# Choice of measurement locations for a nonlinear coupled axial–torsional drill string using proper orthogonal modes and effective independence strategy

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## Abstract

Drill strings are used to search for oil and gas reservoirs. Its dynamic behavior has been the subject of many investigations. In particular, this paper is interested in choosing measurement locations, and a nonlinear coupled axial–torsional dynamic computational model is used for this purpose. Wired drill pipe technology is a reality, and we would like to take advantage of multiple points of measurements to better understand and control the drill string dynamics. This paper proposes to apply the proper orthogonal modes and the effective independence strategy, which automatically choose the measurement locations in an optimal manner. The dynamic response of the computational model is used to construct the proper orthogonal modes (POMs) obtained by means of the proper orthogonal decomposition. And the effective independence distribution vector procedure is employed to eliminate, iteratively, locations that contribute less for the independence of the target POMs. In addition, nondimensional parameters are proposed for the system, aiming at a more general analysis. The results show that, if few sensors are available, one sensor should be placed close to the bit (which is usually the case) and the others should be distributed along the drill pipe.

## Keywords

Sensor placement Coupled axial–torsional dynamics Effective independence Drill string nonlinear dynamics Dimensionless parameters## Notes

### Acknowledgements

I would like to acknowledge that this study was financed in part by the Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES)—Finance code 001—Grant PROEX 803/2018, and the Brazilian agencies: Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPQ)—Grants 303302/2015-1, 400933/2016-0, Fundacao Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro (FAPERJ)—Grant E-26/201.572/2014. In addition, I would like to thank the anonymous reviewers for the meticulous reviews and insightful suggestions.

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