Mathematical Modeling of Axial Oscillation Tools in High-Angle Wells

Abstract

Experimental and field studies continue to demonstrate that downhole vibrations induced by axial oscillation tools (AOTs) in the drill string are the most efficient method for reducing friction and improving axial force transfer in high-angle and extended-reach wells. Modelling the dynamic response of AOT-involving drill string systems is of high importance for validating functional tests of oscillation tools and predicting their performance under downhole conditions. This study presents a mathematical model used for predicting the dynamic response of axial oscillationsupported drill string (AOSD) systems under the surface and downhole conditions. The model is useful to perform placement analysis of axial oscillation tools within the bottom hole assembly. Nonlinear equations of motion and introduction of displacement excitation in the model development make it different from existing models. The spring rate of the axial oscillation tool is a critical input in the determination of displacement excitation. The resulting nonlinear equations of motion are linearized, and solutions are obtained using the Eigenfunction Superposition method. The model is validated using published measurements obtained from experiments conducted using fieldscale axial oscillation tools. Results show reasonable agreement between predictions and measurements at different axial displacements, vibration frequencies, and system pressure drops. The usability of the mathematical model was validated with published experimental data with an observed average deviation of approximately 14.5%. Unlike existing models, the new model accounts for the combined effect of excitation pressure drop and vibration frequency on axial displacement.