On the group velocity of guided waves in drill strings

A key element to verify the drill-bit signal processing is the estimation o f the time delay of the guided waves transmitted through the drill string f rom the bit to the surface. This delay can be measured from drill-bit vibra tions or calculated using the mechanical properties of the drill string. Th e calculation of the complete solution and the exact dispersion relations r equires expensive numerical modeling. In this work, a simple approach to co mpute the group velocity of extensional and torsional waves by averaging th e drill-string properties in the low-frequency approximation is used. The r esult is a generalization of the group velocity for periodic systems in whi ch stationary distribution of properties is assumed. Results obtained with real strings show that the group velocity in the bottom-hole assembly is gr eater than the velocity iii a uniform rod and lower than the velocity in th e drill pipes. (C) 2001 Acoustical Society of America.