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Hole structure interaction

In many engineering problems, we have to know the mechanical behaviour of a hole structure composed of cylinders (drill string, BHA, casing, completion) that are restricted to move into a hole defined by a 3D curve and sequence of radius (casing, open hole). The structure is submitted to mechanical, hydraulic and thermal loading and we need to model its static and dynamic behaviour.

Static

Torque & drag & buckling lab tests

Torque and drag and buckling lab tests

In most of configurations, the structure can be considered in a static or quasi static state (we assume that the structure is in rotation which impact contact conditions). We have developed a quasi-static hole / structure interaction model in collaboration with our academic partner that :

  • takes into account the rigidity in bending (rigid model)
  • calculates the positions of the contact points assuming a unilateral contact with friction
  • does not use FEA to evaluate the deflection (fast calculation)
  • adresses large deflection problems (post buckling)

This model was validated with laboratory and field data.

Dynamic

There are two main approaches to dynamic modeling:

Frequency domain (modal analysis)

Lateral modal shape

Lateral modal shape

In this approach we compute the resonance frequencies and associated deflection shapes of the structure in axial, torsion and lateral modes. Then we analyse the possible sources of excitation (rotation, pumps, bit/rock interaction) to avoid operating the system close to a resonance frequency.

When the source of excitation can be quantified (steerable motors, vibration induced devices), we can perform a forced vibration analysis that provides a quantitative evaluation of the system response.

In this analysis, we have to fix the boundary conditions (free or blocked) which, for lateral vibration, can be a strong assumption as contacts can be intermittent in quasi vertical conditions.

Time domain

Stick-slip minimum rotation speed calculation

Stick-slip minimum rotation speed calculation

Time domain dynamic response of the structure inside the hole is a very complex problem to model because of the strong non linearity associated with the intermittent lateral contact of the structure with the hole. It is usually addressed with FEA and requires very time consuming calculations. To reduce this computation time, the axial, torsion and lateral degrees of freedom are often treated separetely.

Our stick-slip module completes a time domain resolution of the dynamic response of the system in torsion. Torque versus rotation variation at contact points along the structure and at the bit are integrated. Using inputs of surface rotation, we can model the torsion response anywhere along the structure and define appropriate operating conditions to avoid reverse rotation and/or important stick-slip at the bit.

Intermittent contact calculation at stabilizer

Intermittent contact calculation at stabilizer

We are currently working with our academic partners on a time domain simulation of the lateral response of the structure that integrates the intermittent and strongly nonlinear interaction of the structure with the side of the hole.