Torsional model of the drill string, and real-time prediction of the bit rotational speed and the torque on bit, in an oil well drilling tower

In an oil well drilling tower, the Bottom Hole Assembly (BHA) data is needed to optimize the controllable variables such as weight on bit and bit rotational speed for obtaining the optimum drilling rate. In order to acquire the data of the BHA, a simple and low-cost method, can be predicting of these parameters. In this study, first the torsional modelling of the drill string is implemented by dividing its length to some equal sections, then the effects of dividing on the estimation accuracy are evaluated. Using an ADRC (Active Disturbance Rejection Controller) in the vertical and rotational motions dynamics, some proper observers to predict the bit rotational speed, rock stiffness and torque on bit, in real-time are designed and presented. Dividing the drill string length to more sections, leads to design high order observer, so the performance of the designed observers with different orders, are compared and analysed. Employing the integral square error analysis, it is revealed, dividing the drill string length to more sections, leads more accurate in the prediction of bit rotational speed, but not more effect on the estimated rock stiffness, and torque on bit. Also it is shown that increasing of the observer bandwidth, leads to more accurate in the estimation, but concludes the estimation be more sensitive to the sensor noise. Employing the presented observers in this study to estimate the BHA data, in addition to enhance the drill quality and safety, the controllable variables are optimized, and consequently the whole drilling process can be robustly controlled, with no needs to the expensive measurement systems at the BHA.