复杂诱导裂缝网络注水直井试井模型及压力动态分析

Well testing model and pressure transient behavior analysis of water injection vertical wells with complex in-duced-fracture networks

摘要

低渗透油藏在注水直井井筒周围容易形成复杂诱导裂缝网络，诱导裂缝在关井测压过程中发生闭合。为有效反演复杂诱导裂缝网络及井底压力动态，建立复杂诱导裂缝网络注水直井半解析试井模型，耦合裂缝数值渗流方程及裂缝流量节点守恒方程，考虑变裂缝储集表征裂缝闭合状态，采用线源方法、Laplace 变换和 Stehfest 数值反演方法，求解复杂诱导裂缝网络注水直井试井模型，分析注水直井典型压力动态及影响参数。结果表明：复杂诱导裂缝网络注水直井压力动态可划分为 8 个流动阶段；诱导裂缝闭合作用产生双井储现象，压力动态曲线出现裂缝储集及第二过渡流阶段，裂缝闭合速度越快，凸起越明显。次级裂缝导致压力曲线出现裂缝供给阶段，渗透率越大，裂缝供给阶段下凹越明显。该试井模型可以有效处理注水直井周围复杂诱导裂缝网络及在关井测压过程中裂缝闭合作用，为诱导裂缝注水直井的参数解释提供参考。

Abstract

In low-permeability reservoirs, water injection in vertical wells usually generated complex induced fracture networks near the wellbore. These fractures are prone to closure during pressure buildup tests, making it difficult for existing well testing methods to achieve reliable inversion. Therefore, a semi-analytical pressure transient analysis model for water injection vertical wells with complex induced fracture networks is developed. The model couples the numerical solution of discretized fracture panels with the flow balance equation of each vertex to characterize fluid flow in complex fracture networks. Variable fracture storage is introduced to represent fracture closure behavior. By integrating the linesource function, Laplace transform, and Stehfest numerical inversion, the model achieves an efficient solution in such scenarios. The study clarifies the typical pressure transients of water injection vertical wells and quantifies the impact of key parameters. Finally, the model is validated through a field case application. The results demonstrate that the typical pressure transient curve can be divided into eight flow stages. The fracture closure effect generates a dual-well storage phenomenon, manifesting as a fracture storage stage and a second transition flow stage on the pressure derivative curve. The faster fracture closure rates lead to more pronounced "humps" on the curve. The secondary fractures create a fluid feed regime, where higher conductivity in these fractures results in deeper "dips" on the pressure response. The proposed well testing model effectively characterizes complex induced fracture networks around water injection wells and accounts for fracture closure during shut-in periods. Field applications confirm the model's practicality and accuracy, providing a reliable tool for parameter interpretation in such wells.

关键词

注水直井 / 试井模型 / 诱导裂缝网络 / 裂缝闭合 / 压力动态分析 / 双井储效应

Key words

vertical injection well / well testing model / induced fracture network / fracture closure / pressure transient analysis / dual-well storage effect

参考文献

[1] 孙福街, 徐文江, 姜维东, 等. 中国海油低渗及非常规油气藏储层改造技术进展及展望[J]. 中国海上油气, 2024, 36(1):109-116.

[2] SUN Fujie, XU Wenjiang, JIANG Weidong, et al. Progress and prospects of CNOOC's low permeability and unconventional oil and gas reservoir stimulation technologies[J]. China Offshore Oil and Gas, 2024, 36(1):109-116.

[3] 令永刚, 王西强, 高雪, 等. 鄂尔多斯盆地超低渗油藏注采调整技术[J]. 科学技术与工程, 2024, 24(26):11102-11110.

[4] LING Yonggang, WANG Xiqiang, GAO Xue, et al. Injection production adjustment technology for ultra-low permeability reservoirs in the Ordos Basin[J]. Science Technology and Engineering, 2024, 24(26):11102-11110.

[5] 陈建, 叶青, 郇金来, 等. 基于双峰高斯函数的海上低渗储层孔隙结构定量表征:以琼东南盆地 BD21 气田陵水组三段为例[J]. 东北石油大学学报, 2024, 48(1):39-50.

[6] CHEN Jian, YE Qing, HUAN Jinlai, et al. Quantitative characterization of pore structure in offshore low-permeability reservoirs based on double-peak Gaussian function:a case study of the third member of the Lingshui Formation in the BD21 Gas Field,Qiongdongnan Basin[J]. Journal of Northeast Petroleum University, 2024, 48(1):39-50.

