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作者简介:

陈前(1992-),男,博士研究生,研究方向为核测井方法、核测井数据处理及蒙特卡罗模拟。E-mail:chenqian20112015@163.com。

通讯作者:

张锋(1970-),男,教授,博士,研究方向为核测井方法、核测井数据处理及蒙特卡罗模拟。E-mail:zhfxy_cn@upc.edu.cn。

中图分类号:P631-8

文献标识码:A

文章编号:1673-5005(2020)02-0052-06

DOI:10.3969/j.issn.1673-5005.2020.02.006

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参考文献 4
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参考文献 5
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参考文献 6
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参考文献 7
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参考文献 8
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参考文献 9
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参考文献 12
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参考文献 13
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参考文献 14
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参考文献 15
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参考文献 16
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参考文献 17
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目录contents

    摘要

    针对裂缝热中子示踪探测方法,从中子双组扩散理论入手结合蒙特卡洛数值模拟方法,分析压裂前后地层热中子分布影响因素,并模拟不同类型示踪剂及含量的热中子裂缝响应规律,筛选最佳示踪剂并给出其在支撑剂中含量的上、下限。 结果表明:压裂前后热中子计数变化量主要受裂缝宽度和标记支撑剂中示踪剂含量的影响;钆对裂缝宽度变化反应最灵敏,钆元素是作为标记支撑剂的最佳示踪元素;随支撑剂中 Gd2O3 含量的增加,热中子计数率降低,热中子计数变化量 D 增加;示踪剂中氧化钆的上、下限值随裂缝宽度呈指数降低,且当裂缝宽度为 1.0 cm 时, Gd2O3 的质量分数上限为 0.68% ,下限为 0.03% 。

    Abstract

    Aiming at thermal-neutron tracer detection method of fractures, the dual-group diffusion theory and Monte Carlo numerical simulation method are combined to analyze the thermal neutron characteristic distribution of the formation before and after fracturing. In addition, the fracture responses of thermal neutron count-rate to different types and content of tagged proppants were simulated. The best tracer was selected and its upper and lower limits were calculated in tagged proppants. The results show that the change in thermal neutron count before and after fracturing is mainly dominated by fracture width and the tracer content of tagged proppant. The gadolinium is the best tracer for tagged proppant, which is sensitive to the va-riety of fracture width. Moreover, with the increase of gadolinium oxide content in tagged proppant, the thermal neutron count-rate declines and the change of thermal neutron count rate (D) increases accordingly. The upper and lower limits of gadolinium oxide in the tracer decrease exponentially with the fracture width. When the fracture width is 1. 0 cm, the upper and lower limit of Gd2O3 is 0. 68% and 0. 03% , respectively

  • 随着石油天然气的勘探开发,非常规油气成为勘探开发的热点,水力压裂相关技术[1-4]是提高储层整体渗透率、实现页岩油气等非常规储层开发的有效途径[5] ,非放射性示踪裂缝评价技术因其无放射性污染、裂缝识别快速准确等优点[6-8] ,在水力压裂裂缝评价方面发挥了重要作用,对于页岩油气开发增产具有重要的意义。 Mc Daniel 等[9-10] 提出利用中子源和伽马探测器,通过对比测量压裂前后支撑剂中活化物质所放出的伽马射线强度,实现裂缝支撑剂的识别和裂缝参数的确定。 Duenckel、 Han 等[11-15]采用含有高热俘获截面元素(HTNCC) 的示踪材料与支撑剂混合,利用脉冲中子俘获测井和补偿中子测井,通过对比压裂前后地层宏观俘获截面或热中子计数变化来确定支撑剂位置、压裂缝高度等参数以及砾石填充后的裂缝特性。 Chen 等[16] 采用 Gd 示踪剂,通过设计的阵列伽马成像装置,进行近井裂缝成像可以实现裂缝方位、宽度、倾角等参数的识别。 以高热中子俘获截面元素作为支撑剂的示踪剂,利用热中子监测的方法进行近井水力压裂裂缝评价,有效地解决了环保和安全问题,具有广阔的应用前景。 笔者针对以标记压裂砂为载体的热中子监测裂缝评价技术中的示踪剂特性进行研究,筛选最佳示踪剂并给出其在支撑剂中含量的上、下限,为非放射性热中子示踪探测进行井周压裂裂缝评价提供理论基础。

