Development of a conservative scheme for inverse transient analysis in water and gas pipelines

Abstract

The Inverse Transient Method (ITM) uses a forward analysis solver for analysing transient fluid flow and inverse analysis for determining the unknown values (leakage, blockage, and pipeline roughness) through the minimisation of the difference between observed data and simulation results by the numerical model. This paper presents a conservative solution scheme approach to solving the forward problem for analysing fast transients of both compressible and incompressible fluid flows. The programs will be used for the forward analysis part of a leakage and blockage detection model. The mathematical model for simulating unsteady flows is represented by non-linear conservative hyperbolic equations in fluid pipeline systems. A traditional transient analysis model of single-phase fluid in pipelines uses the Method of Characteristics (MOC) because of numerical simplicity of the explicit formulation and fast computational time. However, the numerical simplification of neglecting the convective acceleration terms in the basic equations may result in loss of accuracy of the simulation results when analysing compressible flows. The developed program uses the conservative form of partial differential equations and these equations are computed by an implicit finite difference method (FDM) using the Preissmann scheme [Chaudry, 1993]. The program can also simulate the variation of pipeline area and fluid density in fast transient events. The addition of an area state equation and density state equation allows the program to be easily applied to compressible fluids. Numerical and laboratory experiments have been carried out for the verification of the developed program.