Mathematical modeling of the flow in a pipeline with a leak

Pipeline leaks can lead to excessive economical loss as well as posing environmental hazards. Mathematical modeling of the flow in a pipeline with a leak can be used to evaluate the loss caused by a leak and provide a guide for pipeline operation as well as an aid for leak detection. The mathematical expressions describing the flow in a pipeline with a leak have been formulated. A new approach based on the analogy between pipeline and electric circuit has been proposed to solve these equations. In this approach, an equivalent circuit with a certain structure has been used to simulate the leaking pipeline and the flow characteristics of the pipeline end have been treated with approximation. The mathematical model of the pipeline with a leak has been developed with the solution of the equations. The model was verified by using an experimental gas pipeline and a real oil pipeline. The simulated results agreed well with the experimental recordings confirmed the accuracy of the models and the validity and efficiency of the proposed approach. (C) 2012 IMACS. Published by Elsevier B.V. All rights reserved.