基于水锤效应与倒谱变换的停泵压力分析方法

doi:10.13809/j.cnki.cn32-1825/te.2023.01.012

摘要/Abstract

摘要：

裂缝实时监测评价是水平井多段压裂过程中的一个核心问题，长期以来受到大量学者的关注。压裂施工停泵期间的压力包括水锤压力和渗流压力两部分，通过在井口安装高频压力装置，不仅可以采集停泵压降曲线，还可以完整地采集到水锤波波形曲线。通过对井筒水锤控制方程的数值求解，获得模拟的水锤波压力数据。对模拟的水锤波压力进行倒谱分析验证了水锤波产生的压力具有卷积特性，根据波阻抗及倒谱分析相关理论，利用水锤波可判断水平井多簇压裂的裂缝簇数与深度。在四川页岩气井的现场应用表明：该方法能够发现5个进液点，其中4个进液点的反演结果与4个射孔位置接近，设计中剩余的4簇孔对应的进液点在倒谱分析中并没有监测到。

关键词: 高频压力监测, 停泵数据分析, 倒谱分析, 水平井多段压裂, 裂缝参数反演, 进液点位置

Abstract:

Real-time monitoring and evaluation of fractures is one of the core issues in the multi-stage fracturing process of horizontal wells, and has long been a focus of many scholars. During the fracturing construction, the pressure during pump shutdown includes water hammer pressure and seepage pressure. By installing a high-frequency pressure device at the wellhead, not only the pump shutdown pressure drop curve but also the water hammer waveform curve can be completely collected. In this paper, the simulated pressure data are obtained by numerically solving the governing equation of wellbore water hammer. The cepstrum analysis of the simulated water hammer pressure verifies that the pressure generated by the water hammer has convolution characteristics. According to the related theory of wave impedance and cepstrum analysis, the water hammer wave can be used to determine the number of fracture clusters and the depth in multi-cluster fracturing of horizontal wells. The field application in Sichuan shale gas well shows that this method can find five liquid inlet points, of which the inversion results of four liquid inlet points are close to four perforation positions, and the remaining four clusters of holes in the design correspond to the liquid inlet points It was not detected in the cepstrum analysis.

Key words: high-frequency pressure monitoring, data analysis of pump shutdown, cepstrum analysis, multi-stage hydraulic fracturing for horizontal well, inversion of fracture parameter, liquid inlet location

中图分类号:

TE357

王晓强,赵立安,王志愿,修春红,贾国龙,董研,卢德唐. 基于水锤效应与倒谱变换的停泵压力分析方法[J]. 油气藏评价与开发, 2023, 13(1): 108-116.

WANG Xiaoqiang,ZHAO Li’an,WANG Zhiyuan,XIU Chunhong,JIA Guolong,DONG Yan,LU Detang. Data analysis method of pump shutdown pressure based on water hammer effect and cepstrum transformation[J]. Reservoir Evaluation and Development, 2023, 13(1): 108-116.

图/表 8

图1

图2

图3

图4

表1

数值模拟参数取值"

参数名称	符号	取值
井指数[MPa/（m³·d^-1）]	$R$	5×10^-5
井筒存储常数（m³/MPa）	$C$	0.02
惯性系数（kg/m⁴）	$I$	100
井筒截面积（m²）	$A$	1.52×10^-2
波速（m/s）	c	1 194

