Abstract
As a promising enhanced gas recovery technique, CO2 huff-n-puff has attracted great attention recently. However, hydraulic fracture deformation hysteresis is rarely considered, and its effect on CO2 huff-n-puff performance is not well understood. In this study, we present a fully coupled multi-component flow and geomechanics model for simulating CO2 huff-n-puff in shale gas reservoirs considering hydraulic fracture deformation hysteresis. Specifically, a shale gas reservoir after hydraulic fracturing is modeled using an efficient hybrid model incorporating an embedded discrete fracture model (EDFM), multiple porosity model, and single porosity model. In flow equations, Fick’s law, extended Langmuir isotherms, and the Peng-Robinson equation of state are used to describe the molecular diffusion, multi-component adsorption, and gas properties, respectively. In relation to geomechanics, a path-dependent constitutive law is applied for the hydraulic fracture deformation hysteresis. The finite volume method (FVM) and the stabilized extended finite element method (XFEM) are applied to discretize the flow and geomechanics equations, respectively. We then solve the coupled model using the fixed-stress split iterative method. Finally, we verify the presented method using several numerical examples, and apply it to investigate the effect of hydraulic fracture deformation hysteresis on CO2 huff-n-puff performance in a 3D shale gas reservoir. Numerical results show that hydraulic fracture deformation hysteresis has some negative effects on CO2 huff-n-puff performance. The effects are sensitive to the initial conductivity of hydraulic fracture, production pressure, starting time of huff-n-puff, injection pressure, and huff-n-puff cycle number.
摘要
目的
在页岩气藏CO2吞吐过程中, 水力裂缝处于循环载荷作用下时, 极易发生不可逆变形(变形滞后), 影响吞吐效果。本文旨在建立考虑水力裂缝变形滞后的页岩气藏CO2吞吐流固耦合模型, 形成相应的高效求解方法, 并开展流固耦合数值模拟研究, 以揭示变形滞后对CO2吞吐的影响规律。
创新点
1. 建立考虑水力裂缝变形滞后、复杂裂缝系统和特殊流动机理的页岩气藏多组分流固耦合模型, 并形成相应的三维高效数值模拟技术; 2. 揭示水力裂缝变形滞后对页岩气藏CO2吞吐的影响规律。
方法
1. 建立考虑水力裂缝变形滞后、复杂裂缝系统和特殊流动机理的页岩气藏多组分流固耦合模型; 2. 基于结构化网格构造高效稳定的多组分流固耦合模型数值求解算法; 3. 通过流固耦合数值模拟, 揭示水力裂缝变形滞后对页岩气藏CO2吞吐的影响规律。
结论
1. 水力裂缝变形滞后会阻碍 CO2注入期间裂缝渗透率的恢复, 对CO2吞吐有负面影响; 2. 较低的初始水力裂缝导流能力和生产压力、较晚的吞吐启动时间、较高的注入压力和较多的循环次数均会增强变形滞后的负面影响; 3. CO2吞吐效果与初始水力裂缝导流能力、吞吐启动时间、注入压力和循环次数呈正相关, 与生产压力呈负相关。
Similar content being viewed by others
References
CMG (Computer Modelling Group), 2015. GEM User’s Guide. Computer Modelling Group, Calgary, Canada.
COMSOL, 1998. Introduction to COMSOL Multiphysics®. COMSOL, Burlington, USA.
