When a long gas pipeline is severed, gas escapes through a rarefaction wave that leads away from the break at sonic velocity. Immediately after rupture, the classical inviscid solution of rarefaction holds in which change proceeds evenly across the wave and the discharge is choked. After traveling a relatively short distance (a few hundred diameters) however, friction takes hold and reshapes the inviscid profiles so that the principal changes occur near the outlet. The practical consequences of friction are continual reduction of discharge rate and smoothing of the wavefront. Until the rarefaction reaches a distant boundary, depressurization is closely approximated by the similarity solution of a diffusion equation for density supplemented by evanescent boundary layers at the outlet and leading edge. The similarity solution yields a simple formula for the declining discharge rate with time and reveals that Excess Flow Valves, designed to isolate the line automatically, will not close if placed too far apart.


Accidents in which a pipeline is severed are consequential. Large quantities of toxic or flammable material are rapidly discharged to atmosphere, and prompt action must be taken to protect the neighboring population. Understanding discharge dynamics in these cases is essential to assess potential hazards and develop appropriate risk mitigation plans. Dynamics at the leading edge of the depressurization wave that sweeps through the gas within the pipe also matters. Leak detection systems that rely on prompt identification of the rarefaction wavefront at critical locations may siginificantly lower risk posed by pipeline rupture. Local leak detection is often tied to Excess Flow Valves that shut automatically when the flow exceeds a threshold value. These nonlinear equations extend classical inviscid gas dynamics with algebraic friction and heat transfer terms that account for interaction of the gas with pipe walls.

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