NUMERICAL SIMULATION OF MULTI-SCALE COUPLED FLOW IN AFTER-FRACTURING SHALE GAS RESERVOIRS
-
摘要: 在碳达峰的国策背景之下, 页岩气成为传统能源向绿色清洁低碳能源转型的重要过渡和能源支点. 压后页岩气藏流体流动力学成为高效开发页岩气的关键力学问题. 文章将小尺度低导流天然裂缝等效升级为连续介质, 建立有机质-无机质-天然裂缝三重连续介质模型, 同时对大尺度高导流裂缝采用离散裂缝模型刻画, 嵌入天然裂缝连续介质中, 构建多重连续/离散裂缝模型. 综合考虑吸附气的非平衡非线性解吸附和表面扩散, 自由气的黏性流和克努森扩散, 给出页岩气在多尺度复杂介质中的非线性耦合流动数学模型. 提出多尺度扩展有限单元法对离散裂缝进行显式求解, 创新性构建三类加强形函数捕捉离散裂缝的局部流场特征, 解决了压后页岩海量裂缝及多尺度流动通道的流动模拟难题. 文章提出的模型和方法既能准确刻画高导流裂缝对渗流的影响, 又克服了海量多尺度离散裂缝导致计算量增大的问题. 通过算例展示了压后页岩各连续介质的压力衰减规律, 发现裂缝中自由气、有机质中自由气、无机质中吸附气依次滞后的压力(浓度)扩散现象, 重点分析了吸附气表面扩散系数、自由气克努森扩散系数、天然裂缝连续介质渗透率和吸附气解吸附速率对页岩气产量的影响. 文章重点解决压后页岩多尺度流动通道的表征和复杂耦合流动机理的建模, 并开发了高效的数值模拟算法, 对于压后页岩的产能评价具有一定的意义.Abstract: Under the national policy background of peak carbon dioxide emissions, shale gas becomes an important transition and energy fulcrum for the transition from traditional energy to green, clean and low-carbon energy. And the fluid flow mechanism of shale gas reservoirs after fracturing becomes a key mechanical problem for the efficient development of shale. In this paper, the small-scale low-conductivity natural fractures are equivalently upgraded to a continuous medium, and a triple organic-inorganic-natural fracture continuous medium model is established. The discrete fracture model is used to portray the large-scale high-conductivity fractures, which are embedded into the natural fracture continuous medium, and a multiple continuous/discrete fracture model (MC/DFM) is constructed. The non-equilibrium nonlinear desorption and surface diffusion of adsorbed gas, viscous flow, and Knudsen diffusion of free gas are integrated to give a nonlinear coupled flow mathematical model of shale gas in the multi-scale complex medium. The multi-scale extended finite element method (MXFEM) is proposed to solve the discrete fractures explicitly, and three types of enrichment functions are innovatively constructed to capture the local flow field characteristics of the discrete fractures, which solves the flow simulation problems of the massive fractures and multi-scale flow channels in the after-fracturing shale. The model and method proposed in this paper can not only accurately characterize the effect of high conductivity fractures on gas flow, but also overcome the problem of the dramatic increase in computational amount due to massive multi-scale discrete fractures. The pressure decay law of each continuous medium is demonstrated by a calculation example, and the pressure/concentration diffusion phenomena of free gas in fracture, free gas in organic medium, and adsorbed gas in the inorganic medium are found to lag in sequence. The analysis focuses on the effects of adsorbed gas surface diffusion coefficient, free gas Knudsen diffusion coefficient, natural fracture continuous medium permeability, and adsorbed gas desorption rate on shale gas production. This paper focuses on the characterization of multi-scale flow channels and modeling of complex coupled flow mechanisms in after-fracturing shale reservoirs and developing an efficient numerical simulation algorithm, which is meaningful for the production assessment of the shale formation after fracturing.
