Stress concentration analysis of typical imperfections in girth welds of pure hydrogen long-distance transmission pipelines and exploration of applicability evaluation criteria
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摘要:目的 输氢管道是实现氢能长距高效利用的重要途径，长输管道通常由大量的环焊缝连接而成，焊缝缺欠是造成管道失效的高风险点，但目前尚无对长输纯氢管道施工中可能存在的环焊缝缺欠的风险评级及验收标准。方法 通过对比国内外长输石油天然气管道环焊缝缺欠的分类评级标准，以适合中国标准的典型缺欠提取到的特征尺寸为基础，建立了L245管线钢含缺欠输氢管道有限元模型，分析研究缺欠尺寸、位置等因素对缺欠应力集中系数的影响。结果 中国标准对于焊缝缺欠容限尺寸的限制普遍更为严格。在研究范围内，根部内凹缺欠的应力集中系数相对最高。对于圆形缺欠，其最大应力集中系数KTmax出现在直径为3 mm时，KTmax=2.74；对于条形缺欠，其最大应力集中系数出现在长度为25 mm时，KTmax=1.98；对于根部内凹缺欠，其最大应力集中系数出现在缺欠宽度为0.5 mm、深度为1 mm时，KTmax=3.58；对于错边量为3 mm的错边缺欠，其最大应力集中系数为2.62；附加弯矩会使直径为4 mm的圆形缺欠处的应力集中系数增大，高达3.97。结论 埋藏的圆形和条形缺欠越靠近壁面，尤其是内壁表面，应力集中越显著。圆形缺欠尺寸越大，应力集中越显著，而条形缺欠的长度对应力集中影响不显著。错边量增大时，应力集中系数近似线性增大。根部内凹缺欠的宽度越窄、深度越深时，应力集中越显著。额外的弯矩作用会使缺欠处的应力集中显著增大。应力集中显著的焊接缺欠的存在，增加了在高压气态氢环境中服役管道的风险性，基于纯氢管道缺欠的应力集中定量分析，结合材料的氢脆敏感性随缺口应力集中系数变化的实验数据及工程运行经验，探讨了缺欠适用性评价准则。Abstract:Objective Hydrogen transmission pipelines offer an important solution for the long-distance and efficient utilization of hydrogen energy. Numerous girth welds exist along these pipelines, so weld imperfections are regarded as high-risk points that can lead to pipeline failure. However, there is currently a lack of risk rating and acceptance criteria for girth weld imperfections that may arise in long-distance pure hydrogen pipelines as a result of construction operations.Methods Chinese and foreign classification and ranking standards regarding girth weld imperfections in long-distance pipelines were reviewed and compared. Based on characteristic dimensions extracted from typical imperfections consistent with relevant Chinese standards, a finite element model of hydrogen transmission pipelines constructed with L245 pipeline steel and featuring imperfections was developed. This model was employed to analyze the influence of various factors, such as the sizes and locations of imperfections, on the stress concentration factor associated with weld imperfections in these pipelines.Results The review found that Chinese standards generally impose stricter provisions on the tolerance dimensions of weld imperfections. Within the study range, the maximum stress concentration factor was found in concave imperfections located at the root of the welds. Specifically, the maximum stress concentration factor for circular imperfections was 2.74 at a size of 3 mm; for strip imperfections, it was 1.98 at a length of 25 mm; for concave imperfections at the root, it reached 3.58 with a width of 0.5 mm and a depth of 1 mm; and for misalignment imperfections, it was 2.62 with an offset of 3 mm. Furthermore, the stress concentration factor for 4 mm circular imperfections increased to 3.97 in the presence of any additional bending moment.Conclusion Buried circular and strip imperfections that are closer to the wall surface, particularly the inner wall surface, exhibit more significant stress concentration. Larger circular imperfections demonstrate more pronounced stress concentration; however, the length of strip imperfections does not significantly influence stress concentration. There is an approximately linear relationship between increases in misalignment and the growth of the stress concentration factor. Stress concentration becomes more pronounced in concave imperfections at the root as they become narrower and deeper. Additionally, bending moments are considered a contributing factor to the substantial increase in stress concentration at these imperfections. The presence of weld imperfections with significant stress concentration heightens the risk for pipelines operating in high-pressure gaseous hydrogen environments. Based on the quantitative analysis of stress concentration in imperfections of pure hydrogen pipelines, this study offers valuable insights into the applicability evaluation criterion of imperfections, which incorporates experimental data reflecting changes in hydrogen embrittlement sensitivity with varying stress concentration factors in imperfections, along with practical experience from engineering operations.
