MATHEMATICAL MODELING OF LEAK LOCATION IN PIPELINES

Abstract

Oil and gas pipelines are of great importance to chemical and petrochemicals industries. They are used to transport gas and natural crude oil from gas/oil fields and oil/gas terminals to the user points and the chemical products to their points of use. Pipelines rupture may be due to corrosion sudden change in pressure, causing not only product loss, but also serious environmental damage if the leak is not quickly detected to and the pumps/compressor are not stopped and the pipeline is not repaired. The occurrence of a leak in pipelines causes sudden change in pressure which is followed by a partial recovery to its original value. The pressure wave travels upstream and downstream through the pipeline. Leak detection, hydraulic transient wave propagation velocity and leak location are the basic problems to deal with. In this study, the numerical modelling of high pressure transient flow of natural gas mixtures in rigid pipeline is carried out. The transient regime is created by the rapid closure of downstream shut off valve. The pressure waves are used need to locate the leak in the pipeline. The numerical simulation is performed by solving the mass and momentum conservation equations. These equations form the two coupled non-linear, hyperbolic partial differential equations with pressure dependent coefficients. These equations are solved mathematically by the method of characteristics. The fluid pressure and velocity are considered as two main dependent variables. For leak location there is a mathematical formulation developed and solved by the method of characteristics at specified time intervals. The boundary conditions were imposed by introducing a linear closure law for the upstream and the downstream valves. The III computed results describe the influence of the leak on pressure-time history and leak at different sections of pipe and check the stability and accuracy of model by Courant-Friedlich-Lewy (CFL) condition.