Leak Detection in Pipelines Based on Inverse Transient Modeling and Mixed Integer Nonlinear Programming

For leak detection in a pipeline, transient flows are generated by closing the end control valve. Then the pressure fluctuations are sampled only at the valve location after its full closure. To eliminate undesirable noisy effects and other uncertainties associated with numerical modeling of the valve, a new structure of the method of characteristics (MOC) has been developed independent of the valve type, the method and the duration of closure with no need to impose initial conditions. Using the pressure samples, transient flow through the pipe can be analyzed backward from the downstream end valve to the upstream reservoir. In this condition, the calculated reservoir heads will be functions of leaks parameters containing leaks area as real parameters and the number and location of leaks as integer parameters. In order to find leaks parameters in a pipe an objective function is defined as the sum of squares of differences of the observed and calculated reservoir heads. The Mixed Integer Non Linear Programming (MINLP) is used to minimize nonlinear objective function and determine the integer and real parameters of the leak problem. An optimization method based on genetic algorithm has been developed for this problem. Several examples are solved to show the ability of the presented method. The method was found to be practical, reliable and easy to be used.