Mathematical analysis of the effect of shock sub on the longitudinal vibrations of an oilwell drill string

Abstract

Shock subs have been in use for several years in oilwell drill strings in reduced longitudinal and torsional vibrations. In this paper a mathematical investigation is made into the longitudinal vibrations of a drill string, with and without a shock sub. The Laplace transformation method of solution is used, with the inverse transformation being accomplished by the theory of residues and facilitated by the use of a digital computer. The solution curves are mathematically exact at each computed point and confirm favorable field reports on the use of the sub.