  • 1 裂缝热中子探测原理

  • 地层被压裂开以后,需要向地层裂缝中注入支撑剂来保持裂缝张开,使其形成油气导流通道,利用非放射性的热中子探测裂缝识别技术是将含有高热中子俘获截面元素的标记支撑剂注入压裂裂缝中, 由于标记支撑剂具有强热中子俘获能力,致使压裂前后热中子分布存在很大差异。 标记支撑剂是由一定颗粒直径的均匀石英砂与高热中子示踪剂及烧结助剂混合高温烧制而成,示踪剂主要为高热中子截面元素的氧化物,常见的示踪剂元素主要有 B、Gd 和 Sm,钆的平均中子截面为 49 000 barns,钐为 5 900 barns,硼为 760 barns,它们与中子发生俘获作用的同时会放出伽马射线。

  • 根据双组扩散理论,地层热中子通量Ψ分布[17]

  • ψ=14πD1rL12Le2-L12(e-r/Le-e-N/L1)=14πΣr1Le2-L12(e-r/Le- e-r/L1)                        
    (1)
  • 其中

  • D =ΣL 2 t .

  • 式中,D 热中子扩散系数;Le 为快中子减速长度;L 为热中子扩散长度;Σ为地层客观俘获截面;r 为距离。

  • 压裂前地层宏观俘获截面为

  • Σ0=Σma1-φ+Σwφ 
    (2)
  • 式中,Σ0 为压裂前地层宏观俘获截面;Σma为地层骨架俘获截面;φ为地层孔隙度;Σ 为孔隙流体俘获截面。

  • 地层压裂后,裂缝体积为φi, 假设填充度为 100% ,标记支撑剂中示踪元素的含量为ξ,则压裂后地层宏观俘获截面为

  • Σ=Σm1-φ-φi+Σwφ+Σsi02φi+ΣTracφiρsi02ρTrecξ
    (3)
  • 式中,Σ为压裂后地层俘获截面; Σ0 为压裂前地层俘获截面;ρSiO2为石英砂的密度;ρTrac为示踪剂化合物的密度。 由于示踪剂的存在会导致压裂后地层宏观俘获截面增加,可以表示为

  • Σ=Σ0+ΣTracφiρsio2ρTrecξ
    (4)
  • 压裂前后同一探测器的热中子通量Ψ0和Ψ分别为

  • ψ0=14πΣ0r1Le2-Lt02e-μle
    (5)
  • ψ=14πΣr1Le2-Lt2e-r/Lv
    (6)
  • 式中,L 和 L 分别为压裂前后热中子扩散长度。 压裂前后热中子通量变化为

  • D=ψ0-ψψ0=1-Σ0Σ0+ΣTracφiξρsio2ρTracLe2-Lto2Le2-L12 
    (7)
  • 式中,压裂前后热中子通量变化受支撑剂体积φi、支撑剂中示踪剂含量ξ、扩散长度 L 、减速长度 Le 及压裂前地层宏观俘获截面Σ0 影响,并且地层孔隙决定了减速长度 Le 及宏观俘获截面 Σ0 ,则压裂前后热中子通量变化为地层孔隙度φ、裂缝体积φi 及支撑剂中示踪剂含量ξ的函数,可以表示为

  • D=fφ,φi,ξ  
    (8)
  • 压裂前后地层孔隙度基本认为不变,此时热中子计数变化量 D 主要由裂缝体积φi 及支撑剂中示踪剂含量ξ决定。 本文中将地层裂缝等效为沿轴向呈翼状对称的矩形规则裂缝,以等效裂缝宽度反映裂缝的体积,故可以通过热中子计数变化量建立支撑剂中示踪剂的含量和裂缝宽度的关系来确定支撑剂中示踪剂含量的上、下限。

  • 2 数值计算模型

  • 利用 MCNP 数值模拟软件构建压裂裂缝地层模型,如图 1 所示。 地层为孔隙度 10% 饱含淡水的致密砂岩,井眼中包含水泥环、套管、仪器及淡水,中子测井仪器贴井壁测量。裂缝穿透套管和水泥环延伸进入地层,且呈翼状对称分布于井眼两侧,裂缝中充填标记支撑剂及淡水。

