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Transportation of natural gas through high pressure offshore transmission pipelines has been simulated by numeri–cally solving the governing equations for one-dimensional compressible viscous heat conducting flow. For the implicit method the energy equation is solved one time step behind the continuity and momentum equation. Compared to solving all three equations simultaneously, this will decrease the computational time for each time step during the simulation. Under typical operating conditions for export pipelines in the North Sea this does not affect the results in any major way, indicating that the changes in temperature are sufficiently slow to allow the energy equation to be solved separately from the continuity and momentum equation.
Helgaker et al. (Sun,) studied this question.