Large-scale empirical study on the momentum equation's inertia term

TL;DR

This large-scale empirical study evaluates the significance of the inertia term in the momentum equation for real-world gas networks, confirming its negligible impact in typical operational scenarios.

Contribution

It provides the first comprehensive empirical analysis of the inertia term's importance using three years of real-world gas network data, filling a gap in prior assumptions.

Findings

Infrequent significant inertia events occur less than once every ten days.

The inertia term is negligible in most real-world gas network operations.

Empirical evidence supports simplifying assumptions in gas network simulations.

Abstract

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.