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一. 前言
油气管道半定量风险评价法也称为指数法。1985年，美国的Battelle Columbus研究院在“Guide for Hazard Evaluation Procedures”一文中提出了用指数法对油气管道进行风险评价。在20世纪80年代末和90年代初，各种独立的风险管理(RM)理论研究和试验逐步系统化，形成了较为完整的RM理论和方法。欧美不少公司已有了一些成功的应用经验，其中最具代表性的是1992年美国W Kent Muhlbauer出版的专著《Pipeline RiskManagement Manual》，1996年又发布了修定版(第二版)。
肯特(W Kent Muhlbauer)管道风险评价法[1]是一种半定量的风险评价方法。该方法是在分析各段管道独立的影响因素后，求取指数和，再分析介质的危险性和影响系数，求取泄漏影响系数，最后求取指数和与泄漏影响系数的比值，即得到相对风险数。这种方法的特点是不必建立精确的数学模型和计算方法，不必采用复杂的强度理论和昂贵的现代分析仪器等手段，而是在有经验的现场操作人员和专家意见的基础上，结合一些简单的公式进行打分评判，其评价的精确性取决于专家经验的全面性及划分影响因素的细致性、层次性。
近年来，为了有效处理评分中存在的主观性和不确定因素，已经把模糊数学思想和方法引入到管道风险的半定量评价中，提高了各种因素评分的精确度。但是，以前在计算相对风险数的过程中，只是将各种因素的评分结果简单地进行累加，没有考虑到各种因素的权重分配，然后直接利用所得的相对风险数进行风险排序，使评价结果的准确性受到影响。现根据灰色系统理论中的关联分析对油气管道系统进行灰色综合评价，旨在克服模糊综合评价[2]中存在的不足与缺陷，并采用多层次灰色综合评价法，对油气管道的半定量风险评价做进一步研究。
二. 灰色综合评价模型
灰色关联分析[3]是根据因素之间发展态势的相似或相异程度来衡量因素间关联程度的方法。采用灰色关联分析法进行管道半定量风险的综合评价，就是通过计算影响管道风险的各种评价指标(经模糊综合评判处理后的评分)序列与最优指标集序列的关联度，关联度越大，管道的风险性越小。管道系统风险的灰色综合评价可以分为单层次综合评价和多层次综合评价。
1 灰色单层次综合评价
灰色单层次综合评价主要步骤有，评价指标的确定、最优指标集的确定、数据的无量纲化处理、评价矩阵的确定、各权重的确定、关联度的确定。
1 评价指标的确定
所谓评价指标就是评价对象的各种属性或性能，它们是对被评价对象进行评价的依据。管道系统的评价指标按其属性可分为两类，第一类是趋上优指标，表示该类指标越大越好，例如，第三方破坏指数体系、腐蚀指数指标体系、设计指数指标体系、错误指数指标体系；第二类是趋下优指标，表示该类指标越小越好，例如，介质危险指数。
2 最优指标集的确定
最优指标集是从各评价对象的同一指标中选出最优的一个组成的数集，它是各评价对象比较的基准。最优指标集和各评价对象的指标值组成矩阵：
![](/fileYQCY/journal/article/yqcy/newcreate/href="yqcy-25-4-7-E1.png")
(1) 式中 Xi(k)——第i个评价对象的第k个经模糊处理的指标值。
3 数据的无量纲化处理
由于参评指标通常具有不同的量纲，因而必须对其进行无量纲化处理。常采用的方法是数据的均值化[3]处理：
![](/fileYQCY/journal/article/yqcy/newcreate/href="yqcy-25-4-7-E2.png")
(2) ![](/fileYQCY/journal/article/yqcy/newcreate/href="yqcy-25-4-7-E3.png")
(3) 4 评价矩阵的确定
根据灰色系统理论，可由下式求得Yi对于Y0在第k个指标下的关联系数[3]Ai(k)：
![](/fileYQCY/journal/article/yqcy/newcreate/href="yqcy-25-4-7-E4.png")
(4) 式中 ρ——分辨系数，一般取ρ=0.5。
各评价对象与最优指标的关联系数组成评价矩阵：
![](/fileYQCY/journal/article/yqcy/newcreate/href="yqcy-25-4-7-E5.png")
(5) 5 各权重的确定
由于各评价指标对评价对象的影响程度不同，为了尽量反映实际情况，需要确定各评价指标的权重。确定权重的方法很多，有专家打分法、层次分析法和均方差法等。本研究的权重计算采用层次分析[4]与专家打分相结合的方法。权重矩阵为：
![](/fileYQCY/journal/article/yqcy/newcreate/href="yqcy-25-4-7-E6.png")
(6) 6 关联度的确定
