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In the last several years, there has been a significant growth in research in the field of power harvesting, the process of capturing the energy surrounding a system and converting it into usable electrical energy. This concept has received particular interest in recent years with the ever-increasing production of portable and wireless electronic devices. Many of these devices that are currently in production utilize electrochemical batteries as a power source, which while effective, maintain the drawback of having a finite energy supply, thus requiring periodic replacement. The concept of power harvesting, however, works to solve these issues through electronics that are designed to capture ambient energy surrounding them convert it into usable electronic energy. The use of power harvesting in energy scavenging devices allows for the possible development of devices that are self-powered and do not require their power sources to be replaced. Several models have been developed by Soldano et al [3] and Liao et al [2] that have been proven accurate at predicting the power output of a piezoelectric power harvester in a cantileaver beam configuration. The work in this paper will expand further on the model developed by Liao et al [2], and as its main goal will use a modified form of that model to predict the optimal dimensions for a beam power harvester to achieve the maximum power output possible. The model will be updated b replacing the mode shape function used to approximate the deflection of the beam with the true defletion, which is based on the complex wavenumber that incorporates the complex Young's modulus of the material used. Other changes to account for this replacement will also be presented, along with numerical results of the final model.
ContributorsWinterstein, Joshua (Author) / Liao, Yabin (Thesis director) / Jiang, Hanqing (Committee member) / Chen, Kangping (Committee member) / Barrett, The Honors College (Contributor)
Created2012-05
Description
Pseudo-steady state (PSS) flow is a dominant time-dependent flow regime during constant rate production from a closed reservoir. Recently Chen (2016) has obtained an exact analytical solution for the PSS flow of a fully-penetrated fractured vertical well with finite conductivity in an elliptical drainage area. The availability of this analytical solution shortens the computational time required for such a solution by several orders of magnitude. This paper correlates the PSS flow of a fully-penetrated fractured vertical well in square drainage areas to Chen’s solution for an elliptical drainage area using shape factors. Specifically such a shape factor is established by equating the dimensionless productivity index of the PSS flow in a square domain to that in an elliptical domain of identical area. The shape factor was dependent on the proppant number and fracture penetration ratio. Productivity index data for fractured wells with finite conductivity in square drainage area and no skin from Romero et al. (2003) was compared to Chen’s solution assuming equivalent drainage areas and identical proppant numbers, with the penetration ratio as a parameter. A non-linear multi-variable regression analysis results in a unified shape factor function with a correlation coefficient of 0.80 and a minimized sum of squared error of 36.1. The achieved shape factor allows the analytical solution for PSS flow of fractured well in an elliptical drainage area to be applied to square drainage areas. This generalization of the PSS flow solution is of practical significance in fracture design optimization and production rate decline analysis. Future recommendations including testing the accuracy of the shape factor in predictions of proppant numbers not used in analysis using COMSOL™, and increasing the dataset pool to increase the model accuracy.
ContributorsSharma, Ankush (Author) / Chen, Kangping (Thesis director) / Liao, Yabin (Committee member) / Chemical Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Pseudo-steady state (PSS) flow is a dominant time-dependent flow regime during constant rate production from a closed reservoir. Using Chen's (2016) exact analytical solution for the PSS flow of a fully-penetrated fractured vertical well with finite conductivity in an elliptical drainage area, the computational time required to solve for the PSS constant b_D,PSS is greatly reduced. This constant is the inverse of the productivity index, J_D,PSS, which is often used in modern fracture design optimization. This paper correlates the PSS flow of a fully-penetrated fractured vertical well in triangular drainage areas to Chen's solution for an elliptical drainage area using shape factors. Numerical solutions for the PSS constant are created using COMSOL, which uses a 2D model of the fractured reservoir to output time and pressure data. For equivalent reservoir properties, the numerical data for the triangular reservoir yields a PSS constant that can be directly compared to the PSS constant obtained using Chen's solution. Lack of access to the Subsurface Flow Module of COMSOL greatly limited the number of simulations that could be run, thus more simulations would significantly improve the accuracy and applicability of the triangular shape factor by making it a function of the penetration ratio through nonlinear regression methods.
ContributorsLight, Christopher Ting-Yu (Author) / Chen, Kangping (Thesis director) / Liao, Yabin (Committee member) / Mechanical and Aerospace Engineering Program (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2017-05
Description
Essential to the field of petroleum engineering, well testing is done to determine the important physical characteristics of a reservoir. In the case of a constant production rate (as opposed to a constant pressure), the well pressure drop is a function of both time and the formation's boundary conditions. This pressure drop goes through several distinct stages before reaching steady state or semi-steady state production. This paper focuses on the analysis of a circular well with a closed outer boundary and details the derivation of a new approximation, intended for the transient stage, from an existing steady state solution. This new approximation is then compared to the numerical solution as well as an existing approximate solution. The new approximation is accurate with a maximum 10% margin of error well into the semi-steady state phase with that error decreasing significantly as the distance to the closed external boundary increases. More accurate over a longer period of time than the existing line source approximation, the relevance and applications of this new approximate solution deserve further exploration.
ContributorsKelso, Sean Andrew (Author) / Chen, Kangping (Thesis director) / Liao, Yabin (Committee member) / Mechanical and Aerospace Engineering Program (Contributor) / School of Music (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05