Andreas Hohl

A Combined Analytical and Numerical Approach to Analyze Mud Motor Excited Vibrations in Drilling Systems

Severe vibrations in drillstrings and bottomhole assemblies can be caused by cutting forces at the bit or mass imbalances in downhole tools. One of the largest imbalances is related to the working principle of the so-called mud motor, which is an assembly of a rotor that is maintained by the stator. One of the design-related problems is how to minimize vibrations excited by the mud motor.Simulation tools using specialized finite element methods (FEM) are established to model the mechanical behavior of the structure. Although finite element models are useful for estimating rotor dynamic behavior and dynamic stresses of entire drilling systems they do not give direct insight how parameters affect amplitudes and stresses. Analytical models show the direct influence of parameters and give qualitative solutions of design related decisions. However these models do not provide quantitative numbers for complicated geometries.An analytical beam model of the mud motor is derived to calculate the vibrational amplitudes and capture basic dynamic effects. The model shows the direct influence of parameters of the mud motor related to the geometry, material properties and fluid properties. The analytical model is compared to the corresponding finite element model. Vibrational amplitudes are discussed for different modes and parameter changes. Finite element models of the entire drilling system are used to verify the findings from the analytical model using practical applications. The results are compared to time domain and statistical data from laboratory and field measurements.Copyright

Application of the Transfer Matrix Method for the Analysis of Lateral Vibrations of Drillstrings with Parameter Uncertainties

To compare the susceptibility of different drillstring assemblies to lateral vibrations while taking parameter uncertainties into consideration, a computationally efficient model based on the transfer matrix method (TMM) in combination with a modal reduction is proposed in this study. Changing boundary conditions along the drilling trajectory are taken into account by combining the linear dynamic analysis from the TMM model with a static solution obtained from a finite element model. The statistical evaluation of the results enables a comparison of the dynamic behavior of different drillstring configurations during an early design stage.