![](/fileYQCY/journal/article/yqcy/newcreate/href="yqcy-25-4-7-E7.png")
(7) 2 灰色多层次综合评价
当评价对象的各指标之间有不同的层次结构时，就必须进行多层次综合评价。多层次综合评价是在单层次综合评价的基础上进行的，其评价方法很相似，只是在处理数据方面有所不同，例如第一层次的数据是借助于第二层次评价结果，不需要再进行数据的无量纲化处理，因为它们已经是无量纲化的数据。
三. 油气管道半定量风险灰色综合评价算法举例
1 选取综合评价对象
某在役长输管道，根据评价单元划分原则，管道共分5个单元，管道1，设计压力为6.27 MPa，管径为ϕ355.6×6.4，S290材料；管道2，设计压力为2.5 MPa，管径为ϕ355.6×6.4，S290材料；管道3，设计压力为2.5 MPa，管径为ϕ273×5.6，S240材料；穿越1，穿越长度为2 308 m，离江底深度大于7 m，设计压力为2.5 MPa，管径为ϕ355.6×7.1，S290材料；穿越2，穿越长度超过1 000 m，离江底深度大于7 m，设计压力为2.5 MPa，管径为ϕ273×6.4，S240材料。
2 管道半定量风险综合评价指标体系的设计
管道系统的半定量风险评价可以通过3次评判加以确定，即由3个层次组成，第一层次为TI、CI、DI、OI、NI构成因素评判系统；第二层次分别为TI(dl~d6)、C1、C2、DI(d19~d24)、Ol、O2、O3、O4各构成因素评判系统；第三层次为C1(d7~d8)、C2(d9~d18)、O1(d25~d29)、O2(d30~d35)、O3(d36~d41)、O4(d42~d44)各构成因素的评判系统，各评价指标的权重见表 1。
表 1 各评价指标的权重
3 权重的计算
第一层次的权重计算采用层次分析法，经计算，TI、CI、DI、OI、NI的权重分别为0.057 4、0.181 9、0.181 9、0.038 8、0.540 0。第二层次和第三层次的权重分别根据专家打分分配权重，最后进行组合权重的计算，即每层次中所有元素相对于总目标的相对权重。
例如，第二层次中的TI(d1~d6)，由专家打分分配的权重分别为0.20、0.20、0.10、0.30、0.05、0.15，组合权重的计算为：
![](/fileYQCY/journal/article/yqcy/newcreate/href="yqcy-25-4-7-E7-FE1.png")
灰色多层次综合评价结果见表 2。
表 2 各项指数的风险灰色综合评价结果
评价结果值越大，说明风险越小，管道越安全。由管道的第三方破坏指数风险的灰色综合评价结果可知，穿越2＜管道2＜管道3＜穿越1＜管道1，穿越2的第三方破坏风险性最大，管道1的第三方破坏风险性最小。由管道的腐蚀指数风险的灰色综合评价结果可知，管道3＜穿越2＜管道1＜管道2=穿越1，管道3的腐蚀风险性最大，穿越1和管道2腐蚀风险性最小。由管道的设计指数风险的灰色综合评价结果可知，管道1的设计风险性最大，管道3和穿越2设计风险性最小。由管道的错误指数风险的灰色综合评价结果可知，管道1和穿越1的错误风险性最大。最后由总的评价结果可知，管道风险程度由大到小排序为，管道3＞穿越2＞管道2＞管道l＞穿越1。而由原方法评价得到的最后结果是，穿越2＞管道3＞管道2＞管道1＞穿越1。
四. 结束语
油气管道半定量风险评价技术无论现在，还是将来都具有十分重要的工程意义，它是管道完整性评价的重要组成部分。管道风险评价技术在我国还处在起步阶段，还有很多不足[5]，需要不断完善。油气管道半定量风险评价取决于第三方破坏、腐蚀、设计、错误、介质危险指数等多方面因素。灰色关联分析能够较好地处理这类多因素综合评价问题。灰色关联分析法中最优指标集和权重起着至关重要的作用，合理确定最优指标集和权重，以提高风险值的准确度，能更准确地了解管道的风险状况，以此指导管道的维护工作，降低管道的风险性。
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图 2 6.3 MPa氢气环境下L245钢环焊缝工程应力-应变曲线
Figure 2. Engineering stress-strain curve of L245 steel girth weld in 6.3 MPa hydrogen environment
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图 3 缺欠附近最大等效应力随网格尺寸变化曲线
Figure 3. Variation curve of maximum equivalent stress near the imperfection with mesh size
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图 4 不同相对高度位置3 mm圆形缺欠附近应力分布云图
