixture at 60 bar: two phases from {bubble60.Object.Phases[0].Properties.temperature - 273.15:.1f} C "
      f"(bubble) to {dew60.Object.Phases[0].Properties.temperature - 273.15:.1f} C (dew)")

Output

CO2, 110 bar    : liquid, density 832.6 kg/m3, viscosity 76.7 uPa s
CO2, 30 bar     : vapor, density 64.1 kg/m3, viscosity 15.5 uPa s
Mixture, 110 bar: liquid, density 735.2 kg/m3, viscosity 75.0 uPa s
Mixture dew pressure at 25 C = 70.5 bar
Mixture at 60 bar: two phases from 9.5 C (bubble) to 18.7 C (dew)

DWSIM 10.2.11.0, generated 2026-10-08.

Property methods

How the package calculates each property, as it reports it in PropertyMethodsInfo (the property package editor shows the same list).

Property	Method
Vapor fugacity	Span-Wagner EOS (pure CO2) / Peng-Robinson EOS with the package kij (mixtures)
Liquid fugacity	Span-Wagner EOS (pure CO2) / Peng-Robinson EOS with the package kij (mixtures)
Vapor enthalpy, entropy, Cp/Cv	Span-Wagner EOS (pure CO2) / Ideal Gas (mixtures)
Liquid enthalpy, entropy, Cp/Cv	Span-Wagner EOS (pure CO2) / Ideal Gas less the heats of vaporization (mixtures)
Vapor density	Span-Wagner EOS (pure CO2) / Ideal Gas (mixtures)
Liquid density	Span-Wagner EOS (pure CO2) / Peng-Robinson EOS with the package kij (mixtures)
Vapor viscosity	Fenghour, Wakeham and Vesovic 1998 (pure CO2) / Experimental / Lucas / Jossi-Stiel-Thodos (mixtures)
Liquid viscosity	Fenghour, Wakeham and Vesovic 1998 (pure CO2) / Experimental / Letsou-Stiel (mixtures)
Vapor thermal conductivity	Vesovic et al. 1990 (pure CO2) / Experimental / Ely-Hanley (mixtures)
Liquid thermal conductivity	Vesovic et al. 1990 (pure CO2) / Experimental / Latini (mixtures)
Surface tension	Experimental / Brock-Bird
Solid density	Experimental Data / User-Defined
Solid enthalpy, entropy, Cp/Cv	Experimental Solid Cp / From Liquid Phase Enthalpy + Enthalpy of Fusion

Default flash algorithm: Universal.

Configuration saved with the flowsheet

The package writes its settings to the simulation file (SaveData) and reads them back on load (LoadData). The elements below are the ones this package adds to those of every property package, as written for the example.

This package adds no elements of its own.

Settings common to every property package, as saved for the example

Element	Value
Type	76 characters
ComponentName	CO2 Transport (Span-Wagner/PR)
ComponentDescription	Span-Wagner EOS for pure CO2, PR for CO2-rich mixtures.
Tag	CO2 Transport (Span-Wagner/PR)
UseHenryConstants	true
AutoEstimateMissingNRTLUNIQUACParameters	true
UseImmiscibleListForLiquid2InitialEstimates	true
SingleCompoundCheckThreshold	0.99999
OverrideKvalFugCoeff	false
OverrideEnthalpyCalculation	false
OverrideEntropyCalculation	false
LiquidDensityCalculationMode_Subcritical	Rackett_and_ExpData
LiquidDensityCalculationMode_Supercritical	Rackett_and_ExpData
LiquidDensity_CorrectExpDataForPressure	true
LiquidDensity_UsePenelouxVolumeTranslation	true
LiquidViscosityCalculationMode_Subcritical	ExpData
LiquidViscosityCalculationMode_Supercritical	Letsou_Stiel
LiquidViscosity_CorrectExpDataForPressure	true
LiquidViscosity_MixingRule	MoleAverage
VaporPhaseFugacityCalculationMode	Ideal
SolidPhaseFugacityCalculationMethod	FromLiquidFugacity
SolidPhaseFugacity_UseIdealLiquidPhaseFugacity	false
SolidPhaseEnthalpy_UsesCp	false
EnthalpyEntropyCpCvCalculationMode	LeeKesler
LiquidEnthalpyEntropyCpCvCalculationMode_EOS	EOS
LiquidFugacity_UsePoyntingCorrectionFactor	true
ActivityCoefficientModels_IgnoreMissingInteractionParameters	false
IgnoreVaporFractionLimit	false
IgnoreSalinityLimit	false
CalculateAdditionalMaterialStreamProperties	true
FlashCalculationApproach	NestedLoops
DisplayMissingCompoundPropertiesWarning	false
ForcedSolids	[]
PropertyOverrides	{}
FlashSettings	36 Setting entries

Learn more

• User guide

  ---

  • CO\(_2\) Transport (Span-Wagner / PR)

• Used with

  ---

  • Pipe Segment
  • Compressor
  • Pump
  • Pipe Network
  • Heat Exchanger

API members

Public members declared by this class. Inherited members are documented on the base classes.

