Mongkolcheep, Kathira (2009-08). A Lyapunov Exponent Approach for Identifying Chaotic Behavior in a Finite Element Based Drillstring Vibration Model. Master's Thesis.
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.