Computational modeling of the nonlinear stochastic dynamics of horizontal drillstrings

Abstract

This work intends to analyze the nonlinear stochastic dynamics of drillstrings in horizontal configuration. For this purpose, it considers a beam theory, with effects of rotatory inertia and shear deformation, which is capable of reproducing the large displacements that the beam undergoes. The friction and shock effects, due to beam/borehole wall transversal impacts, as well as the force and torque induced by bit-rock interaction, are also considered in the model. Uncertainties of bitrock interaction model are taken into account using a parametric probabilistic approach. Numerical simulations have shown that the mechanical system of interest has a very rich nonlinear stochastic dynamics, which generate phenomena such as bit-bounce, stick-slip, and transverse impacts. A study aiming to maximize the drilling process efficiency, varying drillstring velocities of translation and rotation is presented. Also, the work presents the definition and solution of two optimizations problems, one deterministic and one robust, where the objective is to maximize drillstring rate of penetration into the soil respecting its structural limits.

Campbell Diagram Computation for a Drillstring Immersed in Curved Wells

“…The steel beam is characterized by the mass density ρ = 7860 kg.m −3 , the Young modulus E = 2.1 10 11 Pa and the Poisson ratio ν = 0.3. The two Rayleigh damping coefficients are c M = 0.03 s −1 and c K = 0 s [13]. The beam vibrations are studied in three cases sketched by Figure 5.…”

“…Liao et al [12] 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 drilling assembly in horizontal wells [13,14] and in curved wells [15,16]. A dynamic model [17] based on the Timoshenko beams has been developed to analyze the suppression of lateral and torsional vibrations of drillstring by using the impact and torsional dampers.…”

Quantification of parametric uncertainties induced by irregular soil loading in orchard tower sprayer nonlinear dynamics

“…By means of the generalized displacement q : t ∈ R → q(t) ∈ R 6 , the initial displacement vector q 0 ∈ R 6 , and the nonlinear mapping f : t, q(t) ∈ R × R 6 → f q(t) ∈ R 6 , where…”

“…In fact, system parameters have uncertainties due to a series of factors such as variabilities intrinsic to the manufacturing process, materials and geometric imperfections, etc [4,5]. Taking such uncertainties into account is essential for making robust predictions, but also, it has been becoming a common practice in engineering [6,7,8,9,10].…”

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

“…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].…”