-
图 11 参考线和参考点压力拟合曲线
Figure 11. Pressure fitting curve of reference line and reference points
图 15 不同表面扩散系数下的累计产气量
Figure 15. Cumulative production at different surface diffusion coefficients
图 18 不同解吸附速率下的累计产气量
Figure 18. Cumulative production at different desorption rate of the adsorbed gas
图 16 不同Knudsen扩散系数下的累计产气量
Figure 16. Cumulative production at different Knudsen diffusion coefficients
图 17 不同天然裂缝连续介质渗透率下的累计产气量
Figure 17. Cumulative production at different micro-fracture-continuum permeability
表 1 验证模型参数取值
Table 1. Parameters of the calculation model
Parameter Value model 100 × 100 ${p_0}$/MPa 20 ${p_w}$/MPa 10 $ {c_s} $/Pa−1 5$ \times $10−11 ${c_f}$/Pa−1 3.33$ \times $10−10 $\phi $ 0.1 $\mu $/(mPa·s) 1 $ \rho $/(kg·m−3) 980 ${k_m}$/m2 1$ \times $10−18 $ {w_f} $/mm 1 $ {\kappa _F} $/m2 1 e−12 t/d 300 
下载: 导出CSV
表 2 模型参数取值
Table 2. Parameters of the calculation model
Parameter Value $ {\kappa _f} $/mD 1 $\phi $ 0.01 $ {\kappa _m} $/nD 20 $\phi_m $ 0.05 $ {D_k} $/(m2·s−1) 1$ \times $10−7 $ {D_S} $/(m2·s−1) 1$ \times $10−9 $ {k_a} $/s−1 1$ \times $10−6 $ {k_d} $/s−1 1$ \times $10−5 $ {p_L} $/MPa 4 $ {\kappa _F} $/mD 10000 $ {w_F} $/mm 5 $ {\kappa _{Fs}} $/mD 5000 $ {w_{Fs}} $/mm 1 $ {\kappa _{fn1}} $/mD 2000 $ {w_{fn1}} $/mm 0.5 $ {\kappa _{fn2}} $/mD 1000 $ {w_{fn2}} $/mm 0.2 $ \mu $/(mPa·s) 3 $ T $/K 330 $ \alpha $/m−2 50 $ {P_0} $/MPa 20 $ {P_w} $/MPa 10
下载: 导出CSV
-
[1] Yuan J, Luo D, Feng L. A review of the technical and economic evaluation techniques for shale gas development. Applied Energy, 2015, 148: 49-65 doi: 10.1016/j.apenergy.2015.03.040 [2] Gao Q, Cheng Y, Han S, et al. Effect of shale matrix heterogeneity on gas transport during production: A microscopic investigation. Journal of Petroleum Science and Engineering, 2021, 201: 108526 doi: 10.1016/j.petrol.2021.108526 [3] 夏阳, 金衍, 陈勉等. 页岩气渗流数学模型. 科学通报, 2015, 60(24): 2259-2271 (Xia Yang, Jin Yan, Chen Mian, et al. Gas flow in shale reservoirs. Chin Sci Bull, 2015, 60(24): 2259-2271 (in Chinese) doi: 10.1360/N972014-01175 [4] 夏阳, 金衍, 陈勉. 页岩气渗流过程中的多场耦合机理. 中国科学:物理学 力学 天文学, 2015, 45(09): 30-43 (Xia Yang, Jin Yan, Chen Mian. The coupling of multi-physics for gas flow in shale reservoirs. Sci Sin—Phys Mech Astron, 2015, 45(09): 30-43 (in Chinese) [5] 柳占立, 庄茁, 孟庆国等. 页岩气高效开采的力学问题与挑战. 力学学报, 2017, 49(3): 507-516 (Liu Zhanli, Zhuang Zhuo, Meng Qingguo, et al. Problems and challenges of mechanics in shale gas efficient exploitation. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(3): 507-516 (in Chinese) doi: 10.6052/0459-1879-16-399 [6] Zhang T, Sun S, Song H. Flow mechanism and simulation approaches for shale gas reservoirs: A review. Transport in Porous Media, 2019, 126(3): 655-681 doi: 10.1007/s11242-018-1148-5 [7] Wang H, Chen L, Qu Z, et al. Modeling of multi-scale transport phenomena in shale gas production−a critical review. Applied Energy, 2020, 262: 114575 doi: 10.1016/j.apenergy.2020.114575 [8] 张抗, 苗淼, 张立勤. “双碳”目标与中国能源转型思考(四)——对能源转型系统工程的几点认识. 中外能源, 2022, 27(6): 1-9 (Zhang Kang, Miao Miao, Zhang Liqing. Carbon peaking and carbon neutrality goals and reflections on china’s energy transition part Ⅳ-some understandings of energy transition systems engineering. Sino-Global Energy, 2022, 27(6): 1-9 (in Chinese) [9] 邹才能, 潘松圻, 马锋. 碳中和目标下世界能源转型与中国能源人新使命. 