页岩规则齿形结构面水化损伤及剪切特性研究

景宇翔, 郭印同, 冯代英, 万洋辉, 郑贺斌

景宇翔,郭印同,冯代英,等. 页岩规则齿形结构面水化损伤及剪切特性研究[J]. 石油钻探技术,2025,53(2):1−12. DOI: 10.11911/syztjs.2025033
引用本文: 景宇翔,郭印同,冯代英,等. 页岩规则齿形结构面水化损伤及剪切特性研究[J]. 石油钻探技术,2025,53(2):1−12. DOI: 10.11911/syztjs.2025033
JING Yuxiang, GUO Yintong, FENG Daiying, et al. Hydration damage and shear characteristics of regular toothed structural planes of shale [J]. Petroleum Drilling Techniques, 2025, 53(2):1−12. DOI: 10.11911/syztjs.2025033
Citation: JING Yuxiang, GUO Yintong, FENG Daiying, et al. Hydration damage and shear characteristics of regular toothed structural planes of shale [J]. Petroleum Drilling Techniques, 2025, 53(2):1−12. DOI: 10.11911/syztjs.2025033

页岩规则齿形结构面水化损伤及剪切特性研究

基金项目: 国家自然科学基金项目“复杂环境下水泥环全生命周期密封理论与控制方法”(编号:U22B6003)资助。
详细信息
    作者简介:

    景宇翔(1995—),男,湖北天门人,2018年毕业于湖南科技大学采矿工程专业,在读硕士研究生,主要从事非常规油气开发研究。E-mail:yxjl102@163.com

  • 中图分类号: TE21

Hydration Damage and Shear Characteristics of Regular Toothed Structural Planes of Shale

  • 摘要:

    页岩储层压裂改造后,地层滑移使套管变形频繁出现,严重影响施工与生产。为了解页岩储层结构面水化损伤及水化前后的剪切特性,采用川南龙马溪组页岩试样,预制了10°和40°的2种规则齿形结构面,模拟了不同粗糙度的断层特征,并在四级法向应力下进行了水化直剪试验。试验结果表明:1)40°高起伏角度结构面在水化后表现出塑性变形特征,剪切位移−剪应力曲线呈阶梯式上升,剪切刚度下降约16.3%;而10°低起伏角度结构面则以摩擦滑移为主,剪切刚度波动较小;高法向应力(≥5 MPa)会加剧水化对结构面的破坏作用,但长时间(≥24 h)水化会使破坏促进作用趋于上限。2)在水化初期(1~2 h),40°高起伏角度结构面抗剪强度平均降低了13.05%,最终整体降低了18.19%,黏聚力与内摩擦角分别降低了16.31%和16.57%;10°低起伏角度结构面的抗剪强度参数受水化影响较小,波动范围小于5%。3)10°低起伏角度结构面在水化360 h后出现微孔洞连通和矿物分层现象,而40°高起伏角度结构面则形成大尺寸张拉裂缝,表面粗糙度增大,这是因为高角度结构面的黏土矿物分布更集中,水化软化效应更显著,导致脆性降低和塑性增强。研究结果可为页岩储层压裂设计与套管防护提供理论依据。

    Abstract:

