Detecting optimal leak locations using homotopy analysis method for isothermal hydrogen-natural gas mixture in an inclined pipeline

The aim of this article is to use the Homotopy Analysis Method (HAM) to pinpoint the optimal location of leakage in an inclined pipeline containing hydrogen-natural gas mixture by obtaining quick and accurate analytical solutions for nonlinear transportation equations. The homotopy analysis method utilizes a simple and powerful technique to adjust and control the convergence region of the infinite series solution using auxiliary parameters. The auxiliary parameters provide a convenient way of controlling the convergent region of series solutions. Numerical solutions obtained by HAM indicate that the approach is highly accurate, computationally very attractive and easy to implement. The solutions obtained with HAM have been shown to be in good agreement with those obtained using the method of characteristics (MOC) and the reduced order modelling (ROM) technique