The main objective of this paper is to improve drilling performance by obtaining a representative dynamic model of a drilling system: top-drive, controls, drill-pipe and bottom hole assembly (BHA). High-fidelity simulations with a representative analytical model are a goal necessary to optimize controller-settings while or before drilling. Goals such as ‘lowest sensitivity to torque disturbance at the bit’ or ‘best reaction to stick-slip events’ can be pursued while guarding stability limits of the full system.

The method is based on spectral correlation between at least two signals: a broad-band signal with frequencies in the relevant band (0.05Hz to 5Hz) added to the top-drive's torque command and second: the measured top-drive speed. Mathematical tools from seismic exploration and control-theory are used to determine key parameters of this closed-loop system. Correlation techniques allow identification even during high background noise generated by varying friction and bit-cutting forces in most cases.

Experimental results from a number of wells in Oman, Malaysia, and USA show that the transmission-line based model can be accurately matched at all depths. Besides the eigen frequency, a number of higher modes of the drill sting are found, including their effective damping. The identified response agrees with expected response based on pre-computed mechanical drill-string composition parameters. In one well a substantial increase in friction and bit-inertia was identified at certain depth intervals. Logs taken afterwards showed wash-outs at these depths, suggesting diagnostic potential of this estimation technique.

Novel is the ability to identify a dynamic drill string model without advance information, yielding auto-tuning capability for most stick-slip mitigation technologies such as ‘softtorque’. A very welcome benefit is the estimation of the string's characteristic impedance and length but also internal and external friction components along the string and at the bit. Traditionally, these damping terms are often neglected, exaggerated or set to an agreeable value to limit the amplitude of resonances in the calculated model. The presented identification method generates updates of these different damping terms every ten minutes or so. During drilling several wells, the found damping terms are spread over a wide range due to mud-pipe, pipe-wall interaction and bit-formation variability. We conclude that damping terms cannot be ignored without severely compromising the dynamic fidelity of the model. Future diagnostic and drilling optimization tools may be based on this new way of harvesting information from down hole.

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