    Formation slip makes casing failure occur frequently after the fracturing of shale reservoirs, which seriously affects construction and production. In order to understand the damage caused by the hydration of shale reservoirs’ structural planes and shear characteristics before and after hydration, shale samples of Longmaxi Formation in southern Sichuan were adopted. Two kinds of regular toothed structural planes of 10° and 40° were prefabricated, and the fault characteristics at different roughness were simulated. Moreover, direct shear tests for hydration were carried out under four normal stresses.The results show that: 1) The structural plane with a high undulating angle of 40° shows plastic deformation characteristics after hydration. The shear displacement–shear stress curve shows the characteristics of stepped rise, and shear stiffness decreases by about 16.3%. However, the structural plane with a low undulating angle of 10° mainly exhibits frictional slip, and the shear stiffness fluctuates slightly. High normal stress (≥ 5 MPa) will aggravate the damage effect of hydration on the structural plane, but the damage promotion effect tends to the upper limit after a long time of hydration (≥ 24 h). 2) At the initial stage of hydration (1–2 h), the shear strength of the structural plane with a high undulating angle of 40° decreases by 13.05% on average, and the overall shear strength decreases by 18.19%; the cohesion and internal friction angle decrease by 16.31% and 16.57%, respectively. In contrast, the shear strength parameters of the structural plane with a low undulating angle of 10° are less affected by hydration, and the fluctuation range is less than 5%. 3) After 360 h of hydration, microporous connectivity and mineral stratification appear on the structural plane with a low undulating angle of 10°, while the structural plane with a high undulating angle of 40° forms large-size tensile fractures, and surface roughness increases. This difference is due to the more concentrated distribution of clay minerals and the more significant hydration softening effect on the structural plane with a high undulating angle, resulting in reduced brittleness and enhanced plasticity. The research results can provide a theoretical basis for shale reservoir fracturing design and casing protection.

  • 沧东凹陷位于黄骅坳陷南部,孔店组二段形成于相对封闭的湖盆环境,发育形成致密油气藏。随着石油工程技术的不断进步及对地质情况认识的深入,沧东凹陷孔二段细粒沉积岩的勘探开发取得了突破,致密油气已成为大港油田重要的接替资源。为了提高沧东凹陷致密油气的开发效益,需要采用长水平段水平井开发。但是,该区域无长水平段水平井钻探先例,可借鉴经验少,需要进行关键技术研究。为此,笔者从井身结构优化、井眼轨道设计、井眼轨迹控制方式优选择、钻井设备及工具优选、钻井液体系优选与性能优化、提速提效技术措施选择和套管安全下入方式优选等方面进行了研究,形成了致密油气藏水平井钻井关键技术,并在2口井进行了成功试验,为实现沧东凹陷致密油气藏的高效开发提供了技术支持。

    沧东凹陷致密油气藏埋深3 500.00~4 000.00 m,水平井造斜点井深超过3 000.00 m、裸眼段长大于2 500.00 m、水平段长大于1 500.00 m,且钻遇巨厚石膏层和多个漏层,给安全高效钻井带来了极大挑战。分析认为,主要钻井技术难点为[12]

    1)水平段和裸眼段长,摩阻高、扭矩大、循环压耗高,对钻井设备和钻具的性能要求高,设备和钻具的优选难度大。

    2)要求靶框范围上下≤2.0 m、左右≤5.0 m,且着陆后的控制点多,需要频繁调整井眼轨迹,对井眼轨迹控制技术的要求很高。钻井过程中携岩困难,尤其在井斜角45.0°~65.0°井段极易形成岩屑床,增大了井眼轨迹控制难度和卡钻的风险。

    3)孔一段地层顶部有厚约110.00 m的石膏层,石膏纯度高,易造成钻井液污染,对钻井液抗污染性能要求高;馆陶组底部砾岩段、沙一段底部生物灰岩段和孔一段断层存在不整合面,钻井过程中发生井漏的风险高,对钻井液封堵性能要求高;水平段和裸眼段长,摩阻大,施加钻压困难,卡钻风险高,对钻井液润滑防卡性能要求高[34]

    4)储层以泥岩和页岩为主,硬脆性强,部分地层含有少量浅灰色细砂岩。泥岩以紫红色和灰色泥岩为主,硬度高、研磨性强,钻头磨损严重,机械钻速低。页岩微裂缝和层理发育,容易发生页岩表面水化及渗透性水化,引起井眼失稳。

    针对上述钻井技术难点,从井身结构、井眼轨道、井眼轨迹、钻井设备、钻进工具、钻井液,以及钻井提速提效技术、套管安全下入技术等方面进行了研究,形成了致密油气藏水平井钻井关键技术。

