Computational modeling and oscillations damping of axial vibrations in a drilling system

Drilling operations face with three types of vibrations torsional, axial and lateral, which are coupled oscillations that occur from the interaction of the drillstring with the rock at the bottom of the borehole. The paper focuses on the numerical and computational modeling of the axial vibrations of a drilling system, considering the case of distributed parameters as being tight connected with the physical description of these phenomena and providing high accuracy of system behavior. The system is modeled by hyperbolic partial differential equations with control and perturbation input signals. The computational solution is derived by means of a well-structured procedure which relies on a “convergent Method of Lines”a semianalytical method used to transform the infinite dimensional system in a finite dimensional one. The computational issues are then tackled via the paradigm of cell-based neural networks which exploit the peculiarities of the approximate system previous obtained. The numerical simulations allow a better understanding of the system dynamics regarding its transient and long-term behavior.