In the current paper, a high-fidelity model of a riser is proposed based on the absolute nodal coordinate formulation (ANCF) method in the arbitrary Lagrangian-Eulerian description (ALE). Unlike other investigations, slug flow here is assumed as a one-dimensional medium – a parcel of material considered as an internal fluid pattern mixed with oil, gas and water moving in the partial riser, which contributes to the unstable fluid loading on the riser, causing the associated riser's dynamic response and influencing the structural stability. In this model, the moving node and variable-length element are introduced to make the internal fluid moving along the cable and the speed of the length of the variable-length element equal to the slug flow's rate. In the current paper, the Euler-beam model is used to model the riser. The equation of motion of the system subjected to the inertial and external fluids is derived based on the generalized D'Alembert principle. The backward Euler formulation is applied to discretize the differential equation in the time domain, leading to differential-algebraic equations. First, the proposed model is validated without considering the inertial and external fluids, where the free-falling pendulum case is conducted. The comparison results show the implementation of the proposed method is very well. Second, the upward slug-flow effects with constant average density affecting the riser dynamics are intensely studied.


The flexible riser plays an essential role in the oil and gas exploration and production operations in deep water, which is used to connect a subsea oil wellhead to the floating or fixed oil platform. The internal fluid transferred inside the riser is a mixture of oil, gas, and water, which means each phase's density is different, and the complex mixtures may cause a flow pattern calling slug-flow. The huge ratio of the length to diameter means the riser can be seen as a flexible beam suffering from the large deformation with internal mass-flowing medium transferred. Due to the characteristics mentioned above and since the riser is exposed to the outside environment's different conditions, it is a highly complex task to model the riser with internal slug-flow.

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