In natural gas pipeline modelling, an appropriate equation of state is needed. The accuracy of this equation is critical to the accuracy of the model results. Such equations, like the Benedict Webb Ruben equation of state, are available, but they require the full composition of the gas, and their computational requirements are quite extensive. Most commonly, only a few parameters of the gas are available, like the specific gravity. Tom van der Hoeven, of Gasunie, developed an equation based on the specific gravity, the gross heating value, and the molar percent of carbon dioxide in the gas. In this paper, we derive an easily computable equation of state, based only on the standard density of the gas, from the well accepted Peng-Robinson equation of state.
The equation of state is defined as: A relationship between the pressure, the density and the temperature, (P/p/T' relationship). In order to be able to compute all the thermodynamic relationships, we add: A relationship giving the heat capacity at constant volume in the ideal gas state, as a function of temperature.
The composition of the gas is considered variable, but should consist essentially of methane and ethane, plus a few heavier hydrocarbons. This hypothesis can be relaxed, but the gas should always consist of similar hydrocarbons (light or heavy). The non-hydrocarbon gas fraction should be small. The only parameter known to characterize the composition of the gas is assumed to be its density at standard conditions.
We are mixing n products. Each of these gases is characterized by its density psT at standard pressure and temperature (PsT, TST). At this standard pressure and temperature, the product can be assumed to be in ideal gas state.
This equation has been used in real time modelling of parts of the NOVA system and has proven to be accurate and easy to use. In the derivation, we have found the inherent limits of such equations: the non-linearity of certain functions of the critical values of the gas mixed, and the existence of non-negligible interaction coefficients.