北京石油管理干部学院学报, 2022, 29(3): 22-32 (Zou Caineng, Pan Songqi, Ma Feng. The world energy transition under the carbon neutrality goal and the new mission of Chinese energy people. Journal of Beijing Petroleum Managers Training, 2022, 29(3): 22-32 (in Chinese) [10] King GE. Thirty years of gas shale fracturing: what have we learned? //SPE annual technical conference and exhibition. OnePetro, 2010 [11] Scanlon BR, Reedy RC, Nicot JP. Comparison of water use for hydraulic fracturing for unconventional oil and gas versus conventional oil. Environmental Science & Technology, 2014, 48(20): 12386-12393 [12] Javadpour F, Singh H, Rabbani A, et al. Gas flow models of shale: a review. Energy & Fuels, 2021, 35(4): 2999-3010 [13] 宋文辉, 姚军, 张凯. 页岩有机质纳米孔隙气体吸附与流动规律研究. 力学学报, 2021, 53(8): 2179-2192 (Song Wenhui, Yao Jun, Zhang Kai. Study on gas adsorption and transport behavior in shale organic nanopore. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(8): 2179-2192 (in Chinese) doi: 10.6052/0459-1879-21-224 [14] Guo C, Xu J, Wu K, et al. Study on gas flow through nano pores of shale gas reservoirs. Fuel, 2015, 143: 107-117(Zhang T, Li X, Wang X, et al. A discrete model for apparent gas permeability in nanoporous shale coupling initial water distribution. Journal of Natural Gas Science and Engineering, 2018, 59: 80-96 [15] Yu H, Chen J, Zhu YB, et al. Multiscale transport mechanism of shale gas in micro/nano-pores. International Journal of Heat and Mass Transfer, 2017, 111: 1172-1180)(Wang H, Chen L, Qu Z, et al. Modeling of multi-scale transport phenomena in shale gas production—a critical review. Applied Energy, 2020, 262: 114575 [16] 姚军, 孙海, 樊冬艳等. 页岩气藏运移机制及数值模拟. 中国石油大学学报:自然科学版, 2013(1): 91-98 (Yao Jun, Sun Hai, Fan Dongyan, et al. Transport mechanisms and numerical simulation of shale gas reservoirs. Journal of China University of Petroleum, 2013(1): 91-98 (in Chinese) [17] 郭为, 胡志明, 左罗等. 页岩基质解吸-扩散-渗流耦合实验及数学模型. 力学学报, 2015, 47(6): 916-922 (Guo Wei, Hu Zhiming, Zuo Luo, et al. Gas desorption-diffusion-seepage coupled experiment of shale matrix and mathematic model. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(6): 916-922 (in Chinese) doi: 10.6052/0459-1879-15-068 [18] 姚同玉, 黄延章, 李继山. 页岩气在超低渗介质中的渗流行为. 力学学报, 2012, 44(6): 990-995 (Yao Tongyu, Huang Yanzhang, Li Jishan. Flow regim for shale gas in extra low permeability porous media. Chinese Journal of Theoretical and Applied Mechanics, 2012, 44(6): 990-995 (in Chinese) doi: 10.6052/0459-1879-12-047 [19] Zhang W, Xu J, Jiang R. Production forecast of fractured shale gas reservoir considering multi-scale gas flow. Journal of Petroleum Exploration and Production Technology, 2017, 7(4): 1071-1083 doi: 10.1007/s13202-016-0281-3 [20] Hu Y, Liu G, Luo N, et al. Multi-field coupling deformation of rock and multi-scale flow of gas in shale gas extraction. Energy, 2022, 238: 121666 doi: 10.1016/j.energy.2021.121666 [21] Cao P, Liu J, Leong YK. A fully coupled multiscale shale deformation-gas transport model for the evaluation of shale gas extraction. Fuel, 2016, 178: 103-117 doi: 10.1016/j.fuel.2016.03.055 [22] 曹成, 李天太, 张磊等. 考虑基质收缩效应的页岩气双孔双渗模型. 天然气地球科学, 2015, 26(12): 2381-2387 (Cao Cheng, Li Tiantai, Zhang Lei, et al. Shale gas dual porosity-dual permeability model with matrix shrinking. Natural Gas Geoscience, 2015, 26(12): 2381-2387 (in Chinese) doi: 10.11764/j.issn.1672-1926.2015.12.2381 [23] 程远方, 董丙响, 时贤等. 