Dynamic analysis and vibration of beam inside annulus for ultra short-radius water jet drilling

Conventional water-jet nozzle systems have been developed and partially used in the oil and gas industry to drill horizontal sidetracks. However, this technique still presents a few shortcomings associated with tube buckling and water jet sagging. Due to these problems, the drilled hole deviates from the desired path and does not reach the target reservoir. The issue becomes more complex due to the continuously moving boundaries representing the borehole profile, which is, in turn, governed by the nozzle dynamics. A mathematical model representing the dynamics of water jet drilling confined in a borehole along with drilling mud is developed to predict the sagging phenomenon during the drilling process. The closed form solution of the governing equation is obtained for horizontal drilling in shallow formation layers. The solution shows the strong influence of nozzle vibration and the magnitude of thrust force at the nozzle tip on the profile and the diameter of drilled hole. For sidetrack drilling of greater than 400 m length, the magnitude of sagging is large enough to miss the target reservoir. Furthermore, the drill string buckles at certain magnitudes of thrust forces and penetration lengths.