Abundant drilling activities had confirmed that the fully rotary drilling can improve the rate of penetration effectively. However, the fully rotary drilling has brought some challenges for the trajectory control ability of the bottom hole assembly (BHA). One of the reasons is the effect of drill-string rotation was ignored in the existing methods, where the bent-housing positive displacement motor (PDM) was regarded as the prebending beam. According to the D’Alembert principle, the dynamical centrifugal force, generated by drill-string rotation, was equivalent to a quasi-static problem. The mechanical model of BHA with bent-housing PDM was established based on the Timoshenko beam theory. The calculated formula of bit side force (BSF) and resultant steering force (RSF) was deduced. The influences of inclination, rotational speed of drill-string, bend angle, eccentricity, stabilizer, weight on bit (WOB) and elbow position on the average BSF and RSF were investigated. The results show that the rotational speed of drill-string has a significant influence on the steering ability. The average BSF increases with the rotational speed of drill-string, while the RSF increases firstly and decreases subsequently. The controlling factor is the transverse component of drill-string gravity in a low rotational speed, while it is the centrifugal force in a high rotational speed. The BSF climbs up and then declines with WOB and rotational speed of drill-string. When the rotational speed of drill-string exceeds 100 RPM or WOB is higher than 80 kN, the BSF will decrease, resulting in a decline in angle buildup. The present method can be utilized to optimize the drilling parameters, BHA configuration and structure of bent-housing PDM.
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