页岩气藏三孔双渗模型的渗流机理. 天然气工业, 2012, 32(9): 44-47 + 130 (Cheng Yuanfang, Dong Bingxiang, Shi Xian, et al. Seepage mechanism of a trip-porosity/dual-permeability model for shale gas reservoirs. Natural Gas Industry, 2012, 32(9): 44-47 + 130 (in Chinese) doi: 10.3787/j.issn.1000-0976.2012.09.010 [24] 朱琴, 张烈辉, 张博宁等. 考虑微裂缝的页岩气藏三重介质不稳定产量递减研究. 科学技术与工程, 2013(29): 8595-8599 (Zhu Qin, Zhang Liehui, Zhang Boning, et al. The research about transient production decline of trip porosity model considering micro fractures in shale gas reservoir. Science Technology and Engineering, 2013(29): 8595-8599 (in Chinese) doi: 10.3969/j.issn.1671-1815.2013.29.009 [25] Watson AT, Gatens JM, Lee WJ, et al. An analytical model for history matching naturally fractured reservoir production data//SPE Production Operations Symposium, 1989. Oklahoma: OnePetro, 1989 [26] Bumb AC, McKee CR. Gas-well testing in the presence of desorption for coalbed methane and devonian shale. SPE Formation Evaluation, 1988, 3(1): 179-185 doi: 10.2118/15227-PA [27] Kuuskraa VA, Wicks DE, Thurber JL. Geologic and reservoir mechanisms controlling gas recovery from the Antrim Shale. SPE Annual Technical Conference and Exhibition, Washington, 1992, OnePetro: 1992 [28] Zhao Y, Zhang L, Zhao J, et al. “Triple porosity” modeling of transient well test and rate decline analysis for multi-fractured horizontal well in shale gas reservoirs. Journal of Petroleum Science and Engineering, 2013, 110: 253-262 doi: 10.1016/j.petrol.2013.09.006 [29] Dehghanpour H, Shirdel M. A triple porosity model for shale gas reservoirs//Canadian Unconventional Resources Conference, Calgary, 2011. OnePetro, 2011 [30] Schepers KC, Gonzalez RJ, Koperna GJ, et al. Reservoir modeling in support of shale gas exploration//Latin American and Caribbean Petroleum Engineering Conference, Cartagena de Indias, Colombia, 2009. OnePetro, 2009 [31] Wei Z, Zhang D. Coupled fluid-flow and geomechanics for triple-porosity/dual-permeability modeling of coalbed methane recovery. International Journal of Rock Mechanics and Mining Sciences, 2010, 47(8): 1242-1253 doi: 10.1016/j.ijrmms.2010.08.020 [32] 韦世明, 陈勉, 金衍等. 缝网页岩储层非线性耦合渗流模型研究. 中国科学:物理学 力学 天文学, 2018, 48(6): 94-108 (Wei Shiming, Chen Mian, Jin Yan, et al. Study on the nonlinear coupling seepage model of shale reservoir with discrete networks. Sci Sin—Phys Mech Astron, 2018, 48(6): 94-108 (in Chinese) [33] 夏阳, 邓英豪, 金衍. 裂缝性储层流体流动数值模拟研究进展. 中国科学基金, 2021, 35(06): 964-972 (Xia Yang, Deng Yinghao, Jin Yan. Advances in numerical simulation of fluid flow in fractured reservoirs. Bulletin of National Natural Science Foundation of China, 2021, 35(06): 964-972 (in Chinese) doi: 10.16262/j.cnki.1000-8217.2021.06.024 [34] Srinivasan R, Auvil SR, Schork JM. Mass transfer in carbon molecular sieves—an interpretation of Langmuir kinetics. The Chemical Engineering Journal and the Biochemical Engineering Journal, 1995, 57(2): 137-144 doi: 10.1016/0923-0467(94)02942-3 [35] Guo C, Wei M, Chen H, et al. Improved numerical simulation for shale gas reservoirs//Offshore Technology Conference-Asia, Kuala Lumpur, 2014. OnePetro, 2014 [36] Lee SH, Lough MF, Jensen