表1

图5

图6

表2

参考文献 31

[1]	ABOU-SAYED I S, SCHUELER S, EHRL E, et al. Multiple hydraulic fracture stimulation in a deep horizontal tight gas well[J]. Journal of Petroleum Technology, 1996, 48(2): 163-168. doi: 10.2118/30532-JPT
[2]	LOVE T G, MCCARTY R A, SURJAATMADJA J B, et al. Selectively placing many fractures in openhole horizontal wells improves production[J]. SPE Production & Facilities, 2001, 16(4): 219-224.
[3]	CHAMBERS M R, MUELLER M W, GROSSMANN A. Well completion design and operations for a deep horizontal well with multiple fractures[C]// Paper SPE-30417-MS presented at the SPE Offshore Europe, Aberdeen, United Kingdom, September 1995.
[4]	雷群, 胥云, 才博, 等. 页岩油气水平井压裂技术进展与展望[J]. 石油勘探与开发, 2022, 49(1): 166-172.
	LEI Qun, XU Yun, CAI Bo, et al. Progress and prospects of horizontal well fracturing technology for shale oil and gas reservoirs[J]. Petroleum Exploration and Development, 2022, 49(1): 166-172.
[5]	U.S. Energy Information Administration. Annual energy outlook 2010[R]. U.S. Energy Information Administration: Washington, 2010.
[6]	LE CALVEZ J H, GRANT W D, MCCARLEY D L, et al. Hydraulic-fracture monitoring as a tool to improve reservoir management[C]// Paper SPE-94048-MS presented at the SPE Production Operations Symposium, Oklahoma City, Oklahoma, April 2005.
[7]	邢岳堃, 黄炳香, 陈大勇, 等. 压裂裂缝非线性断裂的声发射全波形多参量监测[J]. 煤炭学报, 2021, 46(11): 3470-3487.
	XING Yuekun, HUANG Bingxiang, CHEN Dayong, et al. Nonlinear fracturing characterization of hydraulic frac-ture :Utilizing full-waveform and multi-parameter analysis method of acoustic emission[J]. Journal of China Coal Society, 2021, 46(11): 3470-3487.
[8]	段银鹿, 李倩, 姚韦萍. 水力压裂微地震裂缝监测技术及其应用[J]. 断块油气田, 2013, 20(5): 644-648.
	DUAN Yinlu, LI Qian, YAO Weiping. Microseismic fracture monitoring technology of hydraulic fracturing and its application[J]. Fault-Block Oil &Gas Field, 2013, 20(5): 644-648.
[9]	AL-KOBAISI M, OZKAN E, KAZEMI H, et al. Pressure-transient-analysis of horizontal wells with transverse, finite-conductivity fractures[C]// Paper PETSOC-2006-162 presented at the Canadian International Petroleum Conference, Calgary, Alberta, June 2006.
[10]	OZKAN E, BROWN M L, RAGHAVAN R S, et al. Comparison of fractured horizontal-well performance in conventional and unconventional reservoirs[C]// Paper SPE-121290-MS presented at the SPE Western Regional Meeting, San Jose, California, March 2009.
[11]	BROWN M, OZKAN E, RAGHAVAN R, et al. Practical solutions for pressure-transient responses of fractured horizontal wells in unconventional shale reservoirs[J]. SPE Reservoir Evaluation & Engineering, 2011, 14(6): 663-676.
[12]	田树宝, 雷刚, 杨立敏, 等. 微裂缝发育储层分段压裂水平井裂缝参数预测[J]. 石油与天然气地质, 2017, 38(2): 400-406.
	TIAN Shubao, LEI Gang, YANG Limin, et al. A novel method to interpret fracture parameters of multistage fractured horizontal well in reservoirs with micro-fractures[J]. Oil & Gas Geology, 2017, 38(2): 400-406.
[13]	罗红文, 李海涛, 李颖, 等. 低渗透气藏压裂水平井产出剖面与裂缝参数反演解释[J]. 石油学报, 2021, 42(7): 936-947. doi: 10.7623/syxb202107008
	LUO Hongwen, LI Haitao, LI Ying, et al. Inversion and interpretation of production profile and fractured horizontal wells in low-permeability gas reservoirs[J]. Acta Petrolei Sinica, 2021, 42(7): 936-947. doi: 10.7623/syxb202107008
[14]	LUO H, LI H, TAN Y, et al. A novel inversion approach for fracture parameters and inflow rates diagnosis in multistage fractured horizontal wells[J]. Journal of Petroleum Science and Engineering, 2020, 184: 106585.
[15]	LI W C, LU H, JIN Y C, et al. Deep learning for quantitative hydraulic fracture profiling from fiber optic measurements[C]// Paper URTEC-2021-5583-MS presented at the SPE/AAPG/SEG Unconventional Resources Technology Conference, Houston, Texas, USA, July 2021.
[16]	NOLTE K G. Determination of fracture parameters from fracturing pressure decline[C]// Paper SPE-8341-MS presented at the SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada, September 1979.
