Semi-Analytical Model and Seepage Characteristics of Multi-Wing Fracture Off-Center Wells

JI Anzhao

doi:10.21656/1000-0887.430395

Volume 44 Issue 10

Oct. 2023

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2023 > 44(10): 1200-1212

JI Anzhao. Semi-Analytical Model and Seepage Characteristics of Multi-Wing Fracture Off-Center Wells[J]. Applied Mathematics and Mechanics, 2023, 44(10): 1200-1212. doi: 10.21656/1000-0887.430395

Citation:

JI Anzhao. Semi-Analytical Model and Seepage Characteristics of Multi-Wing Fracture Off-Center Wells[J]. Applied Mathematics and Mechanics, 2023, 44(10): 1200-1212. doi: 10.21656/1000-0887.430395

Citation:

JI Anzhao. Semi-Analytical Model and Seepage Characteristics of Multi-Wing Fracture Off-Center Wells[J]. Applied Mathematics and Mechanics, 2023, 44(10): 1200-1212. doi: 10.21656/1000-0887.430395

PDF( 3301 KB)

Semi-Analytical Model and Seepage Characteristics of Multi-Wing Fracture Off-Center Wells

doi: 10.21656/1000-0887.430395

JI Anzhao

Longdong University, Qingyang, Gansu 745100, P.R.China

Received Date: 2022-12-20
Rev Recd Date: 2023-03-04
Publish Date: 2023-10-31

Abstract

Abstract

In view of the actual situation of multi-wing fracture off-center wells, the mathematical model for the wells was established. Based on the Laplace transform and the pressure drop superposition principle, the semi-analytical solution of the bottom hole pressure in the multi-wing fracture off-center well in the Laplace space, was obtained. The semi-analytical solution was discretized with the non-uniform flow method. Combined with Stehfest numerical inversion, the numerical solution of the real space bottom hole pressure and the production distribution were obtained. The numerical well test model for the reservoir was established with the SAPHIR well test analysis software, and the numerical discrete calculation was carried out. The numerical results were compared with the calculation results of the semi-analytical model, which verifies the correctness of the semi-analytical model. The results show that, the bottom hole pressure variation of the multi-wing fracture off-center well can be divided into 8 main flow stages. Finally, the effects of the dimensionless conductivity, the fracture asymmetry factor and the off-center distance on the bottom hole pressure variation and production distribution characteristics, were discussed.
- hydraulic fracturing well,
- off-center well,
- asymmetric fracture,
- Green function,
- multi-wing fracture

FullText(HTML)

References(35)

