Prediction model of build-up rate for bottom-hole assembly in rotary drilling

Ultra-deep drilling plays a crucial role in the development of oil and gas resources, and wellbore trajectory control is key to ultra-deep drilling. While conventional rotary-steerable drilling technology faces limitations due to extreme conditions such as high temperature, high pressure, etc. In ultra-deep drilling, positive-displacement motors (PDM) have become a viable technological alternative owing to their stability and adaptability. Nevertheless, there remains a deficiency in an effective and dependable methodology to accurately depict the mechanical behavior of PDM in the rotary drilling mode. This study proposes a novel model that illustrates the mechanical behavior of the bottom hole assembly (BHA) during rotary drilling, integrating both mechanical model and numerical simulation techniques. Firstly, the mechanical behavior of the BHA under the same parameter is obtained by the mechanical method and numerical simulation respectively. The error compensation mechanism is introduced, and the difference between the two methods is used to correct the mechanical model so that the mechanical method is more suitable for depicting the mechanical behaviors of the BHA during rotary drilling. Then the new mechanical model is combined with the prediction model of the build-up rate to predict the build-up rate of BHA under rotary drilling. A conversion factor is further introduced to amend the prediction mode. The correlation between the calculated and measured values exceeds 90%, thereby meeting the predefined accuracy targets. The results show that the new mechanical model can well depict the mechanical behavior of the drill under rotating conditions. And it can be combined with the prediction model of the build-up rate to predict the build-up capability of BHA in rotary drilling more accurately. Next, to meet the two needs of the high rate of penetration (ROP) and the wellbore trajectory control in the field, a multi-objective optimization model is established, with the maximization of the ROP and minimization of the build-up rate as the optimization objectives. Multi-objective optimization of the drilling parameters, tool structural parameters, and wellbore trajectory parameters is performed. At last, the optimization model is validated through practical examples. After optimization, the ROP reflects a modest reduction of 5.35% less, however, the build-up rate indicates a significant decrease of 56.16%. It provides a very good control of the build-up rate. The results show that this optimization model can better control well deflection while maintaining ROP. Our work can more accurately describe the mechanical behavior of BHA under rotating conditions, and can more accurately predict the buildup rate of BHA under rotating conditions. The multi-objective optimization model can guide the field to select drilling tool parameters and drilling parameters to guarantee both the high ROP and well trajectory control.