The purpose of this work is to present a methodology to predict vibrations of drilllstrings for oil recovery service. The work extends a previous model of the drill collar between two stabilizers in the literature to include drill collar flexibility utilizing a modal coordinate condensed, finite element approach. The stiffness due to the gravitational forces along the drillstring axis is included. The model also includes the nonlinear effects of drillstring-wellbore contact, friction and quadratic damping. Bifurcation diagrams are presented to illustrate the effects of speed, friction at wellbore, stabilizer clearance and drill collar length on chaotic vibration response. Their effects shifts resonance peaks away from the linear natural frequency values and influences the onset speed for chaos. A study is conducted on factors for improving the accuracy of Lyapunov Exponents to predict the presence of chaos. This study considers the length of time to steady state, the number and duration of linearization sub-intervals, the presence of rigid body modes and the number of finite elements and modal coordinates. The Poincare map and frequency spectrum are utilized to confirm the prediction of Lyapunov exponent analysis. The results may be helpful for computing Lyapunov exponents of other types of nonlinear vibrating systems with many degrees of freedom. Vibration response predictions may assist drilling rig operators in changing a variety of controlled parameters to improve operation procedures and/or equipment.

In this study, a novel concept for a downhole flywheel energy storage module to be embedded in a bottom-hole-assembly (BHA) is presented and modeled, as an alternative power source to existing lithium-ion battery packs currently deployed in measurement-while-drilling (MWD) or logging-while-drilling (LWD) operations. Lithium-ion batteries disadvantages include deteriorated performance in high temperature, limited lifetime that necessitates frequent replacement which elevates operational costs, and environmental disposal. Extreme and harsh downhole conditions necessitate that the flywheel module withstands temperatures and pressures exceeding 300 ?F and 20 kpsi, respectively, as well as violent vibrations encountered during drilling. Moreover, the flywheel module should adhere to the geometric constraints of the wellbore and its corresponding BHA. Hence, a flywheel sizing procedure was developed that takes into consideration the required energy to be stored, the surrounding environmental conditions, and the geometric constraints. A five-axis magnetic levitation control system was implemented and tuned to maintain continuous suspension of the flywheel under the harsh lateral, axial and torsional drilling vibrations of the BHA. Thus, an integrated finite element model was developed that included the rotordynamic behavior of the flywheel and the BHA, the component dynamics of the magnetic levitation control system, and the cutting dynamics of the drillbit for both PDC and tricone types. The model also included a newly developed coupling between lateral, axial and torsional vibrations. It was demonstrated through simulations conducted by numerical integration that the flywheel maintains levitation due to all different types of external vibration as well as its own lateral vibration due to mass unbalance. Moreover, a passive proof-mass-damper (PPMD) was developed that suppresses axial bit-bounce vibrations as well as torsional vibrations, and was extended to also mitigate lateral vibrations. Optimized values of the mass, stiffness and damping values of the PPMD were obtained by the hybrid analytical-numerical Chebyshev spectral method that was superior in computational efficiency to iterative numerical integration. This also enabled the fine-plotting of an operating stability chart indicating stability regions where bit-bounce and stick-slip are avoided. The proof-mass-damping concept was extended to the flywheel to be an active proof-mass-damper (APMD) where simulations indicated functionality for a light-weight BHA.