[17]	NOLTE K G, SMITH M B. Interpretation of fracturing pressures[J]. Journal of Petroleum Technology, 1981, 33(9): 1767-1775. doi: 10.2118/8297-PA
[18]	NOLTE K G. Fracturing-pressure analysis for nonideal behavior[J]. Journal of Petroleum Technology, 1991, 43(2): 210-218. doi: 10.2118/20704-PA
[19]	NOLTE K G, MACK M G, LIE W L. A systematic method for applying fracturing pressure decline: Part Ⅰ[C]// Paper SPE-25845-MS presented at the Low Permeability Reservoirs Symposium, Denver, Colorado, April 1993.
[20]	NOLTE K G, MANIERE J L, OWENS K A. After-closure analysis of fracture calibration tests[C]// Paper SPE-38676-MS presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, October 1997.
[21]	温杰雄, 田伟, 毕全福, 等. 基于数字滤波的压裂停泵数据反演方法[J]. 中国科学技术大学学报, 2018, 48(5): 392-399.
	WEN Jiexiong, TIAN Wei, BI Quanfu, et al. A new data inversion analysis method based on digital filtered pump-stop data of hydraulic fracturing[J]. Journal of University of Science and Technology of China, 2018, 48(5): 392-399.
[22]	HOLZHAUSEN G R, GOOCH R P. Impedance of hydraulic fractures: its measurement and use for estimating fracture closure pressure and dimensions[C]// Paper SPE-13892-MS presented at the SPE/DOE Low Permeability Gas Reservoirs Symposium, Denver, Colorado, May 1985.
[23]	CAREY M A, MONDAL S, SHARMA M M. Analysis of water hammer signatures for fracture diagnostics[C]// Paper SPE-174866-MS presented at the SPE Annual Technical Conference and Exhibition, Houston, Texas, USA, September 2015.
[24]	BOGDAN A V, KEILERS A, OUSSOLTSEV D, et al. Real-time interpretation of leak isolation with degradable diverter using high frequency pressure monitoring[C]// Paper SPE-182451-MS presented at the SPE Asia Pacific Oil & Gas Conference and Exhibition, Perth, Australia, October 2016.
[25]	KORKIN R, PARKHONYUK S, FEDOROV A, et al. High frequency pressure monitoring and data analytics for stimulation efficiency determination: New perspectives or potential limits[C]// Paper SPE-199762-MS presented at the SPE Hydraulic Fracturing Technology Conference and Exhibition, The Woodlands, Texas, USA, February 2020.
[26]	RAHMANI A R, SHIRDEL M. Impedance analysis as a tool for hydraulic fracture diagnostics in unconventional reservoirs[C]// Paper SPE-156577-MS presented at the SPE International Production and Operations Conference & Exhibition, Doha, Qatar, May 2012.
[27]	PARKHONYUK S, FEDOROV A, KABANNIK A, et al. Measurements while fracturing: Nonintrusive method of hydraulic fracturing monitoring[C]// Paper SPE-189886-MS presented at the SPE Hydraulic Fracturing Technology Conference and Exhibition, The Woodlands, Texas, USA, January 2018.
[28]	胡晓东, 周福建, 李宇娇, 等. 压裂停泵水击压力波信号滤波方法与特征分析[J]. 石油科学通报, 2021, 6(1): 79-91.
	HU Xiaodong, ZHOU Fujian, LI Yujiao, et al. Filtering methods and characteristic analysis of water hammer pressure—wave signals from fracturing stop pumps[J]. Petroleum Science Bulletin, 2021, 6(1): 79-91.
[29]	WYLIE E B, STREETER V L, SUO L. Fluid transients in systems[M]. New Jersey: Prentice Hall Englewood Cliffs, 1993.
[30]	COLEBROOK C F, WHITE C M. Experiments with fluid friction in roughened pipes[J]. Proceedings of the Royal Society of London Series a-Mathematical and Physical Sciences, 1937, 161: 367-381.
[31]	BOGERT B P, HEALY M J R, TUKEY J W. The quefrency alanysis of time series for echoes: Cepstrum, pseudo-autocovariance, cross-cepstrum and saphe cracking[J]. proceedings of the symposium on time, 1963: 59352135.

簇号	射孔顶、底（m）	倒谱峰值时间（s）	倒谱反演位置（m）
1	2 334.5~2 335.0	3.91	2 336.43
2	2 326.0~2 326.5
3	2 317.5~2 318.0
4	2 309.0~2 309.5	3.87	2 311.20
5	2 300.5~2 301.0	3.85	2 300.01
6	2 292.0~2 292.5
7	2 283.5~2 284.0	3.83	2 286.57
8	2 274.0~2 274.5
9	2 264.5~2 265.0	3.79	2 268.37