References

[1]	郭旭升, 蔡勋育, 刘金连, 等. 中国石化"十三五"天然气勘探进展与前景展望[J]. 天然气工业, 2021, 41(8): 12-22. https://www.cnki.com.cn/Article/CJFDTOTAL-TRQG202108003.htm GUO Xusheng, CAI Xunyu, LIU Jinlian, et al. Natural gas exploration progress of SINOPEC during the 13th Five-Year Plan and prospect forecast during the 14th Five-Year Plan[J]. Natural Gas Industry, 2021, 41(8): 12-22. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-TRQG202108003.htm
[2]	何江川, 余浩杰, 何光怀, 等. 鄂尔多斯盆地长庆气区天然气开发前景[J]. 天然气工业, 2021, 41(8): 23-33. https://www.cnki.com.cn/Article/CJFDTOTAL-TRQG202108004.htm HE Jiangchuan, YU Haojie, HE Guanghuai, et al. Natural gas development prospect in Changqing gas province of the Ordos Basin[J]. Natural Gas Industry, 2021, 41(8): 23-33. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-TRQG202108004.htm
[3]	马新华. 非常规天然气"极限动用"开发理论与实践[J]. 石油勘探与开发, 2021, 48(2): 326-336. https://www.cnki.com.cn/Article/CJFDTOTAL-SKYK202102011.htm MA Xinhua. "Extreme utilization" development theory of unconventional natural gas[J]. Petroleum Exploration and Development, 2021, 48(2): 326-336. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-SKYK202102011.htm
[4]	王继平, 张城玮, 李建阳, 等. 苏里格气田致密砂岩气藏开发认识与稳产建议[J]. 天然气工业, 2021, 41(2): 100-110. https://www.cnki.com.cn/Article/CJFDTOTAL-TRQG202102017.htm WANG Jiping, ZHANG Chengwei, LI Jianyang, et al. Tight sandstone gas reservoirs in the Sulige Gas Field: development understandings and stable-production proposals[J]. Natural Gas Industry, 2021, 41(2): 100-110. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-TRQG202102017.htm
[5]	贾爱林, 何东博, 位云生, 等. 未来十五年中国天然气发展趋势预测[J]. 天然气地球科学, 2021, 32(1): 17-27. https://www.cnki.com.cn/Article/CJFDTOTAL-TDKX202101002.htm JIA Ailin, HE Dongbo, WEI Yunsheng, et al. Predictions on natural gas development trend in China for the next fifteen years[J]. Natural Gas Geoscience, 2021, 32(1): 17-27. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-TDKX202101002.htm
[6]	欧阳伟平, 孙贺东, 张冕. 考虑应力敏感的致密气多级压裂水平井试井分析[J]. 石油学报, 2018, 39(5): 570-577. https://www.cnki.com.cn/Article/CJFDTOTAL-SYXB201805008.htm OUYANG Weiping, SUN Hedong, ZHANG Mian. Well test analysis for multistage fractured horizontal wells in tight gas reservoir considering stress sensitivity[J]. Acta Petrolei Sinica, 2018, 39(5): 570-577. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-SYXB201805008.htm
[7]	CINCO-LEY H, MENG H Z. Pressure transient analysis of wells with finite conductivity vertical fractures in double porosity reservoirs[C]//SPE Annual Technical Conference and Exhibition. Houston, Texas, 1988.
[8]	HUANG T, GUO X, CHEN F. Modeling transient pressure behavior of a fractured well for shale gas reservoirs based on the properties of nanopores[J]. Journal of Natural Gas Science and Engineering, 2015, 23(1): 387-398.
[9]	WANG L, WANG X, DING X, et al. Rate decline curves analysis of a vertical fractured well with fracture face damage[J]. Journal of Energy Resources Technology, 2012, 134(3): 1-9.
[10]	WANG L, WANG X. Type curves analysis for asymmetrically fractured wells[J]. Journal of Energy Resources Technology, 2014, 136(2): 1-8.
[11]	CRAWFORD P B, LANDRUM B L. Effect of unsymmetrical vertical fractures on production capacity[J]. American Invitational Mathematics Examination, 1955, 204(1): 251-254.
[12]	BENNETT C O, ROSATO N D, REYNOLDS A C, et al. Influence of fracture heterogeneity and wing length on the response of vertically fractured wells[J]. Society of Petroleum Engineers Journal, 1983, 23(2): 219-230. doi: 10.2118/9886-PA
[13]	BERUMEN S, TIAB D, RODRIGUEZ F. Constant rate solutions for a fractured well with an asymmetric fracture[J]. Journal of Petroleum Science and Engineering, 2000, 25(1): 49-58.
[14]	NARASIMHAN T N, PALEN W A. A purely numerical approach for analyzing fluid flow to a well intercepting a vertical fracture[C]//SPE California Regional Meeting. Ventura, California, 1979.
[15]	RODRIGUEZ F, CINCO-LEY H, SAMANIEGO-V F. Evaluation of fracture asymmetry of finite-conductivity fracturedwells[J]. SPE Production Engineering, 1992, 7(2): 233-239. doi: 10.2118/20583-PA
[16]	TIAB D, LU J, NGUYEN H, et al. Evaluation of fracture asymmetry of finite-conductivity fracturedwells[J]. Journal of Energy Resources Technology, 2010, 132(1): 012901. doi: 10.1115/1.4000700
[17]	WANG L, WANG X, LI J, et al. Simulation of pressure transient behavior for asymmetrically finite-conductivity fractured wells in coal reservoirs[J]. Transport in Porous Media, 2013, 97(3): 353-372. doi: 10.1007/s11242-013-0128-z