Constructors

CO2TransportPropertyPackage()

C#VB.NET

public CO2TransportPropertyPackage()

Public Sub New()

CO2TransportPropertyPackage(bool)

Parameter	Type	Description
comode	Boolean

C#VB.NET

public CO2TransportPropertyPackage(bool comode)

Public Sub New(comode As Boolean)

Properties

FlashBase: DWSIM's flash, with the starting pressure of a bubble-point or two-phase TV flash of a mixture taken from Wilson...

DWSIM's flash, with the starting pressure of a bubble-point or two-phase TV flash of a mixture taken from Wilson K-values (see TransportFlash).

C#VB.NET

public override FlashAlgorithm FlashBase { get; }

Public Overrides ReadOnly Property FlashBase As FlashAlgorithm

ImplementsAnalyticalDerivatives

C#VB.NET

public override bool ImplementsAnalyticalDerivatives { get; }

Public Overrides ReadOnly Property ImplementsAnalyticalDerivatives As Boolean

ImplementsCrossPlatformEditor

C#VB.NET

public override bool ImplementsCrossPlatformEditor { get; }

Public Overrides ReadOnly Property ImplementsCrossPlatformEditor As Boolean

MobileCompatible

C#VB.NET

public override bool MobileCompatible { get; }

Public Overrides ReadOnly Property MobileCompatible As Boolean

Methods

AUX_LIQDENS(double, Array, double, double, bool)

Parameter	Type	Description
T	Double
Vx	Array
P	Double
Pvp	Double
EXPERIMENT	Boolean

C#VB.NET

public override double AUX_LIQDENS(double T, Array Vx, double P = 0, double Pvp = 0, bool EXPERIMENT = false)

Public Overrides Function AUX_LIQDENS(T As Double, Vx As Array, P As Double = 0, Pvp As Double = 0, EXPERIMENT As Boolean = False) As Double

AUX_VAPDENS(double, double)

Parameter	Type	Description
T	Double
P	Double

C#VB.NET

public override double AUX_VAPDENS(double T, double P)

Public Overrides Function AUX_VAPDENS(T As Double, P As Double) As Double

AUX_Z(double[], double, double, PhaseName)

Parameter	Type	Description
Vx	Double[]
T	Double
P	Double
state	PhaseName

C#VB.NET

public override double AUX_Z(double[] Vx, double T, double P, PhaseName state)

Public Overrides Function AUX_Z(Vx As Double(), T As Double, P As Double, state As PhaseName) As Double

CalculateCO2ThermalConductivity(double, double)

Parameter	Type	Description
T	Double
P	Double

C#VB.NET

public double CalculateCO2ThermalConductivity(double T, double P)

Public Function CalculateCO2ThermalConductivity(T As Double, P As Double) As Double

CalculateCO2Viscosity(double, double)

Parameter	Type	Description
T	Double
P	Double

C#VB.NET

public double CalculateCO2Viscosity(double T, double P)

Public Function CalculateCO2Viscosity(T As Double, P As Double) As Double

Clone()

C#VB.NET

public override PropertyPackage Clone()

Public Overrides Function Clone() As PropertyPackage

DW_CalcCompPartialVolume(Phase, double, double)

Parameter	Type	Description
phase	Phase
T	Double
P	Double

C#VB.NET

public override void DW_CalcCompPartialVolume(Phase phase, double T, double P)

Public Overrides Sub DW_CalcCompPartialVolume(phase As Phase, T As Double, P As Double)

DW_CalcdKdComposition(double[], double[], double, double, State, string): Composition (mole-number) derivative of the equilibrium K-values, d(K_i)/dn_j, with respect to the mole numbers of...