    水平井井身结构设计时,除了考虑地层压力和必封点等因素外,还应考虑钻井设备负荷和井下风险。在保证实现地质目标的前提下,尽可能缩短裸眼段长度、降低摩阻扭矩、缩短裸眼浸泡时间和减轻钻机负荷,并降低井壁垮塌风险[56]

    根据沧东凹陷致密油气藏的地层岩性、三压力剖面、注水情况、漏层分布和施工难度,水平井设计采用三开井身结构:1)一开采用ϕ339.7 mm表层套管封固明化镇组以上松软地层,并安装井口装置,为下部安全钻井提供条件;2)为了兼顾地层压力、注水情况、裸眼段长度和施工难度的需求,二开采用ϕ244.5 mm技术套管封固孔一段枣Ⅲ油组注水层位;3)三开采用ϕ139.7 mm油层套管封隔油、气、水层。

    水平井井眼轨道设计需要综合考虑邻井防碰、井眼轨迹控制方式和难度等因素,进行分段优化,保证井眼轨迹平滑,并精确中靶[710]

    1)造斜点优选。东营组和沙河街组地层有大段硬塑性泥岩,容易发生井眼失稳;ϕ311.1 mm井段深部泥岩层定向钻进托压严重,定向效率低。因此,选择在孔一段造斜,造斜点井深3 000.00~3 200.00 m。

    2)造斜率优化。为了保证井眼轨迹平滑,尽量缩短造斜段长度,降低施工难度,减轻设备负荷、降低钻井风险。因此,将第一增斜段造斜率控制在(2.4°~3.0°)/30m,井斜角控制在30°~35°;第二增斜段造斜率控制在(3.0°~3.5°)/30m,井斜角控制在82°~86°进入第一控制点;微降斜段降斜率控制在(2.1°~2.4°)/30m,井斜角控制在80.0°~82.0°进入第二控制点;第三增斜段造斜率控制在(2.1°~2.4°)/30m,快速进入末端控制点,开始钻进水平段。

    考虑施工难度和井下风险,确定了2种井眼轨迹控制技术方案:若造斜点在ϕ311.1 mm井段,第一增斜段和稳斜段采用“ϕ215.9 mm×1.25°螺杆钻具+ϕ172.0 mm MWD”控制井眼轨迹,后续井段采用“ϕ172.0 mm旋转导向钻具+ϕ172.0 mm LWD”控制井眼轨迹;若造斜点在ϕ215.9 mm井段,则全程采用ϕ172.0 mm旋转导向钻具控制井眼轨迹。由于旋转导向钻井成本高,为了降低成本,建议现场根据水平段的长度选择经济高效的井眼轨迹控制技术:水平段不大于1 000.00 m的水平井,采用“水力振荡器+MWD+螺杆钻具+近钻头地质导向工具”控制井眼轨迹;水平段长度大于1 000.00 m的水平井,采用旋转导向钻具控制井眼轨迹。

    选择钻井设备和钻具时,需要综合考虑大钩载荷、扭矩、循环压耗、井眼清洁和井下故障处理能力等因素。利用软件模拟分析了不同井眼轨道、钻具组合、钻井液性能、钻井参数和摩阻系数等条件下大钩载荷、扭矩、循环压耗和井眼清洁效果等关键参数的变化规律,优选出最佳的钻井设备和钻具。

    1)顶部驱动装置优选。大钩载荷和扭矩模拟计算结果如图1所示。由图1可知,最大扭矩为27.7 kN·m。为了提高井下故障处理能力,选用DQ70BSD型顶部驱动装置,最高转速200.0 r/min,最大连续输出扭矩60.0 kN·m。

    图  1  大钩载荷和扭矩模拟计算结果
    Figure  1.  Simulation calculation results of the hook load and torque

    2)钻井泵优选。循环压耗模拟计算结果如图2所示。由图2可知,最高循环压耗为37.4 MPa。为了提高钻井泵的安全性,选用1台F–2200HL高压钻井泵和2台F–1600加强型钻井泵,其额定工作压力分别为52.0和40.0 MPa。

