A frequency study of a clamped-clamped pipe immersed in a viscous fluid conveying internal steady flow for use in energy harvester development as applied to hydrocarbon production wells

2016

SPIE Proceedings

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Hydrocarbon well operators deploy downhole reservoir monitoring equipment in order to optimize the rate at which hydrocarbons are extracted. Alternative power sources are sought that could be deployed in these harsh environments to replace or supplement standard power sources currently in use. To this end, a three phase proof-of-concept study was performed to gauge the feasibility of such a device. In the first phase a parametric study was performed to understand how high uncertainty variables affect the natural frequency of a producing hydrocarbon well. In a follow up study, the relationship between boundary conditions and system damping was investigated. In the second phase a structural housing was designed to satisfy American Petroleum Institute load cases. Using finite element models and standard tube/casing geometries, design pressures were iterated until a permissible housing design was achieved. This preliminary design provided estimates of the radial width and volume in which energy harvesting and storage elements may be situated. In the last phase a software program was developed to estimate the energy that might be harvested from user specified harvester configurations. The program is dependent on user input production tube accelerations; this permits well operators to use well-specific vibrational data as inputs to generate well-specific energy output estimates. Results indicate that a downhole energy harvesting tool is structurally feasible under reasonable operating conditions but no conclusions can be made as to the sufficiency of generated power as no in-situ acceleration time histories are available. Future work is discussed. Approved for publication, LA-UR-16-21193.

Section: Well Characterizationmentioning

confidence: 99%

“…In a 2015 study, Kjolsing and Todd [1] performed a parametric study to demonstrate how axial force, conveyed fluid velocity, and annulus fluid affects the first natural frequency of a fixed-fixed fluid-conveying pipe surrounded by a coaxial viscous fluid. The linearized equation of motion was written as [5] …”

Section: Natural Frequencymentioning

confidence: 99%

Gauging the feasibility of a downhole energy harvesting system through a proof-of-concept study

2016

SPIE Proceedings

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“…Using Euler-Bernoulli theory and assuming steady plug-flow, the linearized equation of motion for a pipe conveying fluid can be written as [1], [10] * eric.kjolsing@gmail.com The hydrodynamic function (𝛤) is defined in Appendix B and has been thoroughly investigated by others [11]- [16] . It has been shown that the real part of the hydrodynamic function contributes added mass to the system while the imaginary part contributes viscous drag [17] .…”

Section: Numeric Modelmentioning

confidence: 99%

“…In a previous study, the authors characterized the first natural frequency of a braced hydrocarbon well. [1] In the current study, the authors seek to understand how changing the rotational boundary conditions of a braced well impacts the system damping as the conveyed fluid velocity is increased. The three independent variables investigated are the rotational stiffness of the boundary springs, the velocity of the conveyed fluid, and the viscosity of the annulus fluid (the sole source of damping in the current study).…”

Section: Introductionmentioning

confidence: 99%

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

2016

SPIE Proceedings

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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, LA-UR-16-21227.

“…The hydrocarbon industry has a stated interest in developing energy harvesting and storage systems for downhole deployment to supplement currently utilized power sources. Several investigations were previously performed to forward this objective [1]- [4]. Since long deployment cycles are desirable, the selection of an optimal harvester configuration must account for long-term effects, specifically the accumulation of damage.…”

Section: Introductionmentioning

confidence: 99%

The effects of damage accumulation in optimizing a piezoelectric energy harvester configuration

Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2018

2018

Bimorph piezoelectric elements are often used to harvest energy for low-power structural health monitoring systems. When these piezoelectric elements are deployed for extended periods of time and operate under near-resonant conditions, the resulting high amplitude cycling can lead to degradation of the piezoelectric element, resulting in a shift in the design fundamental frequency. For scenarios in which the piezoelectric harvester is subject to slowly-varying time-dependent frequency inputs, the natural frequency shift due to degradation may cause the piezoelectric harvester to detune from resonance, subsequently affecting the harvester's power output. The current study seeks to understand how the accumulation of damage shifts the optimal tip mass and resistive load in a bimorph piezoelectric energy harvester. A cantilever piezoelectric element is modeled utilizing coupled electromechanical equations in a distributed system. The piezoelectric is subject to ground accelerations; the resulting power output is recorded for a range of tip masses and resistive loads. A rainflow analysis is then performed to calculate the piezoelectric element's tip displacement amplitude and the corresponding cycle count. A damage accumulation model based on a weighted form of Miner's rule is then used to degrade the harvester's flexural rigidity, piezoelectric capacitance, and piezoelectric strain constant. The piezoelectric is again loaded and the process repeated. The resulting power output contours reveal how the optimal realization of tip mass and resistive load changes as damage accumulates in the piezoelectric element. Apparent trends in the power output contours are explained. Approved for publication, LA-UR-18-20075.