A stable solution method for natural gas density across a wide temperature range using the GERG-2008 equation of state

Abstract

The GERG-2008 Equation of State (EoS) is recommended by ISO 20765–2 for computing the physical properties of natural gas. Due to the non-monotonic relationship between pressure and molar density described by the GERG-2008 EoS under low temperature conditions, multiple density solutions may exist, making the precise determination of density challenging. This paper first investigates the variation of molar densities with pressure at different temperatures. When the temperature is above $T_r\left(x\right)$(The composition-dependent reducing functions of the mixture temperature), the pressure described by the GERG-2008 EoS increases monotonically with the molar density, and only one molar density solution that satisfies the equation exists. However, when the temperature is below $T_r\left(x\right)$, the pressure described by GERG-2008 EoS no longer changes monotonically with the increase in molar density, resulting in multiple molar density solutions that satisfy the equation. To address this problem, this paper proposes a novel solution method that employs a combination of one-dimensional search and the Newton-Raphson iteration to obtain the required molar density solutions. The true molar density solution is then determined based on the Gibbs free energy criterion, ensuring the correct molar density solution is obtained across a wide temperature range. A total of 903 sets of natural gas density data, covering pressures from 0 to 200 MPa and temperatures from 100 to 450 K, were used to validate this method. The computational results indicate that, when the temperature is above$T_r\left(x\right)$, the average relative deviation (ARD) between the calculated density values and the experimental values ranges from 0.1 % to 0.59 %. For temperatures below $T_r\left(x\right)$, the ARD values using this method range from 0.01 % to 0.39 %. The proposed solution method enhances the stability and accuracy of solving the GERG-2008 equation, particularly for natural gas at low temperatures.