[7] 关耀, 叶青, 张冲, 等. 高压低渗透碎屑岩储层孔隙结构特征及分类评价:以莺歌海盆地东方 A-1区黄流组一段为例[J]. 东北石油大学学报, 2024, 48(5):75-89.

[8] GUAN Yao, YE Qing, ZHANG Chong, et al. Pore structure characteristics and classification evaluation of high-pressure and low-permeability clastic reservoir:taking the first member of Huangliu Formation in Dongfang A-1 Area of Yinggehai Basin as an example[J]. Journal of Northeast Petroleum University, 2024, 48(5):75-89.

[9] 张翔宇, 于田田, 李爱芬, 等. 低渗透夹层分布对正韵律非均质储层渗流规律的影响[J]. 特种油气藏, 2024, 31(5):102-109.

[10] ZHANG Xiangyu, YU Tiantian, LI Aifen, et al. The influence of low permeability interlayers distribution on the seepage law of positive rhythm heterogeneous reservoir[J]. Special Oil & Gas Reservoirs, 2024, 31(5):102-109.

[11] 范天一, 宋新民, 吴淑红, 等. 低渗透油藏水驱动态裂缝数学模型及数值模拟[J]. 石油勘探与开发, 2015, 42(4):496-501.

[12] FAN Tianyi, SONG Xinmin, WU Shuhong, et al. A mathematical model and numerical simulation of waterflood induced dynamic fractures of low permeability reservoirs[J]. Petroleum Exploration and Development, 2015, 42(4):496-501.

[13] 吕文雅, 安小平, 刘艳祥, 等. 致密砂岩储层注水诱导裂缝动态识别及演化特征:以鄂尔多斯盆地姬塬油田 L 井区长 8 油藏为例[J]. 石油与天然气地质, 2024, 45(5):1431-1446.

[14] LYU Wenya, AN Xiaoping, LIU Yanxiang, et al. Dynamic responses and evolutionary characteristics of waterflood-induced fractures in tight sandstone reservoirs:a case study of oil reservoirs in the 8th member of the Yanchang Formation,well block L,Jiyuan Oilfield,Ordos Basin[J]. Oil & Gas Geology, 2024, 45(5):1431-1446.

[15] 师调调, 石立华, 武晓婷, 等. 浅层油藏水平缝形态识别及渗流特征[J]. 特种油气藏, 2024, 31(6):91-99.

[16] SHI Tiaotiao, SHI Lihua, WU Xiaoting, et al. identification of horizontal fracture morphology and flow characteristics in shallow oil reservoirs[J]. Special Oil & Gas Reservoirs, 2024, 31(6):91-99.

[17] 汪洋, 程时清, 秦佳正, 等. 超低渗透油藏注水诱导动态裂缝开发理论及实践[J]. 中国科学:技术科学, 2022, 52(4):613-626.

[18] WANG Yang, CHENG Shiqing, QIN Jiazheng, et al. Development theory and practice of water injection induced fractures in ultralow permeability reservoirs[J]. Scientia Sinica(Technologica), 2022, 52(4):613-626.

[19] 许冬进, 吴应松, 熊齐, 等. 低渗透油藏压驱技术现状及发展趋势[J]. 断块油气田, 2024, 31(3):533-540.

[20] XU Dongjin, WU Yingsong, XIONG Qi, et al. Status and development trend of fracturing-flooding technology in low permeability reservoirs[J]. Fault-Block Oil & Gas Field, 2024, 31(3):533-540.

[21] SPIVEY J P, LEE W J. Variable wellbore storage models for a dual-volume wellbore[C]//SPE Annual Technical Conference and Exhibition.Houston,Texas, USA: Society of Petroleum Engineers, 1999:SPE-56615-MS.

[22] BINAKRESH S A, RAHMAN N M A. Challenges in interpreting well testing data from fractured water injection wells with a dual storage phenomenon[C]//SPE Middle East Oil and Gas Show and Conference. [S.1.]:[s. n.], 2011:SPE-139587-MS.

[23] WANG Yang, CHENG Shiqing, FENG Naichao, et al. Semi-analytical modeling for water injection well in tight reservoir considering the variation of waterflood-induced fracture properties:case studies in Changqing Oilfield,China[J]. Journal of Petroleum Science and Engineering, 2017, 159:740-753.

