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.
KEYWORDS: Energy harvesting, Systems modeling, Error analysis, Lanthanum, Motion models, Fluid dynamics, Smart structures, System integration, Current controlled current source
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.
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.
Hydrocarbon extraction companies are seeking novel methods to generate and store power in down hole applications. Specifically, a robust energy harvesting system, capable of withstanding the harsh environmental and operational demands at the bottom of production wells, is desired to power commercially available well monitoring devices. The wide variety of well configurations makes this a challenging problem. Although some variables relating to the production tube are well defined by American Petroleum Institute standards, other variables may vary widely and be time dependent, such as annulus fluid properties. A first order task, then, is to characterize and understand the dynamics of a well through a study of changes in natural frequency over the broad range of inputs possessing moderate to high uncertainty.
This paper presents the results of an analytical frequency study which illustrates the effect of a select set of variables on the first natural frequency of a producing well. Specifically, axial force effects, fluid flow effects, and hydrodynamic effects, by means of a hydrodynamic function, are investigated. Due to the nature of the hydrodynamic function, the model is derived in the frequency domain and solved using the spectral element method.
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