  • 图 1 压裂前后岩石物理体积模型

  • Fig. 1 Rock bulk physical model before and after fracturing

  • 模型具体参数如下:地层径向半径10 ~ 70 cm, 高度140 cm,地层骨架为二氧化硅,密度2. 65 g / cm 3 ;井眼直径 20 cm,井眼中装有套管,套管与地层之间有水泥环进行胶结,采用中子仪器模型,仪器直径 49 mm,源为 D-T 中子源,长、短源距分别为 55 和 32 cm;裂缝中充填标记支撑剂,裂缝支撑剂充填度为 74.06% ,仪器正对裂缝方向。

  • 3 不同示踪剂的热中子裂缝响应

  • 建立图 2 所示模型,裂缝中充填含高热俘获截面元素的支撑剂,支撑剂中分别填充 Gd、B 和 Sm, 其在支撑剂中所占质量分数均为 0.4% ,改变裂缝宽度,变化范围为 0 ~ 2 cm,其中裂缝宽度在 0 ~ 0.1 cm 时,变化间隔为 0.02 cm,宽度在 0.1 ~ 2 cm 时, 变化间隔为 0. 2 cm,记录探测器热中子计数率,得到探测器计数率及热中子计数变化量 D 随裂缝宽度的变化关系,如图 3 所示。 由图 3 可知,当裂缝中含有高热中子俘获截面元素时,热中子计数率随裂缝宽度的增加呈指数降低,热中子计数变化量增加;当裂缝宽度一定时,支撑剂中含钆时对应的热中子计数变化量最大,含硼次之,含钐最小。 这是由于钆的热中子俘获截面非常大且远大于硼和钐的中子截面,其对热中子的俘获能力更强,当地层裂缝支撑剂中含有少量的钆时, 裂缝处的热中子计数大幅降低,压裂前后裂缝处的热中子计数差异更大。 对比 3 种示踪剂对裂缝的响应灵敏度,钆示踪剂的响应灵敏度最高。 综合考虑裂缝灵敏度、高热截面元素的性价比因素,最终选择钆作为标记支撑剂中的示踪剂。

  • 图 2 MCNP 计算模型

  • Fig. 2 Monte Carlo simulation model

  • 图 3 不同标记示踪剂的热中子对裂缝宽度的响应

  • Fig. 3 Responses of thermal neutrons to fracture width under different tagged tracer

  • 4 示踪剂含量上、下限的确定

  • 当地层裂缝中充填含钆支撑剂时,裂缝区域对热中子的俘获能力大幅增强,热中子计数降低,当支撑剂中的钆含量达到一定值时,裂缝区域的热中子全部被俘获,从而达到一种近似“平衡状态”,此时继续增加钆的含量,热中子计数不再变化,则该临界值即为钆含量上限。

  • 建立图 2 所示模型,设置多种裂缝宽度,分别为0.02、0. 04、0. 06、0.08、0.1、0.2、0. 4、0. 6、0.8、1. 0、 1. 5、2. 0 cm,裂缝中充填含 Gd2O3 的支撑剂和淡水, 改变支撑剂中 Gd2O3 的质量分数,变化范围为 0 ~ 2% ,其中在 0 ~ 0.1% 时,变化间隔为 0. 01% ,质量分数在 0.1% ~ 0. 2% 时,变化间隔为 0. 02% ,记录探测器热中子计数率,得到不同裂缝宽度条件下探测器计数率及热中子计数变化量 D 随支撑剂中 Gd2O3 质量分数的变化关系(图 4)。

  • 图 4 不同裂缝宽度条件下热中子随 Gd2O3 质量分数变化的响应关系

  • Fig. 4 Responses of thermal neutrons to mass fraction of Gd2O3 under different fracture width

  • 将热中子计数变化量的 90% 作为饱和界限,此时对应的支撑剂中钆含量即为上限。 根据图 4(b)分别计算不同裂缝宽度条件下支撑剂中钆含量的上限, 得到其随裂缝宽度的变化关系,如图 5 所示。 由图 5 可知,支撑剂中氧化钆质量分数上限随裂缝宽度的增加,近似呈指数下降,且当裂缝宽度为 1.0 cm 时,支撑剂中氧化钆质量分数的上限约为 0.68% 。 当支撑剂中氧化钆含量一定时,裂缝宽度越小,地层裂缝中钆的数量越少,压裂前后热中子计数差异越小,如果要使其达到饱和,则必须增加支撑剂中钆的含量。 反之,裂缝宽度越大,支撑剂中所需要的钆含量越低。

