**Plenary Lecture
Analytical Methods for Leak and Blockage Detection in Pipelines**

**Professor Andrei Kolyshkin**

Department of Engineering Mathematics

Riga Technical University

Latvia

E-mail: andrejs.koliskins@rbs.lv

**Abstract: **Different methods for leak and blockage detection are proposed in the literature. Solution of a complicated inverse problem is required in order to find the location and magnitude of the leak (or blockage). For a real water distribution system the solution depends on many factors (for example, the age of the system, unknown friction factors and diameters of pipes, the number of segments in the system). In some cases, however, analytical approach to the solution of the problem of leak and blockage detection is possible. The method can be used for a single pipeline. The idea of the method is as follows. A small transient is generated in a pipleline. A linearized equation for unsteady pressure perturbation is solved analytically using the method of the Laplace transform. The solution is obtained in the form of a Fourier series with respect to the longitudinal coordinate. The coefficients of the Fourier series are functions of time. The damping rates of different harmonic components of the solution can be represented as the sum of a steady state friction damping factor and leak-induced (or blockage-induced) damping factor. In general, the leak-induced or blockage-induced damping factors can be calculated as the roots of a transcendental equation. However, for the case of small leak discharge or small blockage resistance parameter a simple formula can be derived which relates the location of the leak (or blockage) with the ratio of two damping rates of leak-induced (or blockage-induced) damping factor. The method is generalized for a finite number of leaks (or blockages). Limitations of the proposed model are discussed.

**Brief Biography of the Speaker:**Andrei Kolyshkin received his undergraduate degree in Applied Mathematics in 1976 at the Riga Technical University. In 1981 he received a Ph.D in differential equations and mathematical physics at the University of St. Petersburg (Russia). Andrei Kolyshkin is currently a full professor at the Department of Engineering Mathematics at the Riga Technical University. His current research interests include investigation of stability problems in fluid mechanics with applications to open-channel flows, transient flows in hydraulic systems and mathematical models for eddy current testing. He is the co-author of three monographs published by Academic Press and CRM. Andrei Kolyshkin has participated in more than 40 international conferences and has published more than 70 papers in refereed journals since 1980. As a visiting professor and visiting researcher he spent a few years at the University of Ottawa and Hong Kong University of Science and Technology.