Mechanism of damage-induced fracture formation in shale reservoir penetrated by shaped charge jet
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摘要: 为研究药型罩对聚能射孔弹侵彻页岩储层的射孔和损伤致裂效果的影响机理，建立了射孔弹-空气-页岩三维模型，设置药型罩的锥角分别为50°、60°、70°和80°，壁厚分别为0.5、1.0和1.5 mm，材料分别为铜、钢、钛和钨。利用ANSYS/LS-DYNA软件进行数值计算，分别从射流速度与形态、页岩射孔效果及页岩孔裂隙形成规律特征等进行系统性分析。研究结果表明：在射孔弹结构中，随着药型罩锥角的减小，射流速度提高、杵体速度降低、侵彻深度增大同时开孔孔径减小。在一定范围内，适当减小药型罩的壁厚，可以提高射流速度、减小杵体质量、增大侵彻深度和开孔倾斜度。药型罩材料对射流速度、杵体结构和页岩射孔效果均有显著影响，其中钨药型罩射孔弹的侵彻深度最大但开孔孔径最小，钛药型罩射孔弹的侵彻深度最小但开孔倾斜度最大，铜比钢药型罩射孔弹的侵彻深度略大但开孔孔径略小。通过研究不同对照组的页岩孔裂隙形成规律特征发现，页岩孔裂隙发育主要发生在杵体对页岩的再扩孔阶段，减小射流初始扩孔孔径、增大杵体直径、提高杵体速度，可以促进页岩孔裂隙发育程度。
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关键词:
- 聚能射孔 /
- 页岩储层 /
- 药型罩 /
- 裂隙扩展 /
- 射孔弹-空气-页岩三维模型
Abstract: To study the influence mechanism of shaped charge liner on the perforation and damage-induced fracturing effect of shale reservoir by shaped charge penetration, a three-dimensional perforating charge-air-shale model was established. The cone angles of the liner are 50°, 60°, 70°, and 80°. The liner thicknesses are 0.5 mm, 1.0 mm, and 1.5 mm. And the materials of the liner are copper, steel, titanium, and tungsten. The numerical calculation was carried out using the ALE-Lagrangian coupling method in the non-linear program ANSYS/LS-DYNA. The ALE method was used to describe shell, explosive, liner, and air, while the Lagrangian method was used to describe the shale reservoir. A systematic analysis was carried out on the aspects of jet velocity and shape, shale perforation effect, and fracture extension characteristics of shale. The results show that with the decrease of the cone angle of the liner, the jet velocity and penetration depth increase, and the pestle velocity and perforation diameter decrease. In a certain range, with the decreasing liner thickness, the jet velocity, penetration depth, and perforation inclination increase, and the mass of the pestle decrease. The liner material significantly influences the jet velocity, pestle structure, and shale perforation effect. Among them, the penetration depth of perforating charge with a tungsten liner is the largest, but the perforation diameter is the smallest, the penetration depth of perforating charge with a titanium liner is the smallest, but the perforation inclination is the largest, and the penetration depth of perforating charge with a copper liner is slightly larger than that with a steel