Build-up rate prediction of rotary steerable tools based on delay differentiation
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摘要:
【目的】旋转导向工具造斜率的准确预测是实现工具精准控制的前提，为掌握旋转导向底部钻具组合造斜率变化规律。【方法】 根据工具结构特点，采用欧拉−伯努利梁方程法对复合式旋转导向工具底部钻具组合进行受力分析。通过结合底部钻具几何关系，得到各节工具转角与钻头预钻进偏角计算方法，并将旋转导向工具各节点与钻头间距离作为空间延时周期，最终建立基于延时微分的旋转导向底部钻具组合的造斜率预测模型。该模型综合考虑了工具本身几何尺寸与结构、与地层有关的钻头切削各向异性、钻压以及工具材料及内外径有关的抗弯刚度等参数对造斜率的定量影响。【结果和结论】研究表明：(1)该模型预测结果与斯伦贝谢成熟应用的基于有限元分析的钻具造斜率预测软件仿真结果具有良好的吻合度，预测结果差值均保持在0.5(°)/30 m以内，符合工程要求。(2)同时该方法还可在钻具姿态测量短节的实际测量数据基础上补偿钻头与测量单元间距带来的测量误差问题，为解决测量盲区提供一种新的途径。基于空间延时微分的造斜率预测方法为旋转导向系统底部钻具组合的结构优化及钻井参数优选提供理论依据和快速分析手段。建立的模型易于仿真和移植，在实际工程应用中可获取较好的实时响应，为基于数字孪生的旋转导向工具研发提供准确的钻具运动模型基础。
Abstract:[Objective] Accurate build-up rate prediction of rotary steerable tools is a prerequisite to achieve the precise control of tools. In order to grasp the variation law of the build-up rate of the rotary steerable bottom-hole assembly (RSBHA). [Methods] Based on the structural charaeteristics of the tool, the Euler-Bernoulli beam equation method is used to analyz the forces outing on the composite RSBHA. At the same time, the calculation method of the tool deflection angle in different sections and the bit pre-drilling deflection angle was obtained with consideration to the geometric relationship of the bottom-hole assembly, and the distance between the connecting points of rotary steerable tool and bit was taken as the spatial delay period. Finally, a prediction model for the build-up rate of the RSBHA based on delay differentiation was established. This model comprehensively considers the qualitative influence of parameters, such as the geometric size and structure of the tool itself, the cutting anisotropy of the drill bit related to the formation, the weight on bit, and the bending stiffness related to the tool material and the inner and outer diameters, on the build-up rate. [Results and Conclusions] The study shows that: (1) The predicted results of this model are in good agreement with the simulation results of Schlumberger's mature build-up rate prediction software based on the finite element analysis, and the difference between the predicted results is maintained within 0.5 (°)/30 m, which meets the engineering requirements. (2) This method can also compensate for the measurement error caused by the distance between the drill bit and the measurement unit based on the actual measurement data of the drilling tool attitude gauging nipple, providing a new way to solve the problem of unmeasurable are. This build-up rate prediction method based on spatial delay differentiation provides theoretical basis and rapid analysis means to optimize the structure of RSBHA and the drilling parameters. The established model is easy to simulate and transplant, and can obtain good real-time response in practical engineering applications, which provides an accurate foundation of drilling tool movement model for the development of rotary steerable tools based on digital twins.
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图 4 RSBHA钻进模型
注：${L_1}$为钻头至万向节之间的工具长度，m；${L_2}$为万向节至下扶正器之间的工具长度，m；${L_3}$为上扶正器至万向节之间的工具长度，m；$ {L_4} $为上扶正器至挠性接头之间的工具长度，m；${L_5}$为下一节钻柱长度，m；$p$为沿轴向施加在RSBHA端部的钻压，kN；${S_2}$、${S_3}$为扶正器与井眼的间隙，cm；${F_{\text{s}}}$为导向单元液压模块推出后，以下扶正器为支点造斜时所受到的等效推靠力，kN。
Fig. 4 RSBHA drilling model
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图 5 RSBHA受力分析
注：${M_{\text{j}}}$、$ {M_{\text{f}}} $为万向节处与挠性接头处的弯矩，N·m；${p_{\text{b}}}$、${p_{\text{j}}}$分别为钻头处钻压与万向节处钻压，kN。
Fig. 5 Stress analysis of RSBHA
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图 6 造斜率预测仿真模型
注：0、1、2、3、4为输入或输出端口编号。
Fig. 6 Simulation model for prediction of build-up rate
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图 7 造斜率与井斜角计算结果曲线
Fig. 7 Calculation results of build-up rate and hole inclination angle
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图 8 相同参数下有限元分析软件造斜率预测结果
Fig. 8 Build-up rate prediction results using finite element analysis software under the same parameters
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图 9 相同参数下有限元分析软件井斜角变化曲线
Fig. 9 Variation of hole inclination angle using finite element analysis software under the same parameters
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图 10 不同参数下本模型与有限元模型造斜率结果对比
Fig. 10 Comparison of build-up rate results between this model and the finite element model under different parameters
表 1 系统中RSBHA各部分长度
Table 1 Length of each part of RSBHA in the system
RSBHA不同单元长度/m 数值 钻头至万向节 0.64 万向节至下扶正器 0.24 上扶正器至万向节 4.27 上扶正器到挠性接头 6.1 下一节钻柱 9.1 
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表 2 工具特性与钻井参数
Table 2 Tool characteristics and drilling parameters
工具特性与钻井参数 数值 钻头各向异性Ka 1/30 抗弯刚度/(N·m−2) 685000 等效推靠力Fs/kN 22.78 钻压p/kN 100 下扶正器与井眼间隙S2/cm 0.16 上扶正器与井眼间隙S3/cm 0.16
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