    图  2  循环压耗模拟计算结果
    Figure  2.  Simulation calculation results of the circulation pressure loss

    3)钻具优选。从图1可以看出,起钻、复合钻进和下钻的最大大钩载荷分别为1 677.6,1 268.0和999.5 kN。兼顾大钩载荷、扭矩和循环压耗,根据满足强度前提下尽可能降低钻机负载的原则,选用ϕ139.7 mm钻杆(钢级S137)×2 000.00 m+ϕ127.0 mm钻杆(钢级G105)。其中,ϕ127.0 mm钻杆采用非标准NC52扣型和ϕ107.7 mm水眼,以进一步降低循环压耗,减轻钻井泵负载。

    综合考虑石膏层抗污染、斜井段携岩、水平段抑制防塌和润滑防卡等因素[11],三开ϕ215.9 mm井段选用钾盐聚合物钻井液,配方为:4.0%~6.0%膨润土+5.0%~7.0% KCl+0.3%~0.5%抗盐强包被抑制剂BYJ–Ⅰ+2.0%~3.0%抗盐降滤失剂+2.0%~3.0%抑制防塌剂BZ–YFT+0.2%~0.3%提切剂+0.8%~1.0%低渗透封堵剂+2.0%~3.0%液体润滑剂+0.2%~1.0%KOH。钻井液性能优化措施为:

    1)提高抗石膏污染能力。钻井液中定时补充六偏磷酸钠胶液,并随钻加入KOH进行处理。但是OH含量过高会分散剥离泥页岩,影响防塌效果,要求pH值维持在8.0~10.0。

    2)提高钻井液的抑制性。为了保证钻井液的抑制防塌效果,钻井期间要求K+含量不低于500.0 mg/L,并及时补充抗盐强包被抑制剂BYJ–Ⅰ和抑制防塌剂BZ–YFT,改善滤饼质量,控制API滤失量不大于3.0 mL、高温高压滤失量不大于10.0 mL。

    3)提高携岩能力。用大分子处理剂和携砂粉等控制钻井液动切力,孔一段和孔二段的钻井液动切力分别控制在8.0~12.0 和12.0~16.0 Pa;保证钻井液动塑比不小于0.5、六速旋转黏度计3 r/min的读数不小于4.0。

    4)提高润滑防卡性能。用原油作为润滑剂,钻井液含油量控制在5.0%~8.0%,保证摩阻系数不大于0.06;同时,进入水平段后全程开启离心机,清除钻井液中的有害固相,降低摩阻。

    1)提高定向效率。ϕ311.1 mm造斜段和稳斜段采用ϕ203.2 mm水力振荡器,减轻滑动钻进托压,提高定向效率。该工具基本结构见图3,主要通过自身产生的轴向振动,将滑动钻进过程中钻柱与井壁之间的静摩擦转变为动摩擦,降低钻柱与井壁之间的摩擦阻力,提高滑动钻进钻压的传递效率[1213]。综合考虑井斜角、钻井液性能、摩阻和工具振荡力等情况,将其安放在距离钻头220.0 m左右处。

    图  3  水力振荡器基本结构
    Figure  3.  The basic structure of the hydraulic oscillator

    2)优化钻井参数。为了提高ϕ215.9 mm井段孔一段和孔二段地层的机械钻速和井眼清洁能力,采用大排量、大钻压和高转速钻进。大排量主要用来提高井眼清洁能力,高转速主要用来提高机械钻速和井眼清洁能力,大钻压主要用来提高机械钻速[5]。具体钻井参数为:钻压100.0~140.0 kN,转速120.0~130.0 r/min,排量32.0~35.0 L/s。