[18]	WANG L, XUE L. A Laplace-transform boundary element model for pumping tests in irregularly shaped double-porosity aquifers[J]. Journal of Hydrology, 2018, 567(1): 712-720.
[19]	WANG L, DAI C, LI X, et al. Pressure transient analysis for asymmetrically fractured wells in dual-permeability organic compound reservoir of hydrogen and carbon[J]. International Journal of Hydrogen Energy, 2019, 44(11): 5254-5261. doi: 10.1016/j.ijhydene.2018.08.082
[20]	ZHAO Y, SHAN B, ZHANG L. Pressure dynamics of asymmetrically fractured wells in an arbitrarily shaped reservoir[J]. Journal of Hydrodynamics, 2019, 31(4): 767-777. doi: 10.1007/s42241-018-0166-7
[21]	ROSA A J, MAGALHAES A A C, HORNE R N. Pressure transient behavior in reservoirs with an internal circular discontinuity[J]. Society of Petroleum Engineers Journal, 1996, 1(1): 83-92.
[22]	DENG Q, NIE R, JIA Y, et al. Pressure transient behavior of a fractured well in multi-region composite reservoirs[J]. Journal of Petroleum Science and Engineering, 2017, 158(1): 535-553.
[23]	姜瑞忠, 郜益华, 孙召勃, 等. 双重介质复合油藏偏心井试井分析[J]. 新疆石油地质, 2016, 37(3): 327-331. https://www.cnki.com.cn/Article/CJFDTOTAL-XJSD201603017.htm JIANG Ruizhong, GAO Yihua, SUN Zhaobo, et al. Off-center well test analysis for composite dual-porosity reservoirs[J]. Xinjiang Petroleum Geology, 2016, 37(3): 327-331. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-XJSD201603017.htm
[24]	姜瑞忠, 高岳, 孙召勃, 等. 双重介质低渗油藏偏心压裂直井井底压力特征[J]. 断块油气田, 2020, 27(6): 778-783. https://www.cnki.com.cn/Article/CJFDTOTAL-DKYT202006022.htm JIANG Ruizhong, GAO Yue, SUN Zhaobo, et al. Bottom pressure characteristics for eccentric fracture vertical well in dual-medium low-permeability reservoir[J]. Fault-Block Oil and Gas Field, 2020, 27(6): 778-783. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-DKYT202006022.htm
[25]	OZKAN E, RAGHAVAN R. New solutions for well-test-analysis problems, part Ⅲ: additional algorithms[C]//SPE Annual Technical Conference and Exhibition. New Orleans, Louisiana, 1994.
[26]	OZKAN E, RAGHAVAN R. New solutions for well-test-analysis problems, part Ⅰ: analytical considerations[J]. SPE Formation Evaluation, 1991, 6(3): 359-368.
[27]	XU Y, LI X, LIU Q. Pressure performance of multi-stage fractured horizontal well with stimulated reservoir volume and irregular fractures distribution in shale gas reservoirs[J]. Journal of Natural Gas Science and Engineering, 2020, 77: 103209.
[28]	GUO J, WANG H, ZHANG L. Transient pressure and production dynamics of multi-stage fractured horizontal wells in shale gas reservoirs with stimulated reservoir volume[J]. Journal of Natural Gas Science and Engineering, 2016, 35(4): 425-443.
[29]	CARSLAW H S, JAEGER J C. Conduction of Heat in Solids[M]. 2nd ed. London: Oxford University Press, 1959.
[30]	PEACEMAN D W. Interpretation of wellblock pressures in numerical reservoir simulation part 3: off-center and multiple wells within a wellblock[J]. SPE Reservoir Engineering, 1990, 5(2): 227-232.
[31]	ZHAO Y, ZHANG L, FENG G, et al. Performance analysis of fractured wells with stimulated reservoir volume in coal seam reservoirs[J]. Oil and Gas Science and Technology, 2016, 71(1): 1-8.
[32]	CHEN Z, LIAO X, ZHAO X, et al. A semi-analytical mathematical model for transient pressure behavior of multiple fractured vertical well in coal reservoirs incorporating with diffusion, adsorption, and stress-sensitivity[J]. Journal of Natural Gas Science and Engineering, 2016, 29(1): 570-582.
[33]	姬安召, 王玉风, 张光生. 不对称裂缝单井渗流模型的Green函数构造方法[J]. 应用数学和力学, 2022, 43(4): 424-434. doi: 10.21656/1000-0887.420237 JI Anzhao, WANG Yufeng, ZHANG Guangsheng. A Green's function construction method of the single well seepage model for asymmetric fractures[J]. Applied Mathematics and Mechanics, 2022, 43(4): 424-434. (in Chinese) doi: 10.21656/1000-0887.420237
[34]	刘启国, 徐有杰, 刘义成, 等. 夹角断层多段压裂水平井试井求解新方法[J]. 应用数学和力学, 2018, 39(5): 558-567. doi: 10.21656/1000-0887.380297 LIU Qiguo, XU Youjie, LIU Yicheng, et al. A new well test analysis method for multi-stage fractured horizontal wells with angle faults[J]. Applied Mathematics and Mechanics, 2018, 39(5): 558-567. (in Chinese) doi: 10.21656/1000-0887.380297
[35]	VAN EVERDINGENA F, HURST W. The application of the Laplace transformation to flow problems in reservoirs[J]. Journal of Petroleum Technology, 1949, 1(12): 305-324.