Analytical modeling of axial oscillation-supported drillstrings in high-angle wells

Abstract

Downhole vibrations generated from axial oscillation tools (AOTs) in axial oscillation-supported drillstrings (AOSDs) has become one of the efficient means of reducing friction and improving weight transfer during sliding operations in horizontal and extended-reach wells. Dynamic modeling of AOT-excited drillstrings is needed for validating the functionality of axial oscillation tools during surface tests and predicting their response under downhole conditions.An analytical model is presented in this study to predict the behavior of axial oscillation-supported drillstrings working under downhole and surface conditions. The model is useful to perform parametric studies, downhole data correlation and placement study of AOTs along the drillstring in horizontal and extended-reach wells. Unlike existing models, the nonlinear equation of motion is derived from a model damped in a viscous medium with Coulomb friction and subjected to displacement excitation. The model also accounts for the spring rate of the axial oscillation tool. The displacement excitation is obtained from the spring rate, which is a critical input to the model. The nonlinear damping is approximated with an equivalent viscous damping coefficient to obtain an analytical solution. The developed model in this study is validated with published experimental measurements obtained from field-scale drillstrings.Correlations between predicted and measured axial displacement and accelerations at different excitation frequencies, pressure drops and spring rates show an approximate average deviation of 14.5%. Also, results from this study strongly accentuates that flow rate is the most critical operating parameter for axial oscillation tools because it affects the amplitude of pressure drop, excitation force, and operating frequency of AOTs.