New Method to Detect Leakage in Long-distance Pipelines

Adopting nonlinear integral-differential equations converted from equation of continuity, momentum equation and state equation describe leakage situation in pressure testing of long-distance gas pipeline.Based on linearization technique, nonlinear integral-differential equations are simplified into linear heat conduction equation.According to the characteristics of gas running during pressure testing stage, linear integral-differential equation model that describes individual point leakage of long-distance gas pipeline during pressure testing stage is established.Identification on leakage level at leakage location Is transformed to the inverse problems of partial differential equation on boundary condition inversion of differential equation, and two supplementary conditions to determine leaking location, leaking level coefficient and leakage attenuation coefficient are given according to the characteristics of leakage pressure testing.A mathematical expression to calculate leaking location, leaking level coefficient and leakage attenuation coefficient is derived by means of Laplace integrate transformation.On that base, numerical calculation form is set up with "contraction mapping theory", and a code procedure is formulated. Calculation results from an actual case show that calculation values are perfectly fitted to actual situation, which can meet the needs of leakage detection for gas transmission and distribution networks during pressure testing stage.