Evaluation model of rock-breaking specific energy for PDC cutter based on fractal characteristics of rock cutting morphology

doi:10.3785/j.issn.1006-754X.2025.02.116

Chinese Journal of Engineering Design

2025, Vol. 32

Issue (1): 23-31 DOI: 10.3785/j.issn.1006-754X.2025.02.116

Theory and Method of Mechanical Design

Evaluation model of rock-breaking specific energy for PDC cutter based on fractal characteristics of rock cutting morphology

Wenhao HE^1,²(

),Xinlong LI^1,²,Runqing ZHANG^1,²,Li LIU^1,²,Huaizhong SHI³(

),Zhongwei HUANG³,Chao XIONG³,Zhenliang CHEN⁴,Hongzhi WU³

^1.Beijing Key Laboratory of Oil and Gas Optical Detection Technology, China University of Petroleum (Beijing), Beijing 102249, China
^2.Basic Research Center for Energy Interdisciplinary, China University of Petroleum (Beijing), Beijing 102249, China
^3.State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum (Beijing), Beijing 102249, China
^4.Petroleum Engineering Research Institute Co. , Ltd. , Sinopec Group, Beijing 102200, China

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Abstract

As the exploration center of oil and gas resources in China moves towards deep and ultra-deep layers, the difficulty of oil and gas exploration has been increasing, which can be recognized poor drilling capacity and low rate of penetration resulted from high strength and strong abrasion of deep hard formation rocks. In order to improve the rock-breaking performance of deep hard rock bits, conical cutters are widely used in the design of hybrid-cutters PDC (polycrystalline diamond compact) bits. However, the rock-breaking volume of conical cutter is small, and its cutter arrangement method needs more comprehensive theoretical support. Therefore, taking the rock-breaking specific energy as the objective function, a rock-breaking specific energy evaluation model for the PDC cutter based on the fractal characteristics of rock cutting morphology was established by quantifying the physical parameters such as cutting force and cutting energy consumption of different types of PDC cutters during the rock-breaking process and using the maximum particle size of rock cuttings and fractal dimension of rock cutting particle size. Meanwhile, the rock-breaking performance of conical PDC cutter was investigated by comparing with the conventional planar PDC cutter, and the effects of cutting depth, cutting angle and cutting speed on the rock-breaking performance were analyzed. The results showed that the conical PDC cutter was suitable for rock breaking with large cutting depth and low energy consumption, while the conventional PDC cutter was suitable for rock breaking with high speed and small cutting depth. The cutting angle of two kinds of PDC cutters was recommended to be about 20°. Conical PDC cutters were suitable for arrangement at the central vertex and crown area of the hybrid-cutters PDC bit, while conventional PDC cutters were suitable for encrypted arrangement from the nose to shoulder area of the bit. The research results can provide theoretical basis for revealing the particle size distribution law of rock cuttings generated by PDC cutter breaking rock and the design of hybrid-cutters PDC bits.

Key words： conical PDC cutter cutting and breaking rock fractal dimension particle size of rock cutting rock-breaking specific energy

Received: 01 December 2023 Published: 04 March 2025

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Corresponding Authors: Huaizhong SHI E-mail: hwh@cup.edu.cn;shz@cup.edu.cn

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	Articles by authors
	Wenhao HE
	Xinlong LI
	Runqing ZHANG
	Li LIU
	Huaizhong SHI
	Zhongwei HUANG
	Chao XIONG
	Zhenliang CHEN
	Hongzhi WU

Cite this article:

Wenhao HE,Xinlong LI,Runqing ZHANG,Li LIU,Huaizhong SHI,Zhongwei HUANG,Chao XIONG,Zhenliang CHEN,Hongzhi WU. Evaluation model of rock-breaking specific energy for PDC cutter based on fractal characteristics of rock cutting morphology. Chinese Journal of Engineering Design, 2025, 32(1): 23-31.

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https://www.zjujournals.com/gcsjxb/10.3785/j.issn.1006-754X.2025.02.116 OR https://www.zjujournals.com/gcsjxb/Y2025/V32/I1/23

基于岩屑形貌分形特征的PDC齿破岩比功评估模型

随着我国油气资源探测重心不断向深层、超深层迈进，油气勘探难度不断增大，且深层硬地层岩石强度高及研磨性强，可钻性变差，导致整体机械钻速偏低。为提高深层硬岩的钻头破岩性能，锥形齿被广泛应用于混合布齿PDC（polycrystalline diamond compact，聚晶金刚石复合片）钻头设计，但锥形齿的破岩体积较小，其布齿方法需要更全面的理论支撑。为此，以破岩比功为目标函数，通过明确不同类型PDC齿在切削破岩过程中的切削力与切削能耗等物理参数，利用最大岩屑粒径和岩屑粒径分形维数建立了基于岩屑形貌分形特征的PDC齿破岩比功评估模型。同时，通过与常规平面形PDC齿对比，探究了锥形PDC齿的破岩性能，并分析了切削深度、切削角度与切削速度对PDC齿破岩性能的影响规律。结果表明，锥形PDC齿适用于大切削深度低能耗破岩，而常规PDC齿适用于高速小切削深度破岩，且2种PDC齿的工作角度均推荐为20°左右。锥形PDC齿适合布置在混合布齿PDC钻头的中心顶点和冠顶区域，而常规PDC齿适合加密布置在钻头的鼻部至肩部区域。研究结果可为揭示PDC齿破岩生成的岩屑粒径分布规律和指导混合布齿PDC钻头设计提供理论依据。

