Nonlinear Drilling Dynamics with Considerations of Stochastic Friction and Axial and Tangential Coupling

Abstract

Drill string dynamics research is one of the important research directions in modern oil and gas drilling technology. Aiming at axial vibration, radial vibration, nonlinear vibration with the consideration of stochastic friction and the tooth wear under the action of torsional loads during the drilling process, theoretical analysis, and example calculation are carried out to obtain the parameter influence result of the drilling dynamics research. The drilling dynamics under axial load is studied. With the combination of the force analysis of the horizontal drill string, the axial vibration analysis model is established. According to the axial vibration dynamic model, example analysis is conducted and vibration displacement, vibration velocity, and spectrum results in different drill string nodes are obtained. The radial inertia effect on vertical vibration of drill string under whether considering the radial inertia or not is analyzed and compared. On the basis of theoretical analysis, according to the real working condition of drill string and based on the Rayleigh-Love model and one-dimensional viscoelastic model, vertical vibration equations of drill string are derived. According to the Laplace transform method and the relationships between parameters of the model, the solutions to complex impedance at the bottom of drill string are obtained, and then the comparison result of radial inertia effect on vertical vibration characteristics of drill string are analyzed. In order to research the dynamic characteristics of drill string with wellbore stochastic friction forces, vibration characteristics analysis of drill string is conducted. On the basis of the wellbore random friction forces, the analysis models of drill string vibration and drilling efficiency of horizontal well are established under the background of shale gas. Then, the wellbore friction randomness is studied to obtain the method of constructing the wellbore friction random field. Combined with solution expressions of each force in the vibration equation, the discrete method of drill string dynamic model is established. According to the result of example analysis, the influence of key parameters on the dynamic characteristics of drill string is analyzed. In actual drilling process, the torsion of the drill string generates torsional load, which acts on the drill bit. The force condition of the cutting teeth is affected by the torsional load, which causes the failure of the cutting teeth. The normal failure of the cutting tooth is due to the tooth wear. Therefore, the effect of torsional load on the cutting teeth wear is studied. According to the force condition with the consideration of the torsional load, a geometric model of the PDC cutter is established and the cutter wear model under the action of the torsional load is obtained by further derivation research.