A Novel Approach to Dynamic Representation of Drill Strings in Test Rigs

Drill strings are used in oil and gas production as well as geothermal wells. They experience destructive vibrations, many of which are highly dependent on drill string modes. In this paper, we show that the lowest frequency modes are not necessarily the most critical and we delineate a methodology for reducing the number of modes representing the drill string. The frequency response function and stability diagram are used as measures of dynamic similarity between the proposed model and the drill string. We also introduce a novel approach to represent a drill string in laboratory test rigs. This approach not only represents the drill string dynamics but also offers flexibility to modify, remove, or augment the modes representing the system. The underlying principle is that in a multi-degree-of-freedom in-series spring-mass system with Rayleigh damping, dynamic modes can be decoupled. Applying the force to the end node (bit), the modes can then be configured separately in a parallel arrangement where their contributions to bit displacement are added algebraically. A practical arrangement for this purpose is proposed in this paper. Construction of a test rig that accurately represents the drill string dynamics is critical to validation of any test data on bits, bottom hole assemblies, instrument subs, and so on.