Simultaneous Estimation of Flow Rate and Location of Leakage in Natural Gas Pipeline Using Levenberg-Marquardt Method

In this paper، mass flow rate and location of leakage in natural gas pipeline has been estimated simultaneously using inverse analysis. For doing so، at first natural gas transient flow in pipeline has been simulated numerically; this simulation is named direct problem. In the direct problem، it is assumed that the mass flow rate and location of leakage is definite and the governing equations are inhomogeneous well-known Euler equations. In these equations، the leakage effect has been considered as a source term. Steger–Warming flux splitting method has been used for numerical analysis of these equations. Then the location and mass flow rate of gas leakage of pipeline have been estimated simultaneously using Levenberg-Marquardt method for parameter estimation. This method is an iterative algorithm and based on minimizing the sum of the squares of the errors which are difference between pressures computed by the direct problem and pressures measured by pressure gauges. The results of the direct problem have good agreement with Mac–Cormack method and characteristics method of specified time intervals. The results of the inverse analysis demonstrate that Levenberg-Marquardt algorithm is stable and efficient enough to estimate simultaneously the mass flow rate and location of leakage in natural gas pipeline.