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

Document Type : Research Article



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.