Composition (mole-number) derivative of the equilibrium K-values, d(K_i)/dn_j, with respect to the mole numbers of the phase indicated by withRespectTo (State.Liquid perturbs Vx, State.Vapor perturbs Vy), on a total-moles = 1 basis. Returns an (nc x nc) matrix. Base implementation is a finite difference; EOS/activity packages override it using the analytical d(ln phi)/dn (or d(ln gamma)/dx) building blocks.

Parameter	Type	Description
Vx	Double[]
Vy	Double[]
T	Double
P	Double
withRespectTo	State
type	String

C#VB.NET

public override double[,] DW_CalcdKdComposition(double[] Vx, double[] Vy, double T, double P, State withRespectTo, string type = "LV")

Public Overrides Function DW_CalcdKdComposition(Vx As Double(), Vy As Double(), T As Double, P As Double, withRespectTo As State, type As String = "LV") As Double(,)

DW_CalcdKdT(double[], double[], double, double, string)

Parameter	Type	Description
Vx	Double[]
Vy	Double[]
T	Double
P	Double
type	String

C#VB.NET

public override double[] DW_CalcdKdT(double[] Vx, double[] Vy, double T, double P, string type = "LV")

Public Overrides Function DW_CalcdKdT(Vx As Double(), Vy As Double(), T As Double, P As Double, type As String = "LV") As Double()

DW_CalcdLnFugCoeffdn(double[], double, double, State): Composition (mole-number) derivative of the natural logarithm of the fugacity coefficients, d(ln phi_i)/dn_j, for...

Composition (mole-number) derivative of the natural logarithm of the fugacity coefficients, d(ln phi_i)/dn_j, for the given phase, evaluated on a total-moles = 1 basis. Returns an (nc x nc) matrix. Base implementation is a finite difference in mole numbers; EOS/activity packages override this with the closed-form partial-molar expression.

Parameter	Type	Description
Vx	Double[]
T	Double
P	Double
st	State

C#VB.NET

public override double[,] DW_CalcdLnFugCoeffdn(double[] Vx, double T, double P, State st)

Public Overrides Function DW_CalcdLnFugCoeffdn(Vx As Double(), T As Double, P As Double, st As State) As Double(,)

DW_CalcdLnFugCoeffdT(double[], double, double, State): Temperature derivative of the natural logarithm of the fugacity coefficients, d(ln phi_i)/dT, for the given phase.

Temperature derivative of the natural logarithm of the fugacity coefficients, d(ln phi_i)/dT, for the given phase. Base implementation is a forward finite difference; EOS/activity packages override this with a closed-form expression. Distinct from DW_CalcdFugCoeffdT, which returns d(phi)/dT (not the logarithm).

Parameter	Type	Description
Vx	Double[]
T	Double
P	Double
st	State

C#VB.NET

public override double[] DW_CalcdLnFugCoeffdT(double[] Vx, double T, double P, State st)

Public Overrides Function DW_CalcdLnFugCoeffdT(Vx As Double(), T As Double, P As Double, st As State) As Double()

DW_CalcEnthalpy(Array, double, double, State): Calculates the enthalpy of a mixture.

Calculates the enthalpy of a mixture.

Parameter	Type	Description
Vx	Array	Vector of doubles containing the molar composition of the mixture.
T	Double	Temperature (K)
P	Double	Pressure (Pa)
st	State	State enum indicating the state of the mixture (liquid or vapor).

C#VB.NET

public override double DW_CalcEnthalpy(Array Vx, double T, double P, State st)

Public Overrides Function DW_CalcEnthalpy(Vx As Array, T As Double, P As Double, st As State) As Double

DW_CalcEnthalpyDeparture(Array, double, double, State): Calculates the enthalpy departure of a mixture.

Calculates the enthalpy departure of a mixture.

Parameter	Type	Description
Vx	Array	Vector of doubles containing the molar composition of the mixture.
T	Double	Temperature (K)
P	Double	Pressure (Pa)
st	State	State enum indicating the state of the mixture (liquid or vapor).

C#VB.NET

public override double DW_CalcEnthalpyDeparture(Array Vx, double T, double P, State st)

Public Overrides Function DW_CalcEnthalpyDeparture(Vx As Array, T As Double, P As Double, st As State) As Double

DW_CalcEntropy(Array, double, double, State): Calculates the entropy of a mixture.

Calculates the entropy of a mixture.

Parameter	Type	Description
Vx	Array	Vector of doubles containing the molar composition of the mixture.
T	Double	Temperature (K)
P	Double	Pressure (Pa)
st	State	State enum indicating the state of the mixture (liquid or vapor).

