Abstract: The method comprises using a transmitting unit and at least two receiving units (8,10) arranged in two different places along well equipment (2). Each receiving unit forms an image or signature of wall portions which pass it. The signatures of wall portions formed by the lower receiving unit (8) when the well equipment is being lowered into the well are stored and the upper receiving unit (10) stores signatures coming from the wall portions which were previously stored by the lower receiving unit. A comparison (for example a correlation) of the signatures respectively coming from the two receiving units allows a common wall portion which has produced two substantially identical compared signatures to be identified. The time interval between the formation of the two substantially identical signatures is measured and the rate of penetration is calculated. As application of the invention is for the measurement of the true rate of penetration of a well tool or of a measuring sonde.

Abstract: A method for determining the wear of cutting portion of a tool during drilling of a formation wherein a measurement is taken of the weight W applied to the tool and the torque T required to rotate said tool, the weight on the tool W and the torque T being linked by an equation of the type T=uW+vW.sup..alpha. in which u and v are parameters and .alpha. is a coefficient depending in part on the formation.