liner, but the perforation diameter is slightly smaller. Because the detonation pressure has an obvious difference before and after the detonation wave transmitted to the end of the explosive, which affects the jet velocity and penetration depth, the charge with a shell has a greater jet velocity and penetration depth than the charge without a shell. By comparing the fracture extension characteristics of shale in different groups, it is found that the fracture extension of shale mainly occurs in the stage of re-reaming of a pestle on shale. It is concluded that the material and structure of the liner have a significant influence on the shaped charge jet and its penetration effect, which then affects the damage-induced fracture formation and extension in shale. The fracture extension of the shale can be promoted by reducing the initial perforation diameter of penetration, increasing the diameter of the pestle, and increasing the speed of the pestle. -
在自然灾害救援和非战争行动中, 经常面临对大块度障碍物快速破除的难题。普通民用爆破中通常采取先机械钻孔、后装药起爆的方法进行施工, 但在缺少时间、机械设备、电力和人员等条件下, 一般方法无法短时内快速清除这些大块度障碍, 常常造成救援目标生命及财产的重大损失。考虑到应急保障的高时效性, 采用串联装药技术更有效[1]。张先锋等[2]、王树有等[3]、曾必强等[4]和涂候杰等[5]分别对串联战斗部前级爆轰对后级的影响进行了数值模拟分析和实验研究, 王成等[6]对同口径串联装药前后级成型关系进行了实验研究。传统的破-爆型串联战斗部前级聚能开孔装药能力有限, 在大块度障碍物破除应用中效果不理想。因此, 本文中根据在坚硬目标上开孔的需要, 提出一种新式破-破型串联爆炸成型弹丸(explosively formed projectile, EFP)聚能装药结构作为多级串联战斗部的前级开孔装药, 并对串联EFP装药隔爆结构和装药前后级延时匹配进行优化设计; 利用有限元程序LS-DYNA对不同起爆延时条件下串联EFP装药侵彻进行数值计算, 并进行实验验证。
1. 串联装药结构
1.1 单级EFP装药选择
本文中选择前期优化设计[7]得到的Ø65 mm球缺型变壁厚EFP装药结构方案。装药结构参数为:炸药采用JH-2, 其密度为1 700 kg/m3, 装药长径比为1.0;药型罩采用紫铜材料, 罩顶厚2.1 mm, 罩内表面曲率半径为67 mm, 外表面曲率半径为62 mm。
1.2 串联EFP关键技术
为确保精确控制两级EFP装药的起爆时间, 采用本课题专门设计的精确延时起爆控制器, 设定延时间隔精度为0.1 μs, 可通过专用的应用软件在0~200 μs区间任意设定延时, 图 1是2路起爆控制信号输出时示波器采集到的触发信号波形。
1.3 隔爆体设计原则
本研究串联EFP采用逆序起爆方式, 前级装药爆炸后产生的爆轰产物和空气冲击波不可避免地作用在后级装药上, 引起后级EFP形状和性能的改变, 从而改变后级EFP的侵彻性能。因此要设计一种简单的隔爆结构, 降低前后级之间的影响。本研究的隔爆结构中选用的聚氨酯泡沫材料是一种密度小、隔爆性能好的抗冲击波材料, 广泛应用于国防、军事领域[8]。
2. 数值模拟分析
2.1 串联EFP数值模型
为了分析隔爆体及起爆延时对串联EFP装药成型性能的影响, 利用有限元软件LS-DYNA3D对其成型过程进行数值模拟, 串联装药模型如图 2所示。模型涉及聚能装药成型和侵彻2个部分, 采用流-固耦合算法来分析此类情况更贴近实际。模型中, 炸药、药型罩、隔爆体和空气等介质均采用Euler算法, 靶板则采用Lagrange算法。串联EFP装药为8701炸药, 采用高能炸药材料模型和JWL状态方程描述; 药型罩材料为军用紫铜, 用Grüneisen状态方程和Johnson-Cook本构模型描述[9-10]; 隔爆体为聚氨酯泡沫, 用Grüneisen状态方程和Elastic_Plastic_Hydro本构模型描述, 各材料状态方程参数[11-12]如表 1~3所示, 其中:ρ为密度, v为爆速, pCJ为炸药的C-J爆压, E0为材料的初始内能, A、B、R1、R2和ω为炸药的材料常数, C为材料的us-up截距, S1、S2和S3为斜度系数, γ0为材料的Grüneisen系数, a为γ0的一阶体积修正。
