  Due to their slow gas flow dynamics, natural gas pipelines function as
short-term storage, the so-called \textit{linepack}. By efficiently utilizing
linepack, the natural gas system can provide flexibility to the power system
through the flexible operation of gas-fired power plants. This requires
accurately representing the gas flow physics governed by partial differential
equations. Although several modeling and solution choices have been proposed in
the literature, their impact on the flexibility provision of gas networks to
power systems has not been thoroughly analyzed and compared. This paper bridges
this gap by first developing a unified framework. We harmonize existing
approaches and demonstrate their derivation from and application to the partial
differential equations. Secondly, based on the proposed framework, we
numerically analyze the implications of various modeling and solution choices
on the flexibility provision from gas networks to power systems. One key
conclusion is that relaxation-based approaches allow charging and discharging
the linepack at physically infeasible high rates, ultimately overestimating the
flexibility.
