ABC for model selection and parameter estimation of drill-string bit-rock interaction models and stochastic stability

The bit-rock interaction considerably affects the dynamics of a drill string. One critical condition is the stick-slip oscillations, where torsional vibrations are high; the bit angular speed varies from zero to about two times (or more) the top drive nominal angular speed. In addition, uncertainties should be taken into account when calibrating (identifying) the bit-rock interaction parameters. This paper proposes a procedure to estimate the parameters of four bit-rock interaction models, one of which is new, and at the same time select the most suitable model, given the available field data. The approximate Bayesian computation (ABC) is used for this purpose. An approximate posterior probability density function is obtained for the parameters of each model, which allows uncertainty to be analyzed. Furthermore, the impact of the uncertainties of the selected models on the torsional stability map (varying the nominal top drive angular speed and the weight on bit) of the system is evaluated.