表 1 JH-2炸药计算参数Table 1. Computational parameters for JH-2ρ/(g·cm-3) v/(m·s-1) pCJ/GPa A/GPa E0/(J·m-3) B R1 R2 ω 1.70 8 400 30 56.4 10.0 6.801 4.1 1.3 0.36 表 2 紫铜和聚氨酯泡沫计算参数Table 2. Computational parameters for copper linerρ/(g·cm-3) C/(m·s-1) S1 S2 S3 γ0 a E0 8.96 4 750 3.8 2.74 0.125 1.346 0.34 0.0 表 3 聚氨酯泡沫计算参数Table 3. Computational parameters for polyurethane foamρ/(g·cm-3) C/(m·s-1) S1 S2 S3 γ0 a E0 0.05 886 0.78 0.0 0.0 1.55 0.00 0.0 2.2 不同炸高条件下单级EFP侵彻过程分析
要充分发挥两级串联EFP装药的侵彻能力, 首先需要确定装药的有利炸高。如果炸高太小, EFP弹丸还未完全成型, 其速度和长径比仍在快速变化中, 侵彻深度和穿孔直径等侵彻效果随炸高变化而发生较大改变。但炸高达到一定程度后, EFP成型性能已经基本稳定时, 侵彻效果变化逐渐减小。文中选取了6种不同炸高进行了数值模拟和实验, 结果如图 3所示, 其中:H为炸高, D为装药直径。
对比图 3中6种炸高条件下钢靶剖面图得出:在炸高与装药直径比小于2.8时, EFP侵彻钢靶孔径较大, 但EFP未得到有效拉伸, 侵彻深度不大; 随着炸高的增加, 侵彻深度逐渐增加, 同时孔径逐渐减小; 在炸高与装药直径比大于3.2时, 炸高增加, 侵彻深度与孔径基本不变。表 4为不同炸高下EPF侵彻钢靶的模拟和实验结果, 其中h为侵彻深度, d为侵彻孔径。分析表 4中的数据发现, 数值模拟与实验结果在侵彻深度和孔径大小上吻合较好, 误差在5%以内, 说明数值模拟结果较贴近实际, 为后面串联装药模拟提供了一种可行的方法。
表 4 EFP侵彻钢靶数值模拟与实验数据Table 4. Simulational and experimental results of EFP penetrating steel targetsH/mm h/D d/D 模拟值 实验值 模拟值 实验值 150 0.73 0.74 0.557 0.563 180 0.80 0.78 0.525 0.530 210 0.85 0.86 0.498 0.495 240 0.89 0.88 0.477 0.472 270 0.90 0.89 0.460 0.454 300 0.90 0.90 0.455 0.451 2.3 不同隔爆体形状串联EFP成型过程数值模拟
隔爆效果不仅与材料性能有关, 隔爆体的形状对后级装药成型影的响也十分巨大。文中选取了3种不同结构的隔爆体进行分析。图 4为圆柱形隔爆体、锥口向上隔爆体和锥口向下3种条件下串联EFP装药200 μs时刻后级EFP成型状态。通过对比图 4中的3种后级EFP形态, 发现隔爆体结构的不同对减少前级爆轰对后级成型的影响差异很大。采用圆柱形隔爆体时后级EFP基本成型, 但头尾连续性差, EFP侵彻能力大大降低; 采用圆柱底部挖出一个锥形空腔且锥口向上的隔爆体, 隔爆效果差, 后级弹丸基本无翻转, 后级装药侵彻能力基本消失; 锥口向下的隔爆体, 隔爆效果较理想, 可作为串联EFP的隔爆结构基本形状, 后级EFP成型较好, 但在前级爆轰场影响下, EFP长径比增大, 需要进一步优化前后级起爆时间, 来提高后级EFP的成型效果。
图 4 不同隔爆体200 μs时刻后级EFP形态Figure 4. Shapes of the postpositive EFP charge at 200 μs with different explosion-proof bodies2.4 不同延时串联EFP侵彻过程数值模拟分析
串联EFP前后级延时起爆时间Δt对后级EFP的成型和侵彻性能影响很大[8]。在两级装药间距一定的情况下, 合理控制延时起爆时间Δt, 使后级EFP受前级装药爆轰场影响最小, 才能最大限度地保持后级EFP装药的成型性能。分别对5种不同延时条件下串联EFP侵彻靶板进行数值模拟, 结果见表 5。
表 5 串联EFP装药侵彻数值模拟结果Table 5. Simulation results of tandem EFP penetrationΔt/μs h/mm h/D d/mm d/D 0 92 1.415 22.2 0.341 10 103 1.584 21.6 0.332 20 115 1.769 21.4 0.329 25 104 1.600 21.7 0.327 30 98 1.507 21.3 0.334 图 5给出了侵彻深度和侵彻孔径随起爆延时的变化关系。分析图 5中孔径和孔深的变化规律可以发现, 随着前后级延时起爆时间的增加, 后级EFP的侵彻深度先增大后快速减小, 说明前级爆轰场到达后级装药时, 会严重影响后级EFP的成型。所以, 该串联结构较为合理的延时为20 μs。图 6为同时起爆和延时20 μs的数值模拟侵彻结果。
图 5 开孔深度和直径随起爆延时的变化Figure 5. Variation of penetration depth and aperture with delay time3. 串联EFP隔爆结构实验研究
3.1 不同隔爆形体状串联EFP侵彻实验
