To investigate the impact of choice of energy equation upon gas-pipeline simulations, a 650 km long model pipeline was simulated using two different forms of the energy equation, internal energy- and enthalpy form. One adiabatic scenario as well as a scenario with heat exchange between the gas and the surroundings was modelled. Two equations of state were compared (BWRS and GERG 2004), together with correlations to calculate the gas heat capacities typically found in commercial software.
It was found that the choice of energy equation can significantly impact the modelled gas temperatures, if using approximate correlations to determine the heat capacity of the gas. If using more accurate heat capacity correlations, the modelled temperatures coincide well. The largest temperatures discrepancies were found in areas of high temperature gradients, like where the pipeline enters and exits the ocean.
The two equations of state were found to agree reasonably well, although some discrepancies were observed.
Natural gas comprise around 22% of the world energy consumption, and is the world's fastest growing fossil fuel, increasing by 1:4% per year. Despite strong growth in LNG trade, pipeline transport is projected to continue to account for 48% of the interregional natural gas flows in 2040 as pipeline infrastructure is further developed (EIA, 2017).
An important tool in the monitoring and planning of gas transport in pipelines is fluid dynamics-based numerical pipeline models, which are used to detect leaks, monitor pressures and temperatures, estimate transport times, etc. The modelled gas temperature can have a significant impact on the density and velocity of the gas, which again affects transport time estimates (Chaczykowski et al., in press 2018). Although considerable efforts have been made on improving the temperature modelling, there are still some discrepancies between measured and modelled gas temperatures (Helgaker et al., 2014; Sund, Oosterkamp, and Hope, 2015).
The starting point when developing numerical gas models are the governing equations of viscous compressible flows. The energy equation is typically written either in terms of internal energy or in terms of enthalpy, and the two forms have both been used extensively in literature, see for example (Abbaspour and Chapman, 2008; Thorley and Tiley, 1987; Deen and Reintsema, 1983) (enthalpy) and (Helgaker et al., 2014; Chaczykowski, 2010; Winterbone and Pearson, 1992) (internal energy). Although the two forms are interchangeable in theory, there might be differences in practice that are not a priori evident. One such difference is that the internal energy form depend on the isochoric heat capacity (cv), while the enthalpy form depend on the isobaric heat capacity (cp).
