Campbell Diagram Computation for a Drillstring Immersed in Curved Wells

Abstract

The drilling operations use a rotary slender structure introduced inside the drill well. The nonlinear dynamics with bit-bouncing, stick-slip phenomena, and pulsating mud flow may yield the premature wear and damage of drilling equipment and should be investigated to improve the reliability of drilling operations. This work presents the beam element formulation to model the drilling nonlinear dynamics. The well-pipe contacts are modeled by the radial elastic stops. The fluid–structure interactions are considered. The first step consists in computing the static position of structure to determine the contact points and calculate the preloaded state. These results are then considered to calculate the Campbell diagram. The potentially unstable speeds of rotation are identified. The results show that the modal coupling phenomena strongly occur for the three-dimensional well. The well-pipe contacts modify the modes in rotation, and the rotating fluid induces a strong deviation of the flexural mode curves.

Nonlinear rotordynamics of a drillstring in curved wells: Models and numerical techniques

“…Instead of the classical contact law which describes two discrete states (contact or no contact) at G = 0 and may induce numerical instabilities, a contact law based on regularized stiffness and damping functions is applied as in [16]:…”

“…When the drillstring rotates and has lateral deflections (see Fig. 2), a well-drillstring contact also includes the tangential friction force and torque which both depend on the sliding velocity v g = (uv − vu)/r + (Ω +θ z )R e [16].…”

“…They have been studied since the mid 1960s and extensively investigated by the finite element method since 1990s [13,14,15] thanks to computer development. Recently, a beam element model with 6 dofs per node has been developed in [16] for computing the Campbell diagram of a drillstring immersed in fluid inside a curved well to determine the potential unstable speeds of rotation which may trigger dangerous vibrations and resonances.…”

“…Liao et al [25] also developed a four-dof model to study the bending and torsional dynamics of drillstrings. The finite element method has been widely implemented for modeling the dynamic behavior of drillstring in horizontal wells [26,27] and in curved wells [16,28] by taking into account different well-structure and fluid-structure interaction models. Recently, Feng et al have implemented a planar curved beam element in order to take into account 3D well profile and the drillstring-well interactions [29].…”

“…The convergence of CB results and the computational time versus the CB mode number are also analyzed. The beam element model of drillstring dynamics is presented in details in [16,28]. The drilling structure is meshed along the axial curvilinear direction using straight beam elements with two nodes per element.…”