    3)PDC钻头设计。根据孔二段砂泥岩研磨性高的特点,对PDC钻头进行了个性化设计[14],具体设计方案为:五刀翼结构(3个长刀翼+2个短刀翼),ϕ16.0 mm主切削齿,28颗前排切削齿,切削齿侧倾角2.0°~10.0°,后倾角15.0°~25.0°;每个刀翼3颗ϕ13.4 mm后排切削齿,后排齿与前排齿的高度差1.5~2.0 mm。另外,为了使切削效率更高,采用顺时针布齿(比逆时针布齿攻击性更强);为了提高钻头的冷却效果、井底清洗效果和射流冲击力,设置5个ϕ7.9 mm喷嘴和2个ϕ8.7 mm喷嘴,可基本实现井底全覆盖。设计的PDC钻头流体动力学数值模拟结果如图4所示。由图4可知,井底最大漫流速度可达28.6 m/s。

    图  4  PDC钻头井底流场速度云图
    Figure  4.  PDC bit bottom hole smooth speed cloud map

    4)提高携岩能力。每钻进1个单根划眼1次,钻进1个立柱正划眼、倒划眼各1次,充分循环携岩。随着井眼延伸和井斜角增大,仅依靠提高排量无法保证井眼清洁。此时,需要在钻具中加入井眼清洁工具,利用其机械刮削和水力旋流的作用清除岩屑床[15]。井眼清洁工具主要由耐磨带、螺旋棱、导流槽和叶轮组成(见图5)。螺旋棱在旋转过程中刮削井壁上的虚滤饼或岩屑床,使其从压实状态变为自由状态;导流槽和叶轮在钻井液流过时产生涡流,将井眼中自由状态的虚滤饼或岩屑向上推移,携带出井口。综合裸眼段长度、井斜角和有效作用距离等因素,确定井眼清洁工具的安放方式为:钻具最底端安放1只,安放在距离钻头60.0 m左右;钻具最顶端安放1只,安放在井斜角40.0°附近;钻具中间每隔90.0~120.0 m安放1只。

    图  5  井眼清洁工具基本结构
    1.耐磨带;2.螺旋棱;3.导流槽;4.叶轮
    Figure  5.  The basic structure of the wellbore cleaning tool

    为了保证套管安全顺利下入,利用软件分析了ϕ139.7 mm套管的下入能力,优化了扶正器的安放位置和数量。同时,为了提高预测精度,在下套管前最后一次通井时,记录起下钻悬重,测算起下钻摩阻系数,作为模拟套管下入的摩阻系数。

    1)井眼准备。下套管前分别带单稳定器、双稳定器和三稳定器进行3次通井。通井时,若下钻阻力超过40.0 kN,立即接顶驱划眼,划眼到底后对划眼井段进行短起下钻验证,确保顺畅后再进行下一步工序;起钻遇阻的井段再次进行划眼,并短起下钻验证。

    2)套管扶正器下入方案。为了保证套管居中度和套管能安全下入,选用ϕ206.4 mm整体式半刚性扶正器。利用软件模拟优化确定了套管扶正器的下入方案:水平段每隔2根套管加1只扶正器,造斜段每隔1根套管加1只扶正器,直井段每隔5根套管加1只扶正器。

    3)套管下入方式优选。考虑裸眼段和水平段较长,以及套管扶正器数量多、套管下入难度系数大等情况,利用软件对常规下套管方式进行了模拟分析。模拟结果表明,下入套管时,套管下放大钩载荷952.3 kN,套管静止大钩载荷1 100.5 kN,套管下放大钩载荷大于静止大钩载荷的30%。结合模拟预测结果和通井情况,确定采用常规下套管方式。

    大港油田沧东凹陷页岩油水平井GD1701H井和GD1702H井试验应用了沧东凹陷致密油气藏水平井钻井关键技术,钻井过程中未发生井下故障,整体效果良好,具体数据见表1。2口井平均井深5 370.00 m,平均水平段长1 379.60 m,平均机械钻速11.4 m/h,平均钻井周期59.2 d。其中,GD1701H井创造了大港油田5 000.00 m以深水平井钻井周期最短、机械钻速最高、钻机月速最高和水平段最长等4项纪录。

