Simplified stochastic modelling of the force on a pipe bend due to two-phase slug flow

Slug flow, a flow pattern with alternating aerated liquid pockets (slugs) and large gas bubbles, is a commonly observed flow pattern in oil and gas pipelines. Due to its unsteady character, the force on a pipe bend is fluctuating which results in unacceptable motions when the piping is insufficiently supported. To investigate the risk of fatigue failure of the system, finite-element models are used to predict the dynamic stresses required to estimate the fatigue life of the system. The excitation force of the slug flow is the essential input required for accurate fatigue damage predictions. A new, simplified model of slug forces on a bend is proposed. The model is calculating the slug force by solving the momentum balance over the pipe bend using slug flow properties as liquid holdup and phase velocities. Average properties predicted by a unit slug model cannot predict the stochastic force variations caused by the slug flow. The new approach introduces the stochastic character of slug flow in the force calculations via a log-normal slug length distribution. A Lagrangian slug tracking method is used to solve the governing equations. The modelled liquid holdup, pressure and predicted forces are compared with available measurements and Computational Fluid Dynamics calculations. The measurements were done under atmospheric conditions and the fluids used were air and water. Whether these measurements are representative for high-pressure oil and gas slug flow is unknown. By using a mechanistic approach where the main equations are based on physical laws instead of fitted measured data, the model is applicable for different fluids and operational conditions. To validate the model for oil and gas flows, the results are compared with Computational Fluid Dynamics calculations done with high gas density and typical oil viscosity.