Slug flow induces vibration in pipelines, which may, in some cases, result in fatigue failure. This can result from dynamic stresses, induced by the deflection and bending moment in the pipe span, growing to levels above the endurance limits of the pipeline material. As such, it is of paramount importance to understand and quantify the size of the pipeline response to slug flow under given speed and damping conditions. This paper utilizes the results of an optimization procedure to devise a surrogate closed-form model, which can be employed to calculate the maximum values of the pipeline loadings at given values of speed and damping parameters. The surrogate model is intended to replace the computationally costly numerical procedure needed for the analysis. The maximum values of the lateral deflection and bending moment, along with their locations, have been calculated using the optimization method of stochastic perturbation and successive approximations ( SPSA). The accuracy of the proposed surrogate model will be validated numerically, and the model will be subsequently used in a numerical example to demonstrate its applicability in industrial situations. An accompanying spreadsheet with this worked example is also given.
Flow of gas in pipelines is subject to thermodynamic conditions which produces twophase bulks (i.e., slugs) within the axial pipeline flow. These moving slugs apply a moving load on the free spanning pipe sections, which consequently undergo variable bending stresses, and flexural deflections. Both the maximum pipeline stress and deflection due to the slug flow loads need to be understood in the design of pipeline spans. However, calculation of a moving mass on a free spanning pipeline is not trivial and the required mathematical model is burdensome for general pipeline design engineering. The work in this paper is intended to investigate the conditions under which simplified analysis would produce a safe pipeline design which can be used by practicing pipeline design engineers. The simulated finite element models presented here prove that replacing the moving mass of the slug by a moving force will produce adequately accurate results at low speeds where the mass of the slug is much smaller than the mass of the pipe section. This result is significant, as the assumption of point load simplifies the analysis to a considerable extent. Since most applications fall within the speed and mass ratio which justify employing this simplified analysis, the work presented here offers a powerful design tool to estimate fatigue stresses and lateral deflections without the need of expensive timeconsuming inputs from specialized practitioners.