Most pipeline control systems use some sort of autonomous leak detection system as a safety feature. Among the pipeline leak detection techniques, state observers stand out as the most sophisticated and promising technique. But its use has been inhibited as the dynamic models employed so far are large and estimating the states of nonlinear systems is not trivial.
Pipeline pressure and flow dynamics have been modelled in the literature by means of different numerical solutions to a pair of first order partial differential equations that express mass and linear momentum conservation. The numerical solution requires discretizing the pipeline length in a finite number of segments, resulting in a system of equations with size of twice the number of segments. Although there is nothing wrong with this approach, a smaller system is more convenient if one is concerned exclusively with pressure and flow at the pipeline entrance and exit sections. In this paper, energetic modelling principles are employed to obtain a pair of first order ordinary differential equations representing the dynamics of long liquid pipelines.
A recently introduced nonlinear observer enables straightforward use of linear, constant-gain observers with Lipschitz nonlinear dynamics. This observer gives the designer freedom to choose the observer eigenvalues and enables mathematically proven asymptotic stability with low gains. In this paper this observer, using a second-order model to represent the pipeline dynamics, is used as a pipeline leak detection algorithm.
Initially the observer was employed directly as a leak detection algorithm, the leak being indicated by a non-transient difference between the measured and the estimated flows. Afterwards the leak was modeled as a disturbance flow and a disturbance observer was designed. Both algorithms were verified by means of computer simulations. It was found that the two methodologies are capable of detecting and estimating very small leaks, but the disturbance observer seems capable of indicating small holes further way from the measuring points.