根据前期研究[1]得到的隔爆体形状对串联EFP装药侵彻性能的影响规律, 进行6发串联EFP侵彻的验证性实验。实验分3组, 分别采用圆柱形、锥口向上和锥口向下3种隔爆体, 每组进行2发实验。图 7为3种不同条件下EFP的侵彻性能实验结果。
图 7 不同隔爆体串联EFP侵彻结果Figure 7. Penetration results of tandem EFPs with different explosion-proof bodies表 6给出了串联装药对靶板的侵彻结果, 通过对比可以发现, 同时起爆条件下, 锥口向下的隔爆体侵彻深度明显优于其他2种结构。但后级侵彻的开孔孔径较小, 难以满足后级爆破子弹随进要求, 需进一步优化。
表 6 串联EFP装药侵彻钢靶实验结果Table 6. Experimental results of tandem EFPs penetrating steel targets隔爆结构 h/mm d/mm 圆柱形 82 15.2 锥口向上 60 16.6 锥口向下 98 16.3 3.2 不同延时条件下串联EFP侵彻钢靶实验
图 8为实验设置图。前级装药炸高取210 mm, 装药间距150 mm条件下, 采用中心起爆方式, 使用8#电雷管同时起爆两级装药, 分别对延时0、10、20、25和30 μs等5种情况进行侵彻靶板分别进行2发实验, 结果依次记录为A1~A10。为对比优化后的侵彻性能, 同时进行2组分2次单独侵彻实验作为参照, 结果记录为B1和B2。侵彻结果显示串联EFP开孔形状前后基本一致。后级EFP受到前级装药爆轰场的影响, 速度和长径比都不可避免有所下降, 开孔直径比前级EFP小。
表 7给出了不同延时条件下的侵彻深度和最小侵彻孔径的实验结果。由表 7可以看出:随着延时的增加, 后级EFP受到前级爆轰场影响, 形状变得更加细长, 侵彻的孔径逐渐变小; 而穿孔深度先逐渐增加, 随后逐渐减小。这说明起爆时间间隔太大, 前级爆轰场到达后级装药后, 会严重影响后级EFP的成型, 大大降低了后级EFP的速度。将表 7与表 5进行比较, 可以看出两者最大仅相差3.7%, 可见实验结果与数值模拟结果吻合较好。
表 7 串联EFP装药侵彻钢靶结果Table 7. Experimental results of tandem EFPs penetrating steel targets编号 Δt/μs h/mm d/mm A1 0 94 21.4 A2 0 95 21.3 A3 10 105 21.0 A4 10 102 21.2 A5 20 117 20.6 A6 20 115 20.8 A7 25 107 20.4 A8 25 108 20.3 A9 30 100 20.3 A10 30 102 20.2 B1 121 21.6 B2 119 21.8 图 9所示靶板, 依次为分2次侵彻、延时0和延时20 μs侵彻实验结果。可以看出:同时起爆(Δt=0)时, 后级EFP长径比和速度受影响较大, 侵彻孔径较分2次侵彻时减小0.4 mm, 后级EFP侵彻深度只有分2次侵彻时第2次侵彻深度的58.9%, 侵彻效果大大降低。延时起爆20 μs时, 侵彻孔径较分2次侵彻时减小1 mm, 两级整体侵彻深度为分2次侵彻时的96.7%, 这体现了延时起爆对后级EFP侵彻性能的重要性。
图 9 不同起爆延时下串联EFP装药侵彻钢靶实验结果Figure 9. Tandem EFP charge penetrating steel targets with different delay time4. 结论
(1) 在已有的研究成果基础上, 分析了隔爆体形状和前后级装药延时对串联EFP侵彻能力的影响, 得到了较合理的串联装药结构。
(2) 通过数值模拟和实验研究, 对串联EFP装药隔爆结构形状和延时匹配进行了比较分析, 延时起爆20 μs时, 串联侵彻深度为分2次侵彻的96.7%, 比同时起爆侵彻深度提高了约22.8%, 大大提高了后级装药的利用效率。这可为下一步多级串联装药研究提供依据。
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图 1 DP46RDX42-Y型射孔弹及其三维模型
Figure 1. Perforating charge and its three-dimensional model
图 2 三维有限元模型及其前处理
Figure 2. The three-dimensional finite element model and its preprocessing
图 4 药型罩的锥角对射流头部速度和页岩侵彻深度的影响
Figure 4. Effect of cone angle of liner on jet tip velocity and shale penetration depth
图 5 药型罩的锥角对射流形态及速度分布的影响
Figure 5. The jet shape and velocity distribution of different cone angle groups
图 6 不同锥角组的开孔半径-侵彻深度变化曲线
Figure 6. Perforation radius-penetration depth curves of different cone angle groups
图 7 药型罩的壁厚对射流头部速度和页岩侵彻深度的影响
Figure 7. Effect of thickness of liner on jet tip velocity and shale penetration depth
图 8 药型罩的壁厚对射流形态及速度分布的影响