[24] WANG Yang, CHENG Shiqing, ZHANG Kaidi. et al. A comprehensive work flow to characterize waterflood-induced fractures by integrating real-time monitoring,formation test,and dynamic production analysis applied to Changqing Oilfield,China[J]. SPE Reservoir Evaluation & Engineering, 2019, 22(2):692-708.

[25] WANG Zhipeng, NING Zhengfu, GUO Wenting, et al. Pressure-transient analysis for waterflooding with the influence of dynamic induced fracture in tight reservoir:model and case studies[J]. SPE Reservoir Evaluation & Engineering, 2023, 26(3):994-1016.

[26] WANG Zhipeng, NING Zhengfu, ZHAN Jie, et al. Evaluation of effects of waterflooding-induced bilayer fractures on tight reservoir using pressure-transient analysis method[J]. SPE Reservoir Evaluation & Engineering, 2023, 26(4):1378-1401.

[27] WANG Zhipeng, NING Zhengfu, GUO Wenting, et al. Pressure transient analysis for water injection wells with waterflooding-induced nonsimultaneously closed multistorage fractures:semianalytical model and case study[J]. SPE Reservoir Evaluation & Engineering, 2023, 26(4):1416-1438.

[28] 金子一, 胡之牮, 贾品. 考虑诱导裂缝和椭圆复合分区特征的注水井试井解释模型研究[J/OL]. 计算物理,1-10[2025-05-08]. http://kns.cnki.net/kcms/detail/11.2011.o4.20240401.1734.002.html.

[29] JIN Ziyi, HU Zhidai, JIA Pin. Study on well test model of injection well considering waterflood-induced fracture and elliptical flow composite[J/OL].Chinese Journal of Computational Physics,1-10[2025-05-08]. http://kns.cnki.net/kcms/detail/11.2011.o4.20240401.1734.002.html.

[30] CUI Yongzheng, JIANG Ruizhong, GAO Yihua, et al. Semi-analytical modeling of rate transient for a multi-wing fractured vertical well with partially propped fractures considering different stress-sensitive systems[J]. Journal of Petroleum Science and Engineering, 2022, 208:109548.

[31] ZHOU Wentao, BANERJEE Ray, POE Bobby, et al. Semi-analytical production simulation of complex hydraulic fracture network[J]. SPE Journal, 2013, 19(1):6-18.

[32] 姜瑞忠, 王星, 王琼, 等. 基于分形和分数阶的煤层气藏多级压裂水平井试井模型[J]. 东北石油大学学报, 2020, 44(3):97-106.

[33] JIANG Ruizhong, WANG Xing, WANG Qiong, et al. Test model for multi-fractured horizontal wells in the coal bed methane reservoir based on the fractal theory and the fractional calculus[J]. Journal of Northeast Petroleum University, 2020, 44(3):97-106.

[34] CINCO-LEY H, SAMANIEGO-V F. Transient pressure analysis for fractured wells[J]. Journal of Petroleum Technology, 1981, 33 (9):1746-1766.

[35] 徐有杰, 向祖平, 张小涛, 等. 考虑诱导缝多段压裂水平井非均质改造压力动态模型研究[J]. 力学学报, 2023, 55(3):656-668.

[36] XU Youjie, XIANG Zuping, ZHANG Xiaotao, et al. Pressure transient model of multi-stage fractured horizontal well with induced fracture for heterogeneous stimulated reservoir volume[J]. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(3):656-668.

[37] 陈志明, YU Wei, 石璐铭, 等. 压裂水平井的多模式裂缝网络试井模型及参数评价:以吉木萨尔页岩油为例[J]. 石油学报, 2023, 44 (10):1706-1726.

[38] CHEN Zhiming, YU Wei, SHI Luming, et al. Well test model and parameter evaluation of multi-mode fracture network in fractured horizontal well:a case study of Jimsar shale oil[J]. Acta Petrolei Sinica, 2023, 44(10):1706-1726.

[39] VAN DEN HOEK P J. Dimensions and degree of containment of waterflood-induced fractures from pressure-transient analysis[J]. SPE Reservoir Evaluation & Engineering, 2005, 8(5):377-387.

基金资助

国家自然科学基金面上项目(52074347)

中国海洋石油有限公司＂十四五＂重大科技项目(KJGG2021-0501)

海洋油气高效开发全国重点实验室主任基金项目(KJQZ-2024-2101)