Comparison of Simple Probabilistic Approach with Deterministic Model for Predicting Surge and Leakage in Water Pipelines

Pipe flows are highly nonlinear and the related structural failure and leakage thereafter may arise from fluid pressures of various nature. Burst leakage may result from high local pressure heads causing circumferential (hoop) stress or longitudinal (axial) stress being larger than the material yield stress. Boiling or cavitation effect in regions of fluid pressure drops below its vapor pressure, which in turn develop as air bubbles and get transported through the pipeline may also cause burst at remote locations. In a multiple pipeline network, such information may be available as an overlapping set of noisy signals. This calls for advanced signal processing, and a reduction in complexity of deducing the signals to be processed would be favorable in a computational environment. Hence as a preliminary step, we investigate the extent to which a simple probabilistic model would better a purely deterministic hydraulic model when employed for the same. We initially developed a purely deterministic hydraulic model with method of characteristics to simulate burst failure and leakage in a pipeline, and further extended it with a simple probabilistic model coupledinto the scheme. A detailed investigation of the influence of successive over relaxation (SOR) on the simulated transients revealed that the use of variable local relaxation techniques could alleviate false numerical oscillations at the interior nodes. We also observed that the simple probabilistic model was only marginally different in its prediction of the transients when compared with the fully deterministic hydraulic model.