CL. Hierarchical modeling of flow in naturally fractured formations with multiple length scales. Water Resources Research, 2001, 37(3): 443-455 doi: 10.1029/2000WR900340 [37] Li L, Lee SH. Efficient field-scale simulation of black oil in a naturally fractured reservoir through discrete fracture networks and homogenized media. SPE Reservoir Evaluation & Engineering, 2008, 11(4): 750-758 [38] Panfili P, Cominelli A, Scotti A. Using embedded discrete fracture models (EDFMs) to simulate realistic fluid flow problems//Second EAGE workshop on naturally fractured reservoirs, Muscat, Oman, 2013. European Association of Geoscientists & Engineers, 2013, cp-371-00022 [39] Moinfar A, Varavei A, Sepehrnoori K, et al. Development of a coupled dual continuum and discrete fracture model for the simulation of unconventional reservoirs//SPE Reservoir Simulation Symposium, The Woodlands, 2013. OnePetro, 2013 [40] Fangqi Z, Anfeng SHI, Xiaohong W. An efficient finite difference model for multiphase flow in fractured reservoirs. Petroleum Exploration and Development, 2014, 41(2): 262-266 doi: 10.1016/S1876-3804(14)60031-8 [41] 严侠, 黄朝琴, 姚军等. 基于模拟有限差分的嵌入式离散裂缝数学模型. 中国科学:技术科学, 2014, 44(12): 1333-1342 (Yan X, Huang ZQ, Yao J, et al. The embeded discrete fracture model based on mimetic finite difference method. Sci Sin Tech, 2014, 44(12): 1333-1342 (in Chinese) doi: 10.1360/N092014-00047 [42] Ţene M, Bosma SBM, Al Kobaisi MS, et al. Projection-based embedded discrete fracture model (pEDFM). Advances in Water Resources, 2017, 105: 205-216 doi: 10.1016/j.advwatres.2017.05.009 [43] Jiang J, Younis RM. Hybrid coupled discrete-fracture/matrix and multicontinuum models for unconventional-reservoir simulation. SPE Journal, 2016, 21(03): 1009-1027 doi: 10.2118/178430-PA [44] Sangnimnuan A, Li JW, Wu K, et al. Development of efficiently coupled fluid flow and geomechanics model for refracturing optimization in highly fractured reservoirs//SPE Hydraulic Fracturing Technology Conference and Exhibition. OnePetro, 2018 [45] Xu Y, Yu W, Sepehrnoori K. Modeling dynamic behaviors of complex fractures in conventional reservoir simulators. SPE Reservoir Evaluation & Engineering, 2019, 22(03): 1110-1130 [46] Huang H, Long TA, Wan J, et al. On the use of enriched finite element method to model subsurface features in porous media flow problems. Computational Geosciences, 2011, 15(4): 721-736 doi: 10.1007/s10596-011-9239-1 [47] D’Angelo C, Scotti A. A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. ESAIM:Mathematical Modelling and Numerical Analysis, 2012, 46(2): 465-489 doi: 10.1051/m2an/2011148 [48] Mohammadnejad T, Khoei AR. An extended finite element method for hydraulic fracture propagation in deformable porous media with the cohesive crack model. Finite Elements in Analysis and Design, 2013, 73: 77-95 doi: 10.1016/j.finel.2013.05.005 [49] Khoei A R, Hosseini N, Mohammadnejad T. Numerical modeling of two-phase fluid flow in deformable fractured porous media using the extended finite element method and an equivalent continuum model. Advances in Water Resources, 2016, 94: 510-528 doi: 10.1016/j.advwatres.2016.02.017 [50] Xia Y, Jin YR, Oswald J, et al. Extended finite element modeling of production from a reservoir embedded with an arbitrary fracture