C#VB.NET

public override double DW_CalcEntropy(Array Vx, double T, double P, State st)

Public Overrides Function DW_CalcEntropy(Vx As Array, T As Double, P As Double, st As State) As Double

DW_CalcEntropyDeparture(Array, double, double, State): Calculates the entropy departure of a mixture.

Calculates the entropy departure of a mixture.

Parameter	Type	Description
Vx	Array	Vector of doubles containing the molar composition of the mixture.
T	Double	Temperature (K)
P	Double	Pressure (Pa)
st	State	State enum indicating the state of the mixture (liquid or vapor).

C#VB.NET

public override double DW_CalcEntropyDeparture(Array Vx, double T, double P, State st)

Public Overrides Function DW_CalcEntropyDeparture(Vx As Array, T As Double, P As Double, st As State) As Double

DW_CalcFugCoeff(Array, double, double, State): Calculates fugacity coefficients for the specified composition at the specified conditions.

Calculates fugacity coefficients for the specified composition at the specified conditions.

Parameter	Type	Description
Vx	Array	Vector of doubles containing the molar composition of the mixture.
T	Double	Temperature in K
P	Double	Pressure in Pa
st	State	Mixture state (Liquid or Vapor)

C#VB.NET

public override double[] DW_CalcFugCoeff(Array Vx, double T, double P, State st)

Public Overrides Function DW_CalcFugCoeff(Vx As Array, T As Double, P As Double, st As State) As Double()

DW_CalcPhaseProps(Phase)

Parameter	Type	Description
Phase	Phase

C#VB.NET

public override void DW_CalcPhaseProps(Phase Phase)

Public Overrides Sub DW_CalcPhaseProps(Phase As Phase)

DW_CalcProp(string, Phase): Provides a wrapper function for CAPE-OPEN CalcProp/CalcSingleProp functions.

Provides a wrapper function for CAPE-OPEN CalcProp/CalcSingleProp functions.

Parameter	Type	Description
property	String	The property to be calculated.
phase	Phase	The phase where the property must be calculated for.

C#VB.NET

public override void DW_CalcProp(string property, Phase phase)

Public Overrides Sub DW_CalcProp([property] As String, phase As Phase)

GetEditingForm(): Returns the binary interaction parameter editor of this package.

Returns the binary interaction parameter editor of this package.

C#VB.NET

public override object GetEditingForm()

Public Overrides Function GetEditingForm() As Object

IsTwoPhase(double, double)

Parameter	Type	Description
T	Double
P	Double

C#VB.NET

public bool IsTwoPhase(double T, double P)

Public Function IsTwoPhase(T As Double, P As Double) As Boolean

MinimumOperatingPressure(double, double)

Parameter	Type	Description
T	Double
safetyFactor	Double

C#VB.NET

public double MinimumOperatingPressure(double T, double safetyFactor = 1.15)

Public Function MinimumOperatingPressure(T As Double, safetyFactor As Double = 1.15) As Double

PopulateCrossPlatformEditor(object): The package has no adjustable parameters: the panel lists the binary interaction parameters, the supported...

The package has no adjustable parameters: the panel lists the binary interaction parameters, the supported components and the model, mirroring the Windows editor.

Parameter	Type	Description
container	Object

C#VB.NET

public override void PopulateCrossPlatformEditor(object container)

Public Overrides Sub PopulateCrossPlatformEditor(container As Object)

ReturnInstance(string)

Parameter	Type	Description
typename	String

C#VB.NET

public override object ReturnInstance(string typename)

Public Overrides Function ReturnInstance(typename As String) As Object

RunPostMaterialStreamSetRoutine()

C#VB.NET

public override void RunPostMaterialStreamSetRoutine()

Public Overrides Sub RunPostMaterialStreamSetRoutine()

SaveData()

C#VB.NET

public override List<XElement> SaveData()

Public Overrides Function SaveData() As List(Of XElement)

SupportsComponent(ICompoundConstantProperties)

Parameter	Type	Description
comp	ICompoundConstantProperties

C#VB.NET

public override bool SupportsComponent(ICompoundConstantProperties comp)

Public Overrides Function SupportsComponent(comp As ICompoundConstantProperties) As Boolean

Fields

ClassId

C#VB.NET

public const string ClassId = "C4D5E6F7-8901-4A23-B456-789012345678"

Public Const ClassId As String = "C4D5E6F7-8901-4A23-B456-789012345678"