A Finite Element Model is developed for investigating the BHA dynamics. The stabilizers, WOB, and gravity effects are considered. The natural frequencies as well as the mode shapes are obtained through modal analysis. The results show that in certain drillstring configurations a small amount of parameter variation (disorder) may cause what is known in structural dynamics literature as "mode localization". If the modes are localized, vibrational energy is confined to small geometric regions instead of being propagated. This in turn results in very large amplitudes at certain locations which are not predictable through analysis of the nominal system. A field case is used to demonstrate the occurrence of this phenomenon under realistic conditions. Several operational and design methods to avoid the occurrence of mode localization are suggested.
A recent survey has shown that the rate of BHA failures seem to be increasing. Based on some failure statistics, it seems that the overall economic impact of drillstring failures in the oil industry is quite significant. Though there has been considerable research in the modeling and analysis of drillstring dynamics, a comprehensive understanding of all the vibration phenomena involved is still lacking. Furthermore, the complex and varying nature of the boundary conditions, and operational characteristics undermine the utility of available models with respect to their predictive capabilities.
Most of the times in real field cases, BHA is assembled as a periodic structure consisting of drillcollars and stabilizers. When modeling structures consisting of numerous repeated segments, it is typically assumed that the geometry and the physical properties (i.e., mass, stiffness and damping) of the repeated elements are identical. The mode shapes obtained from this idealized model are global in nature, and the modal response extends throughout the structure. However in a real BHA, no two segments will be precisely identical in their properties. Imperfect manufacturing processes will invariably produce small random variations in the properties of each segment. The mounting errors while assembling drillcollars may cause considerable length variations from one span (between two stabilizers) to another span.
The presence of irregularities in nominally periodic structures causes the normal modes of vibration to be localized to small geometric regions. This in turn may cause (for a wide range of frequencies) the confinement of incident waves near the excitation source, resulting in a spatially exponential decay in an average sense. In very large one dimensional periodic structures, almost all of the modes are localized, regardless of the amount of disorder. For finite structures, however, a certain amount of disorder is necessary for the localized modes to be seen. In fact, it has been shown that for "strong mode localization" to occur, the ratio of internal coupling to disorder should be small. Consequently, for a small disorder to cause localization, the substructures should be weakly-coupled. In this case, the modes of a disordered weakly-coupled system will resemble those of individual decoupled substructures. Noting that in the ordered case, the eigenvalues of the decoupled structures are identical, it is natural to expect that the structures with high modal densities are also susceptible to mode localization.
To the best of author's knowledge mode localization phenomenon has not been shown to occur in drillstrings. The current work is a preliminary study to investigate the possibility of mode localization in realistic drillstring configurations. First, a simple lumped parameter system is used to illustrate the important concepts. Then, the dynamics of a realistic drillstring configuration is studied to investigate the effect of different types of disorders.
A simple two degrees of freedom system shown in Fig. 1 is considered.