Modeling of gas release following pipeline rupture: Proposing non-dimensional correlation

Conveying natural gas through a pipeline is widely accompanied by accidents in industries. It is important to perform hazard analysis by estimating the amount of released gas at the first step immediately after the happening. The present study proposes a new approach to evaluate the gas release rate and released mass by introducing non-dimensional equations for simulating quasi-one-dimensional transient compressible flow in a ruptured gas pipeline. These equations are derived from Euler equations. The hyperbolic governing equations are solved numerically by the explicit MacCormack's method. The influence of different dimensionless physical parameters on release rate are then investigated; among which relative pressure, relative hole diameter and friction term are the most important parameters. Results show that the release rate has the similar behavior for a wide range of operating pressures from 60 psig (0.4 MPa for distribution pipeline) to 1000 psig (6.9 MPa for transmission pipeline). Since choking condition happens in rupture area, release rate is not a function of pipeline pressure. Therefore, relative hole diameter and friction term are the only effective parameters in this case. By introducing an indicator and its criterion for long pipelines it could be seen that not only is this indicator dependent on geometry (i.e. ratio of length to diameter of pipe), but it also belongs to flow regime (i.e. friction coefficient). Finally, general relations for natural gas release rate in any physical condition are proposed by exploring effective dimensionless parameters on released mass.