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


  • 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.

publication date

  • August 2009