Du FS, Nojabaei B, 2019. A review of gas injection in shale reservoirs: enhanced oil/gas recovery approaches and greenhouse gas control. Energies, 12(12):2355. https://doi.org/10.3390/en12122355
Fan WP, Sun H, Yao J, et al., 2019. An upscaled transport model for shale gas considering multiple mechanisms and heterogeneity based on homogenization theory. Journal of Petroleum Science and Engineering, 183:106392. https://doi.org/10.1016/j.petrol.2019.106392
Fathi E, Akkutlu IY, 2014. Multi-component gas transport and adsorption effects during CO2 injection and enhanced shale gas recovery. International Journal of Coal Geology, 123:52–61. https://doi.org/10.1016/j.coal.2013.07.021
Gala D, Sharma M, 2018. Compositional and geomechanical effects in huff-n-puff gas injection IOR in tight oil reservoirs. SPE Annual Technical Conference and Exhibition, p.1–24. https://doi.org/10.2118/191488-MS
Garipov TT, Karimi-Fard M, Tchelepi HA, 2016. Discrete fracture model for coupled flow and geomechanics. Computational Geosciences, 20(1):149–160. https://doi.org/10.1007/s10596-015-9554-z
Ghanizadeh A, Clarkson CR, Deglint H, et al., 2016. Unpropped/propped fracture permeability and proppant embedment evaluation: a rigorous core-analysis/imaging methodology. Proceedings of the SPE/AAPG/SEG Unconventional Resources Technology Conference, p.1824–1852. https://doi.org/10.15530/URTEC-2016-2459818
Giger F, Reiss L, Jourdan A, 1984. The reservoir engineering aspects of horizontal drilling. SPE Annual Technical Conference and Exhibition, p.1–8. https://doi.org/10.2118/13024-MS
Godec M, Koperna G, Petrusak R, et al., 2014. Enhanced gas recovery and CO2 storage in gas shales: a summary review of its status and potential. Energy Procedia, 63:5849–5857. https://doi.org/10.1016/j.egypro.2014.11.618
Hasan M, Eliebid M, Mahmoud M, et al., 2017. Enhanced gas recovery (EGR) methods and production enhancement techniques for shale & tight gas reservoirs. SPE Kingdom of Saudi Arabia Annual Technical Symposium and Exhibition, p.1–9. https://doi.org/10.2118/188090-MS
Huang JW, Jin TY, Barrufet M, et al., 2020. Evaluation of CO2 injection into shale gas reservoirs considering dispersed distribution of kerogen. Applied Energy, 260:114285. https://doi.org/10.1016/j.apenergy.2019.114285
Hubbert M, Willis DG, 1957. Mechanics of hydraulic fracturing. Transactions of the AIME, 210(1): 153–168. https://doi.org/10.2118/686-G
IEA (International Energy Agency), 2021. Levelised Cost of CO2 Capture by Sector and Initial CO2 Concentration, 2019. IEA, Paris, France. https://www.iea.org/data-and-statistics/charts/levelised-cost-of-co2-capture-by-sector-and-initial-co2-concentra-tion-2019
IEA (International Energy Agency), 2022. Natural Gas Prices in Europe, Asia and the United States, Jan 2020–February 2022. IEA, Paris, France. https://www.iea.org/data-and-statistics/charts/natural-gas-prices-in-europe-asia-and-the-united-states-jan-2020-february-2022
Jaeger JC, Cook NGW, Zimmerman RW, 2007. Fundamentals of Rock Mechanics, 4th Edition. Blackwell Publishing, Oxford, UK, p.189–194.
Jiang JM, Yang J, 2018. Coupled fluid flow and geomechanics modeling of stress-sensitive production behavior in fractured shale gas reservoirs. International Journal of Rock Mechanics and Mining Sciences, 101:1–12. https://doi.org/10.1016/j.ijrmms.2017.11.003
Jiang JM, Shao YY, Younis RM, 2014. Development of a multi-continuum multi-component model for enhanced gas recovery and CO2 storage in fractured shale gas reservoirs. SPE Improved Oil Recovery Symposium, p.1–17. https://doi.org/10.2118/169114-MS
Karlsson H, Jacques GE, Hatten JL, et al., 1991. Method and Apparatus for Horizontal Drilling. US Patent 5074366.
Khoei AR, 2014. Extended Finite Element Method: Theory and Applications. John Wiley & Sons, Chichester, UK.
Kim J, Moridis GJ, 2014. Gas flow tightly coupled to elastoplastic geomechanics for tight-and shale-gas reservoirs: material failure and enhanced permeability. SPE Journal, 19(6):1110–1125. https://doi.org/10.2118/155640-PA
Kim J, Sonnenthal EL, Rutqvist J, 2012. Formulation and sequential numerical algorithms of coupled fluid/heat flow and geomechanics for multiple porosity materials. International Journal for Numerical Methods in Engineering, 92(5):425–456. https://doi.org/10.1002/nme.4340
Kim TH, Cho J, Lee KS, 2017. Evaluation of CO2 injection in shale gas reservoirs with multi-component transport and geomechanical effects. Applied Energy, 190:1195–1206. https://doi.org/10.1016/j.apenergy.2017.01.047
Li HL, Lu YY, Zhou L, et al., 2017. A new constitutive model for calculating the loading-path dependent proppant deformation and damage analysis of fracture conductivity. Journal of Natural Gas Science and Engineering, 46: 365–374. https://doi.org/10.1016/j.jngse.2017.08.005
