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A common approach to reduce the Euler equations' complexity for the simulation and optimization of gas networks is to neglect small terms that contribute little to the overall equations.
An example is the inertia term of the momentum equation since it is said to be of negligible size under real-world operating conditions.
However, this justification has always only been based on experience or single sets of artificial data points.
This study closes this gap by presenting a large-scale empirical evaluation of the absolute and relative size of the inertia term when operating a real-world gas network.
Our data consists of three years of fine-granular state data of one of the largest gas networks in Europe, featuring over 6,000 pipes with a total length of over 10,000 km.
We found that there are only 120 events in which a subnetwork consisting of multiple pipes has an inertia term of high significance for more than three minutes.
On average, such an event occurs less often than once every ten days.
Therefore, we conclude that the inertia term is indeed negligible for real-world transient gas network control problems.
Due to the current and foreseeable shifts in energy production, the trading and transport operations of gas will become more dynamic, volatile, and hence also less predictable.
Therefore, computer-aided support in terms of rapid simulation and control optimization will further broaden its importance for gas network dispatching.
In this paper, we aim to contribute and openly publish two new mathematical models for regulators, also referred to as control valves, which together with compressors make up the most complex and involved types of active elements in gas network infrastructures.
They provide full direct control over gas networks but are in turn controlled via target values, also known as set-point values, themselves.
Our models incorporate up to six dynamical target values to define desired transient states for the elements' local vicinity within the network.
That is, each pair of every two target values defines a bounding box for the inlet pressure, outlet pressure as well as the passing mass flow of gas.
In the proposed models, those target values are prioritized differently and are constantly in competition with each other, which can only be resolved dynamically at run-time of either a simulation or optimization process.
Besides careful derivation, we compare simulation and optimization results with predictions of the commercial simulation tool SIMONE.