Two-way fluid–structure interaction for longitudinal vibration of a loaded elastic rod within a multiphase fluid flow

This paper presents a novel approach for simulating the interaction of long elastic rod strings and the corresponding fluid flow around in sucker rod pump systems. The governing equations of transient multiphase fluid flow are coupled with those of the rod string deformation to improve the numerical analysis of sucker rod pump behavior. For the first time, the transient water-oil-gas multiphase fluid flow containing dissolved gas is related to the rod cyclic loads by the proposed numerical simulation. The derived mathematical model incorporates the dynamics of the rod string and the multiphase fluid flow. Downhole loading of the rod is applied based on the transient pressures of the moving gas–liquid flow in the annular space and the barrel under the plunger, considering different modes of pump operation. A two-way algorithm, for fluid and solid zones, is developed to enhance the performance of the current simulation, and to reduce the complexity of solving process. Several test cases have been analyzed using the proposed simulation method. The obtained results show a good agreement when they are compared and validated with the available numerical and experimental results.