Li ZY, Elsworth D, 2019. Controls of CO2—N2 gas flood ratios on enhanced shale gas recovery and ultimate CO2 sequestration. Journal of Petroleum Science and Engineering, 179:1037–1045. https://doi.org/10.1016/j.petrol.2019.04.098
Liu FS, Borja RI, 2010. Stabilized low-order finite elements for frictional contact with the extended finite element method. Computer Methods in Applied Mechanics and Engineering, 199(37–40):2456–2471. https://doi.org/10.1016/j.cma.2010.03.030
Liu J, Wang JG, Gao F, et al., 2019. A fully coupled fracture equivalent continuum-dual porosity model for hydromechanical process in fractured shale gas reservoirs. Computers and Geotechnics, 106:143–160. https://doi.org/10.1016/j.compgeo.2018.10.017
Liu JS, Chen ZW, Elsworth D, et al., 2011. Interactions of multiple processes during CBM extraction: a critical review. International Journal of Coal Geology, 87(3–4): 175–189. https://doi.org/10.1016/j.coal.2011.06.004
Liu LJ, Yao J, Sun H, et al., 2019. Compositional modeling of shale condensate gas flow with multiple transport mechanisms. Journal of Petroleum Science and Engineering, 172:1186–1201. https://doi.org/10.1016/j.petrol.2018.09.030
Liu LJ, Liu YZ, Yao J, et al., 2020a. Efficient coupled multiphase-flow and geomechanics modeling of well performance and stress evolution in shale-gas reservoirs considering dynamic fracture properties. SPE Journal, 25(3):1523–1542. https://doi.org/10.2118/200496-PA
Liu LJ, Liu YZ, Yao J, et al., 2020b. Mechanistic study of cyclic water injection to enhance oil recovery in tight reservoirs with fracture deformation hysteresis. Fuel, 271:117677. https://doi.org/10.1016/j.fuel.2020.117677
Lohrenz J, Bray BG, Clark CR, 1964. Calculating viscosities of reservoir fluids from their compositions. Journal of Petroleum Technology, 16(10): 1171–1176. https://doi.org/10.2118/915-PA
Mahmoodpour S, Singh M, Turan A, et al., 2022a. Simulations and global sensitivity analysis of the thermo-hydraulic-mechanical processes in a fractured geothermal reservoir. Energy, 247:123511. https://doi.org/10.1016/j.energy.2022.123511
Mahmoodpour S, Singh M, Bär K, et al., 2022b. Thermo-hydro-mechanical modeling of an enhanced geothermal system in a fractured reservoir using carbon dioxide as heat transmission fluid-a sensitivity investigation. Energy, 254:124266. https://doi.org/10.1016/j.energy.2022.124266
Moinfar A, Varavei A, Sepehrnoori K, et al., 2012. Development of a novel and computationally-efficient discrete-fracture model to study IOR processes in naturally fractured reservoirs. SPE Improved Oil Recovery Symposium, p.1–17. https://doi.org/10.2118/154246-MS
Norbeck JH, McClure MW, Lo JW, et al., 2016. An embedded fracture modeling framework for simulation of hydraulic fracturing and shear stimulation. Computational Geosciences, 20(1):1–18. https://doi.org/10.1007/s10596-015-9543-2
Pruess K, 1991. TOUGH2: a General-Purpose Numerical Simulator for Multiphase Fluid and Heat Flow. LBL-29400, Lawrence Berkeley Lab, Berkeley, USA.
Qiu YL, Wu CJ, Chen WF, 2020. Local heat transfer enhancement induced by a piezoelectric fan in a channel with axial flow. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 21(12): 1008–1022. https://doi.org/10.1631/jzus.A2000057
Ren G, Jiang J, Younis RM, 2016. Fully coupled geomechanics and reservoir simulation for naturally and hydraulically fractured reservoirs. The 50th U.S. Rock Mechanics/Geomechanics Symposium, p.1–12.
Ryder RT, 1996. Fracture Patterns and Their Origin in the Upper Devonian Antrim Shale Gas Reservoir of the Michigan Basin: a Review. Open-File Report 96–23, U.S. Geological Survey, Reston, USA.
Shah M, Shah S, Sircar A, 2017. A comprehensive overview on recent developments in refracturing technique for shale gas reservoirs. Journal of Natural Gas Science and Engineering, 46:350–364. https://doi.org/10.1016/j.jngse.2017.07.019
Song WH, Yao J, Li Y, et al., 2016. Apparent gas permeability in an organic-rich shale reservoir. Fuel, 181:973–984. https://doi.org/10.1016/j.fuel.2016.05.011
Striolo A, Cole DR, 2017. Understanding shale gas: recent progress and remaining challenges. Energy & Fuels, 31(10): 10300–10310. https://doi.org/10.1021/acs.energyfuels.7b01023
Sun H, Yao J, Cao YC, et al., 2017. Characterization of gas transport behaviors in shale gas and tight gas reservoirs by digital rock analysis. International Journal of Heat and Mass Transfer, 104:227–239. https://doi.org/10.1016/j.ijheatmasstransfer.2016.07.083
Urban E, Orozco D, Fragoso A, et al., 2016. Refracturing vs. infill drilling—a cost effective approach to enhancing recovery in shale reservoirs. SPE/AAPG/SEG Unconventional Resources Technology Conference, p.2934–2953. https://doi.org/10.15530/URTEC-2016-2461604
Vermylen JP, 2011. Geomechanical Studies of the Barnett Shale, Texas, USA. PhD Thesis, Stanford University, California, USA.
