Method for determination of parameters of leaks in pipelines based on hydrodynamic models

It is known that on the basis of the pipeline non-stationary hydrodynamic model after identification of parameters included in it, it is possible to adequately reproduce the full-scale hydraulic characteristics of transported medium flow by resolving the primal problem of hydraulics, in particular, the primal problem of identifying leakage parameters. The numerical solution of the inverse problem, in contrast to the analytical solution, is usually reduced to a multiple solution of the primal problem. In the present work, the hydrodynamic mathematical model of a pipeline with two parameters that have been identified and fluid withdrawal in the set section is confined to differential equations of evolutionary type for medium cross-section pressure and mass flow. Based on the built partial analytical solutions of these equations, dependences have been obtained for calculation of pressure values in the oil pipeline operated in stationary mode with existing liquid withdrawal (leakage). Results of application of analytical solutions to the method of sensitivity functions in the inverse problem of identifying leakage parameters have been reviewed. Exact analytical solution (in implicit form) of the inverse problem has been obtained to make it possible to relate the location of the leak to readings of pressure sensors, to the pipeline and the transported fluid parameters.