Brazilian subsea exploration is increasing specially after the post salt petroleum field discovery. Several challenges have been imposed for the production of those fields. In this scenery, the transport of oil and gas from the production field to the continent is a problem, especially when the fields are located at a great distance from the coast. A possible solution could be the use of subsea pipeline systems, for the transportation of the fluids produced from the petroleum wells. For the pipeline system design it is highly recommended the evaluation of the transient flow, considering the water hammer phenomenon. The definition for this phenomenon is given by the pressure variation due to operation singularities in the pipe system. The disruption in the flow originated by the operation of valves or failure of a pump can be listed as some of the main causes of the water hammer. The basic equations to model the water hammer in fluid mechanics comes from two partial differential equations, the equation of continuity and momentum. The solution of those equations can be obtained by different numerical methods. In this context, this work seeks to contrast results obtained by finite difference method (FDM), the method of characteristics (MOC) and finite elements method (FEM) solutions for the water hammer problem. Those numerical methods were implemented and used to solve a simple system, which are composed of an infinite reservoir, a pipeline and a valve. In this case the valve is closed, originating the water hammer phenomenon. Although it can be considered a simple problem, it allows the evaluation of those numerical methods. Performance, convergence and accuracy were evaluated in order to support the choice of the best numerical method for the development of a numerical simulator used in complex and greater pipeline system design.

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