Investigation into the effect of friction decay factor on the modelling and attenuation of stick-slip vibrations of oilwell drilling systems

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The self-excited stick-slip oscillations of oilwell drillstrings are attributed to the nonlinear interaction between the drill-bit and the rock formation. Development of more accurate models will lead to improved predictions allowing more potential for successful suppression of the drillstring vibrations, thus reducing damage to the drilling system, prevention of expensive failures and increased output from the oilwell. In this paper, the effect of the transition from static friction to Coulomb friction on modelling of stick-slip phenomenon of oil well drill string is investigated through an analysis of the so called ‘decay factor’. Based on a distributed-lumped parameter model (DLPM) of the drilling system, the governing equations of motion for the system are obtained. By using different values of decay factor (low, high and medium), the stick-slip vibrations of the drill string are validated against published data from full-scale drill strings. The results from the simulation show that lowering the decay factor increases the critical speed and thus reduces the propensity for stick slip motion. However, a reduction in the decay factor also has the effect of inducing worse stick-slip motion once the critical speed has been reached. The results indicate the wider impact of both correct modelling of the decay factor, but also the importance of correct characterisation of the mud viscosity and drill/well contact for more accurate selection of drilling parameters in the field.