Figure 4. Stress distributions near 3 mm circular imperfections at different relative heights
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图 5 圆形缺欠应力集中系数随相对高度变化曲线
Figure 5. Variation curves of stress concentration factor for circular imperfections with relative height
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图 6 不同长度、截面直径3 mm条形缺欠应力集中系数随相对高度变化曲线
Figure 6. Variation curves of stress concentration factor with relative height for strip imperfections with 3 mm of sectional diameter and different lengths
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图 7 不同相对高度25 mm条形缺欠附近等效应力分布云图
Figure 7. Equivalent stress distributions near 25 mm strip imperfections at different relative heights
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图 8 不同深度25 mm根部内凹缺欠应力集中系数随缺欠宽度变化曲线
Figure 8. Variation curves of stress concentration factor with imperfection width for concave imperfections with 25 mm of length and different depths at the root
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图 9 应力集中系数随错边量变化曲线
Figure 9. Variation curve of stress concentration factor with misalignment value
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图 10 氢致断面收缩率损失随应力集中系数变化曲线
Figure 10. Variation curve of loss coefficient due to hydrogen-induced reduction of cross-sectional area as a function of stress concentration factor
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图 11 圆形缺欠应力集中系数随弯矩变化曲线
Figure 11. Variation curves of stress concentration factor for circular imperfections with bending moment
表 1 国内外天然气管道焊缝无损检测验收标准对比表
Table 1 Comparison of acceptance standards for NDT of welds in natural gas pipelines in China and abroad
标准号 标准名称 适用特点 验收准则及分级 缺陷（欠）类型划分 ISO 13847-2013 《石油天然气工业管道-运输系统-管道焊接》 适用于碳钢、低合金钢，对油气管道输送系统的环焊缝、支管、角焊缝的焊接及检验要求有详细规定，在欧洲应用较多 给出了每种缺欠的验收准则，不分验收级别 包括未焊透、未熔合、根部内凹、烧穿、夹渣、气孔、空心焊道、裂纹及咬边9类 API STD 1104-2021 《管道及相关配件的焊接》 作为长输管道的现场焊接及验收标准，在世界范围内广泛使用 CSA-Z662-2015 《油气管道系统》 适用于石油与天然气工业管道系统的设计、建造、运行、维护、停用、废弃全生命周期 SY/T 4109—2020 《石油天然气钢质管道无损检测》 — 将射线检测的结果分为I、Ⅱ、Ⅲ、V级，天然气管道环焊缝缺欠按Ⅱ级评判 未涉及无夹渣、气孔、空心焊道等缺欠，仅分为条形缺欠与圆形缺欠两种 
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