A New Method of Predicting the Bridging Lost Circulation Materials and Their Particle Size Distribution
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摘要: 准确快速预测堵漏材料及其配方粒度分布是桥接堵漏配方数字化、智能化设计的关键。针对现有桥接堵漏材料及其配方粒度分布的实验测试法和粒度分布函数方法的不足，提出了基于分段三次Hermite插值方法的桥接堵漏材料及其配方粒度分布的表征及快速预测新方法。基于单一桥接堵漏材料粒度分布实测数据，对比分析了新方法与常用粒度分布函数方法对堵漏材料粒度分布表征的适用性；提出了新方法预测了不同堵漏配方的粒度分布，并利用实测数据验证了新方法的可靠性。结果表明，相较于常用粒度分布函数方法，基于分段三次Hermite插值法的新方法对桥接堵漏材料配方粒度分布的表征更加准确；堵漏配方的预测累积粒度分布曲线与实测数据高度吻合；新方法不需要预先设定粒度分布函数形式，且适用于具有多峰粒度分布的颗粒物料，新方法可用于预测不同配比颗粒混合物的粒度分布。Abstract: Accurate and rapid prediction of the types of lost circulation materials (LCMs) and their particle size distribution (PSD) plays a key role in the digital and intelligent design of bridging lost circulation material slurry. A new method of characterizing and rapid predicting the bridging lost circulation materials and the PSD thereof is presented based on the PCHIP method in an effort to overcome the deficiencies existed in the methods presently in use. Using the data obtained in the experiments on the PSD of a single bridging LCM, the applicability of the new method and the commonly used particle size distribution function methods in characterizing the PSD of LCMs was compared and analyzed. The new method was used to predict the PSDs of different LCM compositions, and the data collected in the measurement were used to verify the reliability of the new method. It was demonstrated that, compared with the commonly used PSD function methods, the new method can be used to more accurately characterize the PSDs of bridging LCM compositions. The cumulative PSD curve predicted with the new method is highly consistent with the measured data. Without the need of pre-setting a PSD function, the new method is suitable for predicting the PSD of particle matters with multiple peaks. The new method can be used to predict the PSDs of mixtures with different ratios of particle sizes.
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表 1 堵漏材料激光累积特征粒度值数据
材料
名称特征粒度/μm 10% 30% 40% 50% 70% 90% 100% 蛭石 41 109 141 173 241 369 800 核桃壳 31 77 117 172 341 865 2000 碳酸钙 111 251 287 321 398 549 1135 
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表 2 堵漏材料粒度分布不同表征方法结果对比
材料
名称特征
粒度实测
值/μm分段三次Hermite
插值方法R-R函数
拟合方法预测
值/μm相对
误差/%预测
值/μm相对
误差/%蛭石 D10 41 39.775 −2.987 45.818 11.751 D50 173 172.507 −0.285 166.784 −3.593 D90 369 369.833 0.226 379.418 2.823 核桃壳 D10 31 30.348 −2.103 20.384 −34.245 D50 172 171.841 −0.093 180.991 5.227 D90 865 847.352 −2.040 728.158 −15.820 碳酸钙 D10 111 107.490 −2.28 150.843 35.895 D50 321 321.413 0.129 322.425 0.444 D90 549 551.513 0.458 522.387 −4.848
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表 3 堵漏配方特征粒度值预测与实测结果
配方组成 特征
粒度实测
值/μm预测
值/μm相对
误差/%蛭石∶核桃壳∶
碳酸钙=5∶1∶1D10 39 36.4 −6.6 D50 192 189.1 −1.5 D90 490 478.4 −2.4 蛭石∶核桃壳∶
碳酸钙=1∶5∶1D10 36 31.9 −11.3 D50 187 188.2 0.6 D90 829 777.7 −6.2 蛭石∶核桃壳∶
碳酸钙=1∶1∶5D10 46 41.5 −9.8 D50 285 280.5 −1.6 D90 580 573.3 −1.2
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