Stochastic mechanistic modelling of two-phase slug flow forces on bends in horizontal piping

Slug flow through piping systems may cause severe mechanical vibrations. Finite element models, commonly used to predict dynamic pipe stresses and fatigue, require the slug excitation force as boundary condition. In this paper, a stochastic mechanistic model of the slug force acting on a pipe bend is proposed. The force induced by continuous hydrodynamic two-phase slug flow is modelled by the momentum balance over the bend using slug quantities as liquid holdup and phase velocity. The two-phase flow is described by a train of slug units. Each unit is divided into a film zone with a constant liquid height and a slug zone with aerated liquid. Two-phase flows have a stochastic character, but models based on a fixed slug length cannot predict stochastic force variations. A new approach is introduced that includes the stochastic character of slug flow in the force calculations. A unit slug model is adapted with a log-normal distribution as closure for the slug zone length, resulting in an improved model with stochastic properties. A Lagrangian approach is used to solve the governing equations. Results of the new model are compared with bend force measurements found in the literature. Most of the published measurements were done with air and water under atmospheric conditions. In many field applications, the fluids and operational conditions are different from those used in laboratory experiments. The stochastic mechanistic approach, where the main equations are based on physical laws, increases the models applicability outside the atmospheric air and water conditions used for the validation.