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Thermodynamic Properties
Functional Forms
Natural Gas Calculation - Helmholtz Energy
The Helmholtz free energy is a thermodynamic potential that measures the »useful« work obtainable from a closed thermodynamic system at a constant temperature and volume. The Helmholtz energy is defined as
(9.14)All single-phase thermodynamic properties can be calculated as derivatives of the Helmholtz energy, as a function of temperature and density.
(9.15)The dimensionless Helmholtz energy Φ uses independent variables of dimensionless density and temperature.
(9.16)For a certain composition of a mixture the ideal Helmholtz energy is
(9.17)The ideal gas part as well as the real fluid behavior is often described using empirical models.
Symbols
cp°
molar ideal gas specific isobaric heat capacity [kJ/(kmol·K)]
cp
molar isobaric heat capacity [kJ/(kmol·K)]
cv
molar isochoric heat capacity [kJ/(kmol·K)]
f°
ideal gas contribution to the molar Helmholtz energy [kJ/kmol]
f
molar Helmholtz free energy [kJ/kmol]
fr
residual part contribution to the molar Helmholtz energy [kJ/kmol]
h°
molar ideal gas entalpy [kJ/kmol]
h0°
ideal gas integration constant for zero enthalpy at the reference state of 298.15 K and 0.101325 MPa [kJ/kmol]
M
molar mass [kg/kmol]
R
molar gas constant 8.31451 kJ/(kmol·K)
s°
molar ideal gas entropy [kJ/(kmol·K)]
s0°
ideal gas integration constant for zero entropy at the reference state of 298.15 K and 0.101325 MPa [kJ/(kmol·K)]
s
molar entropy [kJ/(kmol·K)]
T
absolute temperature [K]
u
molar internal energy [kJ/kmol]
w
speed of sound [m/s]
xi
mole fraction of component i [-]
δ°
molar density at the reference state of 298.15 K and 0.101325 MPa [-]
δ
reduced density δ=K³·ρ [-], where K is a mixture size parameter using the constants from annex D of ISO 20765-1
κ
isentropic exponent [-]
μ
Joule-Thomson coefficient [K/MPa]
Φ°
ideal gas contribution to the reduced Helmholtz energy [-]
Φ
reduced Helmholtz energy f/(RT) [-]
Φr
residual part contribution to the reduced Helmholtz energy [-]
ρ
molar density [kmol/m³]
τ
inverse reduced temperature (Tr/T) [-], where Tr =1K
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Natural Gas Calculation - Thermodynamic Properties
The functions for calculating compressibility factor, internal energy, enthalpy, entropy, heat capacity, speed of sound and other caloric properties are all related to the Helmholtz free energy and its derivates.
Compression Factor
(9.18)Internal Energy
(9.19)Enthalpy
(9.20)Entropy
(9.21)Isochoric Heat Capacity
(9.22)Isobaric Heat Capacity
(9.23)Joule Thomson Coefficient
(9.24)Isentropic Exponent
(9.25)Speed of Sound
(9.26)with
(9.27)and
(9.28)Top of Page | Symbols
Functional Forms
The common functional forms of the fundamental equations are
(9.29)
(9.30)
(9.31)
(9.32)
(9.33)
(9.34)The various constants are given in the detailed documentation for the equation of state in annex D of ISO 20765-1.
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