  • 非放射性示踪利用压裂前后热中子计数变化来进行裂缝评价,测量得到的热中子计数存在放射性统计涨落,在裂缝评价过程中支撑剂中氧化钆质量分数的下限必须满足在任意裂缝宽度下能够利用压裂前后热中子计数差区分出裂缝地层和未压裂地层。

  • 压裂前后热中子计数 N0 、NB 均服从正态分布[17] ,故热中子计数差值ΔN 也服从正态分布,标准差为

  • σΔN=N0+NB 
    (9)
  • 利用压裂前后热中子计数差区分出裂缝地层和未压裂地层,则ΔN 应满足:

  • ΔN>kαN0+NB 
    (10)
  • 式中,kα 为正态分布区间对应系数。

  • 当 α= 0.01 时,查表可知 kα = 2.326,则

  • ΔN>2.3262N0
    (11)
  • 对同一致密地层,压前热中子探测器计数取决于中子测井仪器的探测器转换效率ε和源距 L,热中子计数随源距的响应如图 6 所示。

  • 图5 支撑剂中 Gd2O3 质量分数上限随裂缝宽度的变化关系

  • Fig. 5 Relationship between the upper limit of mass fraction for Gd2O3 in proppant and fracture width

  • 图 6 热中子计数随源距的响应关系

  • Fig. 6 Relationship between thermal neutron count and spacing

  • 利用公式(11)求解得到对应的支撑剂中 Gd2O3 质量分数的下限随裂缝宽度的响应关系,如图 7 所示。 支撑剂中 Gd2O3 质量分数下限随裂缝宽度的增

  • 图7 支撑剂中 Gd2O3 质量分数下限随裂缝宽度的变化关系

  • Fig. 7 Relationship between the lower limit of mass fraction for Gd2O3 in proppant and fracture width

  • 加而呈指数减小,当裂缝宽度为 1. 0 cm 时,支撑剂中Gd2O3 质量分数的下限约为0. 03% ,在利用热中子计数差异进行支撑裂缝的评价时,必须使支撑剂中 Gd2O3 质量分数大于支撑剂中 Gd2O3 质量分数的下限,才能实现裂缝的评价。

  • 5 结论

  • (1)压裂前后热中子计数变化量主要受裂缝宽度和标记支撑剂中示踪剂含量的影响。

  • (2)钆对裂缝宽度变化反应最灵敏,结合硼、钆和钐的截面、物理特性和价格,得出钆元素是作为标记支撑剂的最佳示踪元素。

  • (3)随支撑剂中 Gd2O3 含量的增加,热中子计数率降低,热中子计数变化量 D 增加。 给出支撑剂中 Gd2O3 质量分数上、下限随裂缝宽度的响应关系,且当裂缝宽度为 1. 0 cm 时,Gd2O3 的质量分数上限为 0.68% ,下限为 0.03% 。

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    • [2] 曲占庆,田雨,李建雄,等.水平井多段分簇压裂裂缝扩展形态数值模拟[J].中国石油大学学报(自然科学版),2017,41(1):102-109.QU Zhanqing,TIAN Yu,LI Jianxiong,et al.Numerical simulation study on fracture extension and morphology of multi-cluster staged fracturing for horizontal wells [J].Journal of China University of Petroleum(Edition of Natu-ral Science),2017,41(1):102-109.

    • [3] 仲冠宇,王瑞和,周卫东,等.水力深穿透射孔对压裂裂缝形态影响的数值模拟[J].中国石油大学学报(自然科学版),2016,40(5):79-86.ZHONG Guanyu,WANG Ruihe,ZHOU Weidong,et al.Numerical simulation of hydraulic deep jet perforation on fracture propagation and orientation[J].Journal of China University of Petroleum(Edition of Natural Science),2016,40(5):79-86.

    • [4] 张丁涌,袁士宝,田相雷,等.低渗油藏径向水力射流压裂裂缝延伸规律[J].中国石油大学学报(自然科学版),2016,40(2):129-134.ZHANG Dingyong,YUAN Shibao,TIAN Xianglei,et al.Research on fracturing extension by radial hydraulic jet in low permeability reservoirs[J].Journal of China Univer-sity of Petroleum(Edition of Natural Science),2016,40(2):129-134.

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    • [17] 黄隆基.放射性测井原理[M].北京:石油工业出版社,1985:134-135.

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