    表  1  沧东凹陷致密油气藏水平井钻井关键技术试验数据
    Table  1.  Key technical test data for horizontal well drilling in tight oil and gas reservoirs of Cangdong Sag
    井号 水平位移/m 水平段长/m 井深/m 垂深/m 井斜角/(°) 方位角/(°) 钻井周期/d 机械钻速/(m·h–1
    GD1701H 1 984.00 1 449.10 5 465.00 3 851.30 91.3 91.5 55.2 13.2
    GD1702H 1 835.90 1 310.10 5 275.40 3 930.40 85.1 193.4 63.2 10.0
    下载: 导出CSV 
    | 显示表格

    GD1701H井采用三开井身结构,施工过程中未出现漏失、溢流和井眼失稳等问题,且钻井效率高。该井钻进过程中井眼轨迹控制良好,钻井液润滑性能高,采用常规下套管方式未出现遇阻现象。其中,二开采用“水力振荡器+MWD+螺杆钻具”控制井眼轨迹,定向机械钻速达到3.3 m/h,且无托压现象;三开采用“旋转导向钻具+LWD”控制井眼轨迹,平均机械钻速达到9.2 m/h。

    GD1701H井最大悬重1 900.0 kN,最大扭矩26.0 kN·m,循环压耗最高达29.0 MPa,选用的钻机、钻井泵和钻具满足了安全高效钻进要求。应用设计的PDC钻头钻进孔一段和孔二段紫红色泥岩、灰色砂岩、灰色泥岩和油页岩,单只钻头完成造斜段和水平段,进尺1 177.00 m,平均机械钻速9.7 m/h,提速效果显著,说明设计的个性化PDC钻头地层适应性强。

    该井馆陶组钻遇8.0 m厚的杂色砾岩,沙一段钻遇8.0 m厚的生物灰岩,孔一段钻遇断层及不整合面,钻进过程中及时补充随钻堵漏剂BZ–DSA,未出现漏失现象。孔一段钻遇厚约149.0 m的石膏层,进入石膏层之前配制六偏磷酸钠胶液,维持钻井液pH值始终在9.0以上,待振动筛处发现石膏侵时加入胶液,未出现钻井液受钙污染的问题。定时测量钻井液含油量、API滤失量、高温高压滤失量和动切力等关键参数,控制含油量在5%以上、API滤失量不超过3.0 mL、高温高压滤失量不超过10.0 mL、动切力在15.0 Pa左右,保证了钻井液抑制防塌、润滑防卡和携岩性能满足要求。

    1)沧东凹陷致密油气藏埋藏深,水平井具有造斜点深和水平段长的特点,摩阻、扭矩和循环压耗高,对钻井设备要求高;从上到下钻遇多个漏层和巨厚石膏层,对钻井液性能要求高;孔一段和孔二段地层有大段硬度高、研磨性强的泥岩,机械钻速低,对钻头匹配性要求高。

    2)沧东凹陷致密油气藏水平井钻井关键技术可以解决长水平段水平井钻井过程中存在的技术难题,尤其是井身结构及井眼轨道优化设计、高润滑抗污染强抑制防塌钻井液和钻井提速提效等方面,实现了沧东凹陷致密油气藏的高效开发。

    3)钻前利用软件对大钩载荷、扭矩、循环压耗和井眼清洁程度等进行预测,为优选钻井设备和钻具提供了理论依据。高性能钻井设备和高强度钻具确保了长水平段水平井的安全高效施工。

    4)为了兼顾水平段施工难度和钻井成本,建议根据水平段的长度选择经济高效的井眼轨迹控制技术。对于水平段小于1 000.00 m的水平井,采用“水力振荡器+MWD+螺杆钻具+近钻头伽马地质导向工具”控制井眼轨迹;对于水平段长度大于1 000.00 m的水平井,采用旋转导向钻具控制井眼轨迹。

