Pressure transients in a ruptured gas pipeline with friction and thermal effects included
A theoretical model has been developed which can simulate a linebreak occurring in a gas pipeline. By assuming one-dimensional homogeneous gas flow and neglecting minor losses and changes in cross-sectional area of the pipe, three simultaneous non-linear partial differential equations were derived from first principles which mathematically model pressure transients in a non-perfect gas. A constant value steady-flow friction factor was used to calculate the frictional losses which was considered to be a reasonable approach since it would not be possible to account for all the variations in friction. The heat transfer into the pipe was accounted for using a constant value Stanton Number approach which again was an acceptable approximation considering the comparatively small effect that heat transfer has on the pressure transients. The equations were converted to ordinary differential equations using the Method of Characteristics and these were then solved numerically using a Taylor expansion. A novel feature of this project was the incorporation of a reduced grid size in the vicinity of the break allowing closer monitoring of the expansion waves in this area. Also included was a means of modelling flow reversal in the pipe which enabled situations with a non-zero initial flow rate to be simulated. A computer code solving the mathematical model was written in Fortran 77 for use on a Gould PN9005 mainframe computer. Both tabular and graphical output were produced which could then be compared with available experimental data. The experimental data that was selected for validation of the theoretical model included shock tube test results and some full size tests. Reasonable agreement was obtained between the theoretical and experimental results and any possible error sources were investigated.
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