A Novel Methodology to Estimate the Critical Damping Factor in Fluid-Structure Interaction: Application to Crossflow through Downhole Control Lines

Faced with increasingly challenging production scenarios, the oil industry has been forced to expand operational limits to higher flow rates, temperatures, and pressures. From a structural integrity point of view, this scenario leads to a reduction in the life expectancy of current equipment, such as hydraulic, electrical, or fiber-optic control lines, which are encapsulated by small diameter metallic tubes and placed into the well along the external wall of the production/injection tubing string. These lines are subjected to high external flow rates of the produced/injected fluid near the inlet/outlet of the downhole flow control valves installed in the production intervals of the well. A key point for evaluating fatigue life is an accurate stress evaluation. To achieve that, it is necessary to determine the load and critical damping factor (⁠$ζ$⁠) required for the structural vibration analysis of control lines subjected to transversal flow. The main purpose of this work is to present a methodology to improve the estimation of the $ζ$ by considering a simplified geometry that incorporates the main aspects as the desired configuration. The methodology consists of three steps. The first two steps involve obtaining vibration frequencies and establishing a relationship between displacement amplitudes and force through a fluid-structure interaction (FSI) simulation of a simpler geometry. Then, an optimization strategy is used to determine the critical damping based on finite element analysis (FEA) having an objective function with a $ζ$ as the optimization variable. Here, the selected simplified geometry was a turbulent crossflow over an elastic cylinder. The turbulence was modeled via detached delayed eddy simulation (DDES) for Reynolds number 10,000. The structure was modeled as linear elastic. The coupling between fluid and solid domains was bidirectional. Three open-source codes were used based on the finite element numerical method for the fluid and solid domains and one for the coupling between them. The results obtained show that the present methodology can be used to predict $ζ$ in a deterministic way (⁠$ζ=0.41%$⁠), and it is in good agreement with literature for a similar problem (⁠$ζ=0.5%$⁠).