Drill String dynamics and hole cleaning problems are some of the most important limiting factors in extended reach applications. Here, long sections of the drill string lie on the low side of the wellbore while rotating. When the rotary speed exceeds a critical threshold the drill string starts to "snake", sliding up and down the borehole wall. If rotated well beyond the threshold speed, the drill string will eventually start to "whirl" which can cause severe damage to string components after only a short period of time.

In this paper an analytical solution for the threshold rotary speed is derived and presented. It is shown to be in the range of the rotary speeds used in modern extended reach applications. The analytical results are verified using a versatile finite element formulation to model the drill string in greater detail. Animated time domain simulations with this model provide deeper insight into the dynamic behaviour of the drill string.

Conclusions on improved drilling practices in extended reach applications - especially with respect to hole cleaning problems - are drawn from the theoretical results.


Lateral drill string vibrations can cause severe problems such as: Twist-offs due to accelerated fatigue in thread connections; premature bit failure due to bit whirl; failure of Measurement-While-Drilling (MWD) tools due to high shock loads during impacts of the bottom hole assembly (BHA) against the borehole wall.

Over the last twenty years, theoretical work based on mathematical models has lead to a good understanding of the influence of bit and BHA design, drilling parameters and other parameters such as stabilizer clearances and friction factors on the onset and severity of lateral BHA vibrations1–11. Most of these models of a BHA in a borehole use the finite element method14 which allows a detailed mathematical description of this complex system.

Linear models are solved in the frequency domain and provide either the natural frequencies and mode shapes of the BHA or the frequency response of the BHA to a harmonic excitation source in the model. Linear models are applied today on a more or less routine basis for vertical or near vertical drilling operations. In this case they are used to calculate natural frequencies of the stabilized BHA section close to the bit and to predict safe RPM operating limits. Jogi et al.12 recently successfully verified a linear model by comparing predicted resonance frequencies with downhole measured vibration data from a shallow vertical well.

Non-linear models are solved by numerical integration in the time-domain and provide a simulation of the dynamic behaviour of the BHA in the borehole. Parameter studies with non-linear models have undoubtedly contributed much to today's understanding of lateral drill string dynamics. However, the complexity of these models and the long computation times involved limit their application mainly to research studies.

In almost all the models described in the literature only the BHA up to the so-called point of tangency1,3,10 is taken into account by the dynamic analysis. Only two models in the literature6,8 include continuous wall contact. These two models, however, focus on the parametric excitation of lateral vibrations due to fluctuating weight-on-bit which is outside the scope of this paper. The point of tangency approach is based on the assumption that the portion of the BHA in contact with the borehole wall is less likely to develop lateral vibrations at higher hole inclinations. This assumption probably holds true for conventional BHAs with heavy drill collars in inclined wellbores. However, the BHAs used in highly inclined or horizontal well sections of extended reach wells consist of a very short stabilized string section followed by long sections of drillpipe lying on the low side of the wellbore. The drillpipe is loaded under compression and rotated at rotary speeds of up to 200 RPM for hole cleaning purposes, making lateral vibrations more likely to occur.

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