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The hydrocarbon industry has expressed interest in developing vibration based energy harvesting systems that can be deployed downhole and supplement or replace existing power sources. The energy output of such harvesters is highly dependent on the level of damping in the supporting structure which, in this case, would drive the systems vibrational input. A first step towards optimizing an energy harvester configuration is then to understand how key variables influence system damping. To this end an investigation was undertaken to identify how changing system boundary conditions effect damping in a fluid conveying pipe confined by a viscous fluid (i.e. a producing hydrocarbon well). The key variables investigated included the rotational boundary springs, the velocity of the conveyed fluid, and the viscosity of the annulus fluid. The system was modeled using Euler-Bernoulli beam theory and included a hydrodynamic forcing function to capture the effects of the viscous annulus fluid. The natural frequencies of the system were solved in the frequency domain with the system damping subsequently calculated. Lower damping ratios were observed: in stiffer systems, for lower conveyed fluid velocities, and for lower annulus fluid viscosities. A numeric example is provided to illustrate the interaction between the three variables of interest. These results are of direct interest to researchers and engineers developing vibrational energy harvesting systems for downhole deployment. Approved for publication, LAUR-16-21227.

The impact of boundary conditions and fluid velocity on damping for a fluid conveying pipe in a viscous fluid