A new model to detect leaks optimally in liquid pipelines is presented. The model uses the concept based on the Liapunov stability criteria to evolve a criterion for pipeline leak detection. A flow model was derived for a typical pipeline flow system, and the inclusion of leak factor k(L) in the flow model gives an indication of the relative degree of deviation from equilibrium or no leak situation. The numerical solution by the implicit finite difference scheme was used to solve the transient second-order partial differential equations describing the flow process. A set of parametric velocity and pressure profiles were generated and validated using industry data. A stability matrix, useful for determining the eigenvalues (lambda's), evolves from the deviation model of velocity and pressure. A leak is detected whenever any of the eigenvalues is less than -1, whereas a surge in the pipeline is detected whenever any of the eigenvalues is greater than 1. The simulation profiles of eigenvalues of a crude oil transporting pipeline segment, of a pipeline network of an operating oil company in the Niger Delta region of Nigeria, show that pressure deviations are more sensitive parameter for leak detection than volume deviations. Volume deviations appear to be good indicators for larger leak systems. Single leak situation as well as double leak situations in a pipeline system were analyzed and discussed. (C) 2003 Elsevier B.V. All rights reserved.