network. International Journal for Numerical Methods in Fluids, 2018, 86(5): 329-345 doi: 10.1002/fld.4421 [51] Xia Y, Jin Y, Chen M, et al. An enriched approach for modeling multiscale discrete-fracture/matrix interaction for unconventional-reservoir simulations. SPE Journal, 2019, 24(01): 349-374 doi: 10.2118/194012-PA [52] Lu Y, Wei S, Xia Y, et al. Modeling of geomechanics and fluid flow in fractured shale reservoirs with deformable multi-continuum matrix. Journal of Petroleum Science and Engineering, 2021, 196: 107576 doi: 10.1016/j.petrol.2020.107576 [53] Fathi E, Akkutlu IY. Mass transport of adsorbed-phase in stochastic porous medium with fluctuating porosity field and nonlinear gas adsorption kinetics. Transport in Porous Media, 2012, 91(1): 5-33 doi: 10.1007/s11242-011-9830-x [54] Zhang M, Yao J, Sun H, et al. Triple-continuum modeling of shale gas reservoirs considering the effect of kerogen. Journal of Natural Gas Science & Engineering, 2015, 24: 252-263 [55] Wei S, Xia Y, Jin Y, et al. Quantitative study in shale gas behaviors using a coupled triple-continuum and discrete fracture model. Journal of Petroleum Science and Engineering, 2019, 174: 49-69 doi: 10.1016/j.petrol.2018.10.084 [56] 邓英豪, 夏阳, 金衍. 基于扩展有限元的离散缝网渗流数值模拟方法. 石油学报, 2022, 43(10): 1474-1486 (Deng Yinghao, Xia Yang, Jin Yan. Numerical simulation method of discrete fracture network flow based on the extended finite element method. Acta Petrolei Sinica, 2022, 43(10): 1474-1486 (in Chinese) [57] Sukumar N, Chopp DL, Moës N, et al. Modeling holes and inclusions by level sets in the extended finite-element method. Computer Methods in Applied Mechanics and Engineering, 2001, 190(46/47): 6183-6200 [58] Moës N, Cloirec M, Cartraud P, et al. A computational approach to handle complex microstructure geometries. Computer Methods in Applied Mechanics and Engineering, 2003, 192(28/30): 3163-3177 [59] Mathias SA, van Reeuwijk M. Hydraulic fracture propagation with 3-D leak-off. Transport in Porous Media, 2009, 80(3): 499-518 doi: 10.1007/s11242-009-9375-4 [60] Chen KP, Jin Y, Chen M. Pressure-gradient singularity and production enhancement for hydraulically fractured wells. Geophysical Journal International, 2013, 195(2): 923-931 doi: 10.1093/gji/ggt272 [61] Berrone S, Pieraccini S, Scialo S. On simulations of discrete fracture network flows with an optimization-based extended finite element method. SIAM Journal on Scientific Computing, 2013, 35(2): A908-A935 doi: 10.1137/120882883 [62] Flemisch B, Fumagalli A, Scotti A. A review of the XFEM-based approximation of flow in fractured porous media. Advances in Discretization Methods, 2016: 47-76 [63] Kast W, Hohenthanner CR. Mass transfer within the gas-phase of porous media. International Journal of Heat and Mass Transfer, 2000, 43(5): 807-823 doi: 10.1016/S0017-9310(99)00158-1 [64] 金衍, 陈勉. 井壁稳定力学. 北京: 科学出版社, 2012Jin Yan, Chen Mian. Wellbore Stability Mechanics. Beijing: Science Press, 2012(in Chinese) [65] Zhang H, Liu J, Elsworth D. How sorption-induced matrix deformation affects gas flow in coal seams: a new FE model. International Journal of Rock Mechanics and Mining Sciences, 2008, 45(8): 1226-1236 doi: 10.1016/j.ijrmms.2007.11.007 -
下载:
点击查看大图
图(18) / 表(2)
计量
- 文章访问数: 59
- HTML全文浏览量: 18
- PDF下载量: 12
- 被引次数: 0