关键词： 锥形PDC齿, 切削破岩, 分形维数, 岩屑粒径, 破岩比功

Fig.1 Rock-breaking mechanics model of PDC cutter cutting with uniform speed

Fig.2 Testing device for PDC cutter cutting and breaking rock

Fig.3 Variation curve of mass fraction of rock cuttings generated by PDC cutter breaking rock with particle size

齿形	切削参数			水平切削力 $F h / N$	岩屑粒径分形维数 $D l$	最大岩屑粒径 $l m a x / m m$	总破岩体积 $V T / c m 3$	岩性相关系数 $C$
齿形	深度 $d / m m$	角度 $θ / (°)$	速度 v/(mm/s)	水平切削力 $F h / N$	岩屑粒径分形维数 $D l$	最大岩屑粒径 $l m a x / m m$	总破岩体积 $V T / c m 3$	岩性相关系数 $C$
常规PDC齿	0.3	20	5.0	246.60	2.68	1.45	0.08	64.53
	0.6	20	5.0	635.81	2.64	1.76	0.26	227.37
	0.9	20	5.0	1 067.25	2.52	1.89	0.54	404.26
	1.2	20	5.0	1 589.72	2.52	3.09	0.86	486.23
	1.5	20	5.0	2 161.02	2.52	5.26	1.21	501.49
	0.9	10	5.0	1 025.10	2.49	1.89	0.57	411.40
	0.9	20	5.0	1 065.94	2.52	1.88	0.54	402.77
	0.9	30	5.0	1 290.98	2.65	1.73	0.54	420.89
	0.9	20	5.0		2.52	1.91
	0.9	20	10.0		2.49	2.12
	0.9	20	15.0		2.48	2.17
	0.9	20	20.0		2.48	2.20
锥形PDC齿	1.0	20	5.0	1 282.29	2.67	2.36	0.42	309.46
	1.5	20	5.0	1 660.66	2.64	7.34	0.75	361.11
	2.0	20	5.0	2 115.15	2.62	14.45	1.12	393.77
	2.5	20	5.0	2 645.76	2.55	20.91	1.65	410.14
	3.0	20	5.0	3 236.82	2.67	53.90	2.37	376.95
	2.0	10	5.0	1 650.91	2.65	10.72	0.79	309.46
	2.0	20	5.0	2 115.15	2.62	14.45	1.12	393.77
	2.0	30	5.0	2 516.55	2.62	15.23	1.02	393.77
	1.0	20	5.0	1 290.00
	1.0	20	10.0	1 304.00
	1.0	20	15.0	1 274.00
	1.0	20	20.0	1 292.00
	1.0	20	25.0	1 291.00

Table 1 Key parameters of PDC cutter rock-breaking specific energy evaluation model

齿形	参数	关键参数拟合公式	确定系数 $r 2$
常规PDC齿	F_h	$- ? 628.632 ? 9 + 1 ? 594.251 x 1 ? + 13.293 ? 915 x 2 + 370.999 ? 04 x 1 - ? 0.9 2 + 0.859 ? 677 (x 2 - ? 20) 2$	0.999 9
	D_l	$2.561 ? 879 ? 1 - ? 0.139 ? 8 x 1 + 0.007 ? 85 x 2 - ? 0.006 ? 665 x 3$	0.790 4
	l_max	$- ? 0.407 ? 394 + 2.984 ? 364 ? 9 x 1$	0.700 8
	C	$9.732 ? 238 ? 9 + 397.108 ? 84 x 1 - ? 110.530 ? 8 (x 1 - ? 0.9) 2$	0.994 5
锥形PDC齿	F_h	$- ? 623.423 ? 4 + 934.350 ? 06 x 1 + 43.282 ? 1 x 2 + 152.242 ? 34 x 1 - ? 1.833 ? 33 2 - ? 0.314 ? 206 (x 1 - ? 1.833 ? 33) 2$	1.000 0
	D_l	$2.796 ? 095 ? 2 - ? 0.085 ? 729 x 1 - ? 0.063 ? 343 (x 1 - ? 1.833 ? 33) 2$	0.908 5
	l_max	$- ? 15.035 ? 46 + 12.197 ? 243 x 1 + 0.225 ? 426 ? 3 x 2$	0.983 6
	C	$242.590 ? 57 + 54.885 ? 017 x 1 + 2.261 ? 666 ? 7 x 2 - ? 0.708 ? 972 (x 2 - ? 20) 2$	0.986 7

Table 2 Fitting results of key parameters of PDC cutter rock-breaking specific energy evaluation model

Fig.4 Fitting results of predicted and measured values of PDC cutter rock-breaking specific energy

Fig.5 Variation law of horizontal cutting force and rock-breaking specific energy of PDC cutters with cutting depth （θ=20°， v=5 mm/s）

Fig.6 Variation law of horizontal cutting force and rock-breaking specific energy of PDC cutters with cutting angle (d=2 mm, v=5 mm/s)

Fig.7 Variation law of horizontal cutting force and rock-breaking specific energy of PDC cutters with cutting speed (d=2 mm, θ=20°)


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