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
f ≡ u - T·s (1)
All single-phase thermodynamic properties can be calculated as derivatives of the Helmholtz energy, as a function of temperature and density.
f(ρ,T) = f0(ρ,T) + fr(ρ,T) (2)
The dimensionless Helmholtz energy Φ uses independent variables of dimensionless density and temperature.
Φ(δ,τ) = Φ0(δ,τ) + Φr(δ,τ) (3)
For a certain composition of a mixture the ideal Helmholtz energy is
f0 = h0 - RT - Ts0 = T∫T0cp0dT + h00 - RT - T[T∫T0cp0/TdT - Rlnρ/ρ0 - RlnT/T0 + s00 - Rn∑i=1xi·lnxi] (4)
Φ0 = -ττ∫τ0cp0/R·τ2dτ + h00/Rτ - 1 + τ∫τ0cp0/R·τdτ + lnδ/δ0 + lnτ0/τ - s00/R + n∑i=1xi·lnxi (5)
The ideal gas part as well as the real fluid behavior is often described using empirical models.
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.
Isochoric Heat Capacity
Isobaric Heat Capacity
Joule Thomson Coefficient
Speed of Sound
The common functional forms of the fundamental equations are
The various constants are given in the detailed documentation for the equation of state in annex D of ISO 20765-1.