Transient Behavior Analysis of Fractured Horizontal Wells Based on an Improved Green Element Method

doi:10.19596/j.cnki.1001-246x.7977

Abstract

Abstract: We proposed a modified Green element method based on edge-based element concept. Unknowns and matrix dimension are reduced. Then, a local grid refinement method is proposed based on the improved Green element, which ensures precision in early flow regimes for fractured horizontal wells with complex fractured networks. Solution of a degradation model solved with the method is compared with solutions obtained with a semianalytical model and numerical simulation. It verifies accuracy and efficiency of the improved Green element method based on local grid refinement. Finally, effects of model parameters on transient behavior is analyzed. It shows that the Green element method is a high precision dynamic simulation method, which improves computational efficiency of dynamic simulation of fractured horizontal well by setting node on edge of grid. In addition, local grid refinement method applied to the modified Green element method is based on superposition principle, in which interpolation approximation is not needed. The method is of high accuracy. Under same grid systems, local grid refinement based on improved Green element method is better than using finite difference. On the other hand, conductivity of complex fracture, permeability and size of stimulated reservoir volume have great influence on transient behavior of fractured horizontal wells. These effects should be taken into consideration and interpreted in transient behavior analysis.

Key words: fractured horizontal well, improved Green element method, transient behavior analysis, local grid refinement, unconventional reservoir

CLC Number:

TE122

FANG Sidong, WANG Weihong, WU Yonghui, CHENG Linsong. Transient Behavior Analysis of Fractured Horizontal Wells Based on an Improved Green Element Method[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2020, 37(1): 69-78.

References

[1] 邹才能, 翟光明, 张光亚, 等. 全球常规-非常规油气形成分布、资源潜力及趋势预测[J]. 石油勘探与开发, 2015, 42(1):13-25.
[2] 邹才能, 朱如凯, 吴松涛, 等. 常规与非常规油气聚集类型、特征、机理及展望——以中国致密油和致密气为例[J]. 石油学报, 2012, 33(2):173-187.
[3] NOBAKHT M, CLARKSON C R, KAVIANI D. New type curves for analyzing horizontal well with multiple fractures in shale gas reservoirs[J]. Journal of Natural Gas Science & Engineering, 2013, 10(1):99-112.
[4] WU Y, CHENG L, HUANG S, et al. A practical method for production data analysis from multistage fractured horizontal wells in shale gas reservoirs[J]. Fuel, 2016, 186:821-829.
[5] STALGOROVA K, MATTAR L. Analytical model for unconventional multifractured composite systems[J]. Spe Reservoir Evaluation & Engineering, 2013, 16(3):246-256.
[6] 苏玉亮, 王文东, 盛广龙. 体积压裂水平井复合流动模型[J]. 石油学报, 2014, 35(3):504-510.
[7] BROWN M L, OZKAN E, RAGHAVAN R S, 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.
[8] FANG S, CHENG L, XIN Y, et al. Linear element method for multi-angle fractured horizontal well in anisotropic reservoir[J]. Chinese Journal of Computational Physics, 2015, 32(5):595-602.
[9] 吴永辉, 程林松, 黄世军, 等. 页岩凝析气井产能预测的三线性流模型[J]. 天然气地球科学, 2017, 28(11):1745-1754.
[10] KUCHUK F J, BIRYUKOV D. Pressure-transient behavior of continuously and discretely fractured reservoirs[J]. SPE Journal, 2014, 17(1):82:97.
[11] 糜利栋, 姜汉桥, 李俊键. 页岩气离散裂缝网络模型数值模拟方法研究[J]. 天然气地球科学, 2014, 25(11):1795-1803.
[12] DU Dianfa, WANG Yanyan, FU Jingang, et al. Shale gas seepage mechanism and transient pressure analysis[J]. Chinese Journal of Computational Physics, 2015, 32(1):51-57.
[13] JIA P, CHENG L, HUANG S, et al. A semi-analytical model for the flow behavior of naturally fractured formations with multi-scale fracture networks[J]. Journal of Hydrology, 2016, 537:208-220.
[14] JIANG J, YOUNIS R M. Hybrid coupled discrete fracture-matrix and multicontinuum models for unconventional reservoir simulation[J]. SPE Journal, 2016, 21(3):1009-1027.
[15] WU Y S, LI J, DING D, et al. A generalized framework model for simulation of gas production in unconventional gas reservoirs[J]. SPE Journal, 2014, 19(5):845-857.
[16] 王本成, 贾永禄, 李友全, 等. 多段压裂水平井试井模型求解新方法[J]. 石油学报, 2013, 34(6):1150-1156.
[17] HUANG Tao, HUANG Zhaoqin, ZHANG Jianguang, et al. Non-Darcy flow simulation of oil-water phase in low permeability reservoirs based on mimetic finite difference method[J]. Chinese Journal of Computational Physics, 2016, 33(6):707-716.
[18] 贾品, 程林松, 黄世军, 等. 压裂裂缝网络不稳态流动半解析模型[J]. 中国石油大学学报(自然科学版), 2015, 39(5):107-116.
[19] 方思冬, 战剑飞, 黄世军, 等. 致密油藏多角度裂缝压裂水平井产能计算方法[J]. 油气地质与采收率, 2015, 22(3):84-89.
[20] MAYERHOFER M J, LOLON E, WARPINSKI N R, et al. What is stimulated reservoir volume?[J]. SPE Produciton and Operation, 2010, 25(1):89-98.
[21] CIPOLLA C L, LOLON E P, ERDLE J C, et al. Reservoir modeling in shale-gas reservoirs[J]. SPE Reservoir Evaluation & Engineering, 2010, 13(4):638-653.
[22] 孙致学, 姚军, 樊冬艳, 等.基于离散裂缝模型的复杂裂缝系统水平井动态分析[J]. 中国石油大学学报(自然科学版), 2014, 38(2):109-115.
[23] 万义钊, 刘曰武, 吴能友, 胡高伟. 基于离散裂缝的多段压裂水平井数值试井模型及应用[J]. 力学学报, 2018, 50(1):147-156.
[24] LI L, LEE S H. Efficient field-scale simulation of black oil in a naturally fractured reservoir through discrete fracture networks and homogenized media[J]. SPE Reservoir Evaluation & Engineering, 2008, 11(4):750-758.
[25] MOINFAR A, VARAVEI A, SEPEHRNOORI K, et al. Development of a coupled dual continuum and discrete fracture model for the simulation of unconventional reservoirs[C]. SPE-163647-MS, 2013.
[26] YAN X, HUANG Z, YAO J, et al. An efficient embedded discrete fracture model based on mimetic finite difference method[J]. J Petroleum Science and Engineering, 2016, 145:11-21.
[27] LI X, ZHANG D, LI S. A multi-continuum multiple flow mechanism simulator for unconventional oil and gas recovery[J]. Journal of Natural Gas Science & Engineering, 2015, 26:652-669.
[28] TAIGBENU A E. The Green element method[J]. International Journal of Numerical Method Engineering, 1995, 38(13):2241-2263.
[29] ARCHER R A, HORNE R N. Green element method and singularity programming for numerical well test analysis[J]. Engineering Analysis of Boundary Element, 26(6):537-546.