  Given the critical role played by natural gas in providing electricity, heat,
and other essential services, better models are needed to understand the
dynamics of natural gas networks during extreme events. This paper aims at
establishing appropriate and fast simulation models to capture the slow
dynamics of linepack depletion for ideal isothermal natural gas pipeline
networks. Instead of solving partial differential equations (PDE) on a large
scale, three alternative implicit ordinary differential equation (ODE)
simulation techniques are derived and discussed. The first one is commonly used
in the literature with a slack node assumption. We show that the system of
equations associated with this model is degenerate when flux injections are
controlled (i.e. specified) at all nodes. To recover regularity under such a
condition, two novel implicit ODE models are proposed, both with different
techniques for specifying boundary conditions. They are easy to derive and
efficient to simulate with standard ODE solvers. More importantly, they present
useful frameworks for analyzing how networks respond to system-wide mass flux
imbalances. These techniques offer different alternatives for simulating system
dynamics based on how sources and loads are chosen to be modeled, and they are
all proven to be regular (non-degenerate) in tree-structured networks. These
proposed techniques are all tested on the 20-node Belgium network. The
simulation results show that the conventional model with the slack node
assumption cannot effectively capture linepack depletion under long term
system-wide mass flux imbalance, while the proposed models can characterize the
network behavior until the linepack is completely depleted.