Figure 8. The jet shape and velocity distribution of different thickness groups
图 9 不同壁厚组的开孔半径-侵彻深度变化曲线
Figure 9. Perforation radius-penetration depth curves of different thickness groups
图 10 药型罩的材料对射流头部速度和页岩侵彻深度的影响
Figure 10. Effect of liner material on jet tip velocity and shale penetration depth
图 11 药型罩的材料对射流形态及速度分布的影响
Figure 11. The jet shape and velocity distribution of different material groups
图 12 不同材料组的开孔半径-侵彻深度变化曲线
Figure 12. Perforation radius-penetration depth curves of different material groups
图 13 外壳对聚能射流及其侵彻深度的影响
Figure 13. Effect of shell on shaped charge jet and its penetration depth
图 14 不同锥角药型罩组的页岩损伤和裂隙发育情况
Figure 14. Shale damage and fracture extension of different cone angle liner groups
图 15 不同壁厚药型罩组的页岩损伤和裂隙发育情况
Figure 15. Shale damage and fracture extension of different thickness liner groups
图 16 不同材料药型罩组的页岩损伤和裂隙发育情况
Figure 16. Shale damage and fracture extension of different material liner groups
表 1 金属材料的本构模型参数
Table 1. Parameters of the constitutive model of metallic materials
材料 ρ2/(kg·m−3) A1/MPa B1/MPa C n m Tmelt/K Troom/K 铜 8960 90 292 0.025 0.31 1.09 1356 293 钢 7830 792 510 0.014 0.26 1.03 1793 293 钛 4510 1111 106 0.025 0.29 1.10 1710 293 钨 17000 1506 177 0.016 0.12 1.00 1723 293 
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表 2 金属材料的状态方程参数
Table 2. Parameters of the equation of state of metallic materials
材料 c/(m·s−1) S1 S2 S3 γ0 a E2/J 铜 3940 1.490 0 0 1.99 0.46 0 钢 4569 1.490 0 0 2.17 0.46 0 钛 5210 1.620 0 0 2.32 0.46 0 钨 4029 1.237 0 0 1.54 0.46 0
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表 3 页岩本构模型参数
Table 3. Parameters of the shale constitutive model
ρ3/(kg·m−3) G/GPa A2 B2 ˙ε/s−1 εfmin Smax pcr/GPa µcr D1 2650 12.00 0.71 1.84 2.9×10−5 0.01 5.0 0.035 8×10−4 0.045 D2 T/MPa fc/MPa µlock C7 N plock/GPa K1/GPa K2/GPa K3/GPa 1.00 13.8 121.36 0.1 0.007 1.00 1.035 85 −171 208
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表 4 射孔弹模型的分组
Table 4. Grouping of perforating charge models
编号 锥角/(°) 壁厚/mm 材料 A-1-Ⅰ 50 1.0 铜 B-1-Ⅰ 60 1.0 铜 C-1-Ⅰ 70 1.0 铜 D-1-Ⅰ 80 1.0 铜 C-2-Ⅰ 70 0.5 铜 C-3-Ⅰ 70 1.5 铜 C-1-Ⅱ 70 1.0 铁 C-1-Ⅲ 70 1.0 钛 C-1-Ⅳ 70 1.0 钨
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1. Shuai Qin，Hao Liu，Jianhui Wang，Qiang Zhao，Lei Zhang. Physics-data coupling-driven method to predict the penetration depth into concrete targets. Theoretical & Applied Mechanics Letters. 2024(03): 184-192 . 
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