Extending the reach of high-angle and extended-reach wells through slide drilling operations are hindered by high downhole friction (static and dynamic), which emanates to inefficiencies, such as poor weight transfer from surface to bit, limited rate of penetration (ROP), high mechanical specific energy, bit-wear, and erratic toolface control. Experimental and field studies have demonstrated that downhole vibrations induced by axial oscillation tools (AOTs) in the drillstring is one of the most efficient methods for friction reduction and improving axial force transfer while slide drilling with mud motors in high-angle and extended-reach wells.
Modeling the dynamic response (axial displacement and accelerations) of axial oscillation-supported drillstrings is of high importance and required to predict the performance and functionality of AOTs under the surface and downhole conditions. Even though, reliable predictions are needed during the performance evaluation of AOTs, an accurate drillstring dynamic model that is capable of predicting the dynamic response of axial oscillation-supported drillstrings is currently lacking. Hence, this study is aimed to perform mathematical analysis of axial oscillation-supported drillstrings to provide an accurate prediction of the dynamic response of these systems under the surface and downhole conditions. This study includes experimental studies on axial oscillation tools and mathematical modeling of the dynamic response of axial oscillation-supported drillstrings operating at the surface and downhole conditions. To perform experimental studies, a flow loop has been developed to assess the dynamic response of the axial oscillation tool at the surface. During the test, the pressure drop across the tool and axial displacements of the tool were measured while varying flow rate and spring rate within the tool. The axial oscillation-supported drillstring is modeled as an elastic continuous system subjected to viscous damping, Coulomb friction, and displacement (or support) excitation using the dynamic equilibrium approach. The introduction of the spring rate as an experimental variable in the test and the mathematical modeling approach used are unique to this study. The model developed in this investigation can predict natural frequencies, axial displacements, and acceleration of axial oscillation-supported drillstrings. The model is validated with experimental results and published measurements obtained from experiments conducted using field-scale drillstring models. Results show reasonable agreement (maximum discrepancy of approximately 14.5%) between model predictions and measurements at different excitation frequencies and pressure drops. In addition, results emphasize that flow rate is the most critical parameter in the operations of axial oscillation tools because it affects the magnitude of pressure drop, operating frequency of the tool and vibrating force. Furthermore, incorporating the spring rate in the model formulation improves the accuracy of the model.