gas property calculations

7/29/2019 Gas Property Calculations

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Comparison of AGA Report

No. 8 and GERG 2004Equations for Gas PropertyCalculations

Eric W. Lemmon

Thermophysical Properties Division

National Institute of Standards and Technology

Boulder, Colorado


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History of Equations of State

Ideal gas law van der Waals equation

Cubic equations

Peng-Robinson

Soave-Redlich-Kwong

Virial equations Benedict-Webb-Rubin equations (BWR)

Helmholtz energy equations

RTbvv

ap

2


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EOS Characteristics

VaporPhase LiquidPhase Criticalregion Accuracy Speed Iteration

Ideal gas law Low High No

vdW Low High No

Cubics Moderate High No

Virials Moderate Med Yes

BWRs High Med Yes

Helmholtz Very High Low Yes

All calculate pressure as a function of density and temperature, except

for the Helmholtz energy


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pv

RT =1=Z(for an ideal gas)


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Z=1+Bp


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Z=1+Bp+Cp2


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Why not just use pressure for the independent variable inour equation of state?

T

p

RTRT

TRTu

2

20

2

1ln

Equations of state


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Whats the big deal

with all thisHelmholtz stuff?

Hermann Ludwig Ferdinand von Helmholtz (1821 1894)


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a

p2

T

aTau

T

as

Why the Helmholtz energy is best


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A thermodynamically consistent representation of the properties of a fluid

A

RT ideal Ni

tidki

Njtj

dj exp ajlj

j

Nktkdk exp ak k

lk

k

exp k k mk

where: crit , Tcrit T

Gaussian terms (critical region)

traditional terms

All other properties by differentiation:

p RT 1r

, CV R

2 2

2

Helmholtz Energy Equation of State


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Given density and temperature, all other properties can becalculated

Iterative solutions required given input conditions of pressure

and temperature; pressure and enthalpy; pressure andentropy; saturation temperature; vapor pressure; etc.


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Mixture equations of state

SGERG-88, AGA8-DC92 (volumetric properties):compression factor, density (ISO 12213, GERG TM5,

AGA report No.8)

AGA8-DC92 (caloric properties):speed of sound, enthalpy (ISO 20765-1, AGA reportNo.10)

GERG-2004:(ISO WD 20765-2 and 3, GERG TM15)

compression factor, caloric propertiesfundamental equation of state, valid over the entire fluidregion


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AGA-8 mixture model

AGA Report No. 8, K.E. Starling and J.L. Savidge,Compressibility Factors of Natural Gas and Other RelatedHydrocarbon Gases

Current industry standard

Valid for gas phase only, cannot calculate phaseequilibrium

Temperature range: -130 C to 400 C (-200 F to 760 F) Pressures up to 280 MPa (40,000 psia)

Detail characterization method for compressibility factor:hybrid type has features of virial EOS (power series indensity) for low density calculations and exponential

functions for high density calculations (similar to mBWREOS)


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SGERG-88 equation (gross method):

Z compression factor density (reduced)

B second virial coefficient T abs. temperature

C third virial coefficient

2)()(1 TCTBZ

AGA report no.8 (detail method):

Du, Dv coefficients

7

3 ,

)exp()()(u

w

w

v

wv

v

u

u cTDTD

Structure of Existing Equations

2)()(1 TCTBZ


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Excess Helmholtz Energy Mixture Model

Excess property model explicit inHelmholtz energy Independent parameters are density and

temperature

Generalized/Predictive

High accuracy Quicker than ECS models

Requires accurate pure fluid equations of state

Allows mixing of Helmholtz and BWR equations, andECS models for the pure fluids

Calculates all thermodynamic properties, includingheat capacities, speed of sound, vapor-liquidequilibria, liquid-liquid equilibria, and critical lines


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GERG-2004 developers


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Helmholtz free energy:

Departurefunction

Contribution of thepure fluid equationsIdeal gas part

k

i

i,i X,,,xX,,X,,1

rr

o

o

Reducing functions: Xr XTr

Reduced variables: TXTr / Xr /

Structure of GERG-2004 Equation


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Reducing function of temperature:

4 parameters for each binary mixture: T, kTand v, kv

Structure of GERG-2004 Equation


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Ranges of application

0

100

200

300

-183 -150 -100 -50 0 50 77-3

liquid gas

criticalpoint

phaseenvelope

AGA8-DC92

AGA8-DC92SGERG-88

0.1- 0.2 %

w 0.2 %

0

100

200

300

-183 -150 -100 -50 0 50 77-3

liquid gas

criticalpoint

phaseenvelope

AGA8-DC92

AGA8-DC92SGERG-88

0.1- 0.2 %

w 0.2 %

Temperature

Pressure

1500

3000

4300

bar psia

C

F-150-240 -60 120320

100

200

300

-183 -150 -100 -50 0 50 77-3

liquid gas

criticalpoint

phaseenvelope

AGA8-DC92

AGA8-DC92SGERG-88

0.1- 0.2 %

w 0.2 %


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Overview of components


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Experimental data

18 components (soon to be 21)

70,000 experimental binary mixture data forcorrelation work (153) binary mixtures

22,000 experimental natural gas data andnatural gas like multicomponent data for

testing the new equation More than 95% of all experimental natural

gas and natural gas like multicomponentmixture data listed in the GERG Databank ofHigh-Accuracy Compression FactorMeasurements (GERG TM4 and TM7) aredescribed with deviations of less than 0.1% .


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Methane/Ethane VLE data


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www.nist.gov/srd/nist23.htm

90 pure fluids

Mixtures with up to 20 components

All thermodynamic and transport properties

GERG-2004 is main mixture model, but can useAGA-8 or cubics as well

Table and plot generation

Fluid search menu

REFPROP program


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Methane


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Methane/Ethane: 99/1


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Methane/Ethane: 95/5


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Methane/Ethane/Propane: 92/6/2


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Methane/Ethane/Propane/Butane: 90/5/3/2

C /C2/C3/C /C 8 /8/ /2/


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C1/C2/C3/C4/C5: 85/8/4/2/1

C1/C2/C3/C4/C5 75/12/8/3/2


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C1/C2/C3/C4/C5: 75/12/8/3/2

C1/C2/C3/C4/C5/N2/CO2 75/8/4/2/1/2/8


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C1/C2/C3/C4/C5/N2/CO2: 75/8/4/2/1/2/8

C1/C2/C3/C4/C5/N2/CO2 75/8/4/2/1/8/2


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C1/C2/C3/C4/C5/N2/CO2: 75/8/4/2/1/8/2

C1 8/N2/CO2 80/6/3/1/ 6/ 2/ 1/ 1/2/7


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C1-8/N2/CO2: 80/6/3/1/.6/.2/.1/.1/2/7

C1/C2/C3/C4/C5/C6/C7/C8 75/12/8/2/1/ 8/ 7/ 5


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C1/C2/C3/C4/C5/C6/C7/C8: 75/12/8/2/1/.8/.7/.5


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Program is available at:

http://www.boulder.nist.gov/div838/theory/refprop/REF-DEVS/REF-DEVS.HTM

(upper/lower case is required in address)

Program calculates deviations in density,

speed of sound, and isobaric heat capacities.

gas property calculations

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