Mud Motor PDM Dynamics: An Analytical Model

Abstract

Abstract In a fast drilling environment, suchas shale drilling, refining advanced technologies for preventing downhole toolfailures is paramount. Challenges are still very much associated with complex bottom-hole assemblies and the vibration of the drill string when used with a downhole mud motor. The mud positive displacement motor with various lobe configurations and designs becomes an additional excitation source of vibration. Further, it affects the transient behavior of the performance mud motor. Unbalanced force exists because the center ofmass of the motor rotor does not coincide with the axis of rotation.Further, the vector of full acceleration of the center of the rotor can be decomposed into two perpendicular projections—tangent and normal—which aretaken into account and integrated intothe full drill string forced frequency modelas force and displacement at the motorlocation. The paper includes two models, first one to predict the critical speeds and the second one to see the transient behavior of the downhole parameters when the mud motor is used.The model also considers the effect of the stringspeed. The unbalanced force is more pronounced at the lower pair or lobe configuration as compared to the higher pairlobe configuration because of the larger eccentricity. The unbalance is modeled in terms of an equivalent mass of therotor with the eccentricity of the rotor. Also, the analysis provides an estimation of relative bending stresses, shear forces, lateral displacements and transient bit rpm, bit torque, and weightone bit for the assembly used. Based onthe study, severe vibrations causing potentially damaging operating conditionswhen transient downhole forcing parametersare used for the vibration model.It has been found that when a mud motor isused using static forcing parameters may not provide the conservative estimation of the critical speeds as opposed totransient parameters. This is because coupled oscillations fundamentally can create new dynamic phenomena, which cannot be predicted from the characteristics of isolated elements of the drilling system.