  • 图  1   长方体岩样的层理

    Figure  1.   Layered structure of rectangular rock sample

    图  2   剪切时结构面的受力情况

    Figure  2.   Stress situation of structural planes under shear action

    图  3   10°起伏角度结构面不同法向应力下的剪切位移−剪应力曲线

    Figure  3.   Shear displacement–shear stress curve of structural plane with an undulating angle of 10°

    图  4   40°起伏角度结构面不同法向应力下的剪切位移−剪应力曲线

    Figure  4.   Shear displacement–shear stress curve of structural plane with an undulating angle of 40°

    图  5   10°与40°起伏角度结构面剪切刚度−水化时间曲线

    Figure  5.   Shear stiffness–hydration time curves of structural planes with undulating angles of 10° and 40°

    图  6   10°起伏角度结构面中部区域高程云图

    Figure  6.   High-level cloud map of middle area of structural plane with an undulating angle of 10 °

    图  7   40°起伏角度结构面中部区域高程云图

    Figure  7.   High-level cloud map of middle area of structural plane with an undulating angle of 40°

    图  8   10°起伏角度结构面峰值剪应力−水化时间曲线

    Figure  8.   Peak shear stress-hydration time curve of structural plane with an undulating angle of 10°

    图  9   40°起伏角度结构面峰值剪应力−水化时间曲线

    Figure  9.   Peak shear stress-hydration time curve of structural plane with an undulating angle of 40°

    图  10   不同水化时间下10°结构面的微观特征

    Figure  10.   Microscopic characteristics of structural plane with an undulating angle of 10° under different hydration time

    图  11   不同水化时间下40°结构面的微观特征

    Figure  11.   Microscopic characteristics of structural plane with an undulating angle of 40° under different hydration time

    图  12   部分结构面破坏实物图与高程云图

    Figure  12.   Photo of partial structural plane damage and high-level cloud map

    表  1   不同结构面在不同条件下的剪切试验结果

    Table  1   Shear test results of different structural planes under different conditions

    水化时间/h 法向应力/MPa 峰值强度/MPa C/MPa ϕ/(°) R2 峰值强度/MPa C/MPa ϕ/(°) R2
    起伏角度为10° 起伏角度为40°
    0 2.5 3.90 2.29 33.02 0.931 11.32 9.44 42.60 0.975
    5.0 6.20 14.45
    7.5 7.03 16.74
    10.0 8.29 18.22
    1 2.5 3.93 2.36 31.75 0.995 10.98 8.53 41.34 0.973
    5.0 5.31 12.33
    7.5 7.19 15.61
    10.0 8.46 17.22
    2 2.5 4.09 2.38 32.66 0.995 10.46 8.30 37.87 0.990
    5.0 5.50 11.98
    7.5 7.03 13.90
    10.0 8.92 16.30
    12 2.5 4.05 2.19 31.95 0.973 9.96 7.93 36.07 0.949
    5.0 4.96 10.93
    7.5 6.63 14.02
    10.0 8.69 15.00
    24 2.5 3.64 2.37 32.93 0.930 9.56 7.71 35.13 0.988
    5.0 6.40 11.26
    7.5 6.72 12.62
    10.0 8.93 14.97
    120 2.5 3.89 2.36 32.47 0.991 10.51 8.06 35.24 0.837
    5.0 5.92 11.19
    7.5 6.85 12.14
    10.0 8.66 16.08
    360 2.5 3.76 2.23 32.86 0.982 9.60 7.96 35.82 0.904
    5.0 5.10 11.30
    7.5 7.53 12.37
    10.0 8.55 15.58
    720 2.5 3.90 2.37 33.44 0.996 9.94 7.84 35.97 0.919
    5.0 5.81 11.53
    7.5 7.41 12.30
    10.0 8.87 15.73
    下载: 导出CSV
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  • 收稿日期:  2023-12-09
  • 修回日期:  2025-03-02
  • 网络出版日期:  2025-03-24

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