Download - 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.