Drill-strings are slender structures used to dig into the rock in search of oil and gas.udFailures of drill-strings are time and money consuming and therefore the dynamics ofuddrill-strings must be investigated and carefully controlled.udIn the thesis, a dynamic model of the drill-string that is suitable for predicting axial,udtorsional and lateral vibrations is built using Euler-Bernoulli beam theory. The drillstringudis driven by a DC motor on the top and is subjected to distributed loads dueudto its own weight as well as bit/formation interaction. The model is axial-torsional,udlateral-torsional coupled. Under deterministic excitations, the model captures stickslipudbehavior in drilling operation. Analysis on its negative effect on drilling performanceudis made, and potential mitigation measures are also discussed. In randomudmodel, the excitations to the drill-bit are modeled as combination of deterministicudand random components. Monte Carlo (MC) simulation is employed to obtain theudstatistics of the response. Two cases of random excitation with different intensitiesudare investigated. The results from MC simulation are compared against that fromuddeterministic case.udSecondly, the thesis focuses on the drill-string torsional vibration and its stick-slipudanalysis. A finite element model of the drillstring with inclusion of both deterministicudand random excitations is also developed. Simulation is carried out under certainudparameters and it is shown that in deterministic case the torsional vibration may behave stick-slip. With change of some parameters, bifurcation and chaos of theudsystem are observed. In the random case, Monte Carlo simulation and path integrationudmethod are used to capture the probabilistic information of the response. The resultsudof path integration match well to those of deterministic cases.udAlthough there are some limitations, this thesis will help the author better understanduddrill-string downhole behaviors and lay a foundation for further research work.
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