Shifts in the Fundamental Frequency of a Fluid Conveying Pipe Immersed in a Viscous Fluid for use in the Optimization of an Energy Harvesting System to be Deployed in a Producing Hydrocarbon Well

摘要

Novel methods for harvesting energy in down hole applications are desired. Specifically, it is hoped that sufficient power can be generated near a hydrocarbon reservoir to operate commercially available well monitoring equipment. Vibration based harvesters are the most likely systems to be developed. The efficiency of such harvesters is highly dependent on the natural frequency of the structural system. To optimize the harvester design, the dynamic properties of the down hole system must be characterized. This paper presents the results of an analytical frequency study undertaken to identify the role axial force effects, annulus fluid geometry, and annulus fluid properties have on the first natural frequency of a production string as the conveyed fluid velocity was varied. The system was modeled using an Euler-Bernoulli formulation and includes a hydrodynamic forcing function to account for annulus fluid effects. The problem was solved in the frequency domain using the spectral element method, which conveniently provides natural frequency information. The results of the study are in-line with previously published studies on analogous systems. It was found that the well annulus geometry, annulus fluid density, and annulus fluid viscosity have a strong role in determining the behavior of the system. Additionally, the axial force, added mass, and viscous effects were found to shift the natural frequency of the system while only axial force and viscous effects cause a shift in the fluid velocity at which bifurcation occurs. These findings, along with the method outlined in this paper, provide a useful tool in the characterization of hydrocarbon producing wells which is a first step towards developing an energy harvesting system. Although the problem of determining the dynamics of a fluid conveying pipe immersed in a viscous fluid has been approached using a shell formulation in the past, to the authors knowledge this is the first time the problem has been solved with a beam formulation. Approved for publication, LA-UR-15-21089. Copyright for this paper have been transferred to SPE.