﻿ 粒子冲击破岩深度的理论模型研究与室内试验

Theoretical Study and Experimental Tests of Rock Breaking Depth under Particle Impacting
WANG Fangxiang, WANG Ruihe, ZHOU Weidong, LI Luopeng
School of Petroleum Engineering, China University of Petroleum (Huadong), Qingdao, Shandong, 266580, China
Abstract: To accurately analyze the mechanism of impacts of particles on rocks during partical impact drilling and to optimize hydraulic parameters, it is necessary to perform theoretical calculations of particle impacting depth. Based on dynamic spherical expansion theory, correlation between resistance and intial incident velocity was derived. From differential equations of particle motion, the calculation model for the particle impacting depth was established. In addition, definite solution conditions and relevant algorithm were clarified. Based on actual calculation, the correlation between impact depth and incident velocity and that between the impact depth and time were studied. Experimental results showed theoreticalresults match well with experimental one. So the theoretical model can be used in theoretical analyses of particle impacting processes. Research results demonstrated that the dimensionless rock breaking depth would increase linearly with the the initial incident velocity and would increase logarithmically with time. Relevant research conclusions may provide necessary theoretical support for the application of particle impact drilling techniques.
Key words: particle     impact     rock breaking depth     cavity expansion     theoretical model     experimental test

1 粒子冲击破岩的理论模型 1.1 动态球形空腔膨胀理论

 图 1 球形空腔膨胀示意图 Fig.1 Schematic diagram of spherical cavity expansion

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1.2 粒子冲击过程分析

 图 2 粒子冲击岩石过程受力分析

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θ的积分区间为θ∈[0, φ]，根据图 2中的几何关系，可得：

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1.3 理论模型的建立与求解 1.3.1 粒子的冲击破岩深度与初始入射速度关系

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1.3.2 粒子冲击破岩深度与时间的关系

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2 室内试验及结果分析 2.1 室内试验

 图 3 粒子冲击破岩试验装置 Fig.3 Schematic diagram of experimental system for particle impacting on rocks

 图 4 花岗岩岩心粒子冲击破岩后岩样形态 Fig.4 Granite samples after breaking under particle impacting
2.2 结果分析 2.2.1 粒子初始入射速度对破岩深度的影响

 图 5 无因次破岩深度与粒子入射速度的关系曲线 Fig.5 Correlation between incident velocity and dimensionless depth

2.2.2 岩石破碎坑深度与冲击时间的关系

 图 6 无因次破岩深度-时间曲线 Fig.6 Time and dimensionless depth plot for rock breaking

3 结论与建议

1) 基于动态球形空腔膨胀理论建立了粒子冲击破岩深度的理论模型，并通过室内试验对理论计算结果进行了验证，结果表明该理论模型准确可行，可用于粒子冲击破岩过程的理论分析。

2) 无因次破岩深度随粒子初始入射速度增大呈线性增大，但并非粒子初始入射速度越大越好。考虑粒子冲击钻井的工程应用需求，粒子初始入射速度为150~160 m/s较为合适。

3) 无因次破岩深度随破岩时间增长呈现出对数增长的规律，由于岩石内空腔膨胀的过程是一个能量转化、积累和释放的过程，使无因次破岩深度呈快慢交替的阶跃式增长。

4) 对粒子冲击破岩的理论分析尚未完善，实际应用中，粒子以一定角度倾斜冲击破岩，建议考虑倾斜角度对破岩深度的影响，建立粒子倾斜冲击破岩深度的理论计算模型，以便全面分析粒子对岩石的冲击作用规律。

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#### 文章信息

WANG Fangxiang, WANG Ruihe, ZHOU Weidong, LI Luopeng

Theoretical Study and Experimental Tests of Rock Breaking Depth under Particle Impacting

Petroleum Drilling Techniques, 2016, 44(6): 36-41.
http://dx.doi.org/10.11911/syztjs.201606006