The present invention is a
system and method for generating an alarm relative to effective longitudinal behavior of a
drill bit fastened to the end of a
drill string driven in rotation in a well by a driving device situated at the surface, using a
physical model of the drilling process based on general
mechanics equations. The following steps are carried out: the model is reduced so to retain only pertinent
modes, at least two values Rf and Rwob are calculated, Rf being a function of the principal oscillation frequency of weight on hook WOH divided by the average instantaneous rotating speed at the surface, Rwob being a function of the standard deviation of the
signal of the
weight on bit WOB estimated by the reduced
longitudinal model from measurement of the
signal of the weight on hook WOH, divided by the average
weight on bit WOB0, defined from the weight of the string and the average weight on hook. Any danger from the longitudinal behavior of the
drill bit is determined from the values of Rf and Rwob.