Versteeg HK, Malalasekera W, 1995. An Introduction to Computational Fluid Dynamics: the Finite Volume Method. Longman Scientific & Technical, New York, USA.
Wang DY, Yao J, Chen ZX, et al., 2019. Image-based core-scale real gas apparent permeability from pore-scale experimental data in shale reservoirs. Fuel, 254:115596. https://doi.org/10.1016/j.fuel.2019.06.004
Webb SW, Pruess K, 2003. The use of Fick’s law for modeling trace gas diffusion in porous media. Transport in Porous Media, 51(3):327–341. https://doi.org/10.1023/A:1022379016613
Wu YS, Li JF, Ding DY, et al., 2014. A generalized framework model for the simulation of gas production in unconventional gas reservoirs. SPE Journal, 19(5):845–857. https://doi.org/10.2118/163609-PA
Xu RN, Zeng KC, Zhang CW, et al., 2017. Assessing the feasibility and CO2 storage capacity of CO2 enhanced shale gas recovery using triple-porosity reservoir model. Applied Thermal Engineering, 115:1306–1314. https://doi.org/10.1016/j.applthermaleng.2017.01.062
Yan X, Huang ZQ, Yao J, et al., 2016. An efficient embedded discrete fracture model based on mimetic finite difference method. Journal of Petroleum Science and Engineering, 145:11–21. https://doi.org/10.1016/j.petrol.2016.03.013
Yan X, Huang ZQ, Yao J, et al., 2018a. An efficient hydro-mechanical model for coupled multi-porosity and discrete fracture porous media. Computational Mechanics, 62(5):943–962. https://doi.org/10.1007/s00466-018-1541-5
Yan X, Huang ZQ, Yao J, et al., 2018b. An efficient numerical hybrid model for multiphase flow in deformable fractured-shale reservoirs. SPE Journal, 23(4):1412–1437. https://doi.org/10.2118/191122-PA
Yan X, Huang ZQ, Zhang Q, et al., 2020. Numerical investigation of the effect of partially propped fracture closure on gas production in fractured shale reservoirs. Energies, 13(20):5339. https://doi.org/10.3390/en13205339
Ye X, Tonmukayakul P, Weaver JD, et al., 2012. Experiment and simulation study of proppant pack compression. SPE International Symposium and Exhibition on Formation Damage Control, p.1–12. https://doi.org/10.2118/151647-MS
Yu W, Sepehrnoori K, 2014. Simulation of gas desorption and geomechanics effects for unconventional gas reservoirs. Fuel, 116:455–464. https://doi.org/10.1016/j.fuel.2013.08.032
Zeng QD, Yao J, Shao JF, 2018. Numerical study of hydraulic fracture propagation accounting for rock anisotropy. Journal of Petroleum Science and Engineering, 160:422–432. https://doi.org/10.1016/j.petrol.2017.10.037
Zeng QD, Yao J, Shao JF, 2019. Study of hydraulic fracturing in an anisotropic poroelastic medium via a hybrid EDFM-XFEM approach. Computers and Geotechnics, 105: 51–68. https://doi.org/10.1016/j.compgeo.2018.09.010
Zhang Q, Borja RI, 2021. Poroelastic coefficients for anisotropic single and double porosity media. Acta Geotechnica, 16(10):3013–3025. https://doi.org/10.1007/s11440-021-01184-y
Zhang Q, Yan X, Shao JL, 2021. Fluid flow through anisotropic and deformable double porosity media with ultra-low matrix permeability: a continuum framework. Journal of Petroleum Science and Engineering, 200:108349. https://doi.org/10.1016/j.petrol.2021.108349
Zhang Q, Yan X, Li ZH, 2022. A mathematical framework for multiphase poromechanics in multiple porosity media. Computers and Geotechnics, 146:104728. https://doi.org/10.1016/j.compgeo.2022.104728
Zhu GP, Kou JS, Yao BW, et al., 2019. Thermodynamically consistent modelling of two-phase flows with moving contact line and soluble surfactants. Journal of Fluid Mechanics, 879:327–359. https://doi.org/10.1017/jfm.2019.664
Zienkiewicz OC, Taylor RL, 2000. The Finite Element Method: Solid Mechanics. Butterworth-Heinemann, Oxford, UK.
Zuloaga P, Yu W, Miao JJ, et al., 2017. Performance evaluation of CO2 huff-n-puff and continuous CO2 injection in tight oil reservoirs. Energy, 134:181–192. https://doi.org/10.1016/j.energy.2017.06.028
Acknowledgments
This work is supported by the National Natural Science Foundation of China (Nos. 52004321, 52034010, and 12131014), the Natural Science Foundation of Shandong Province, China (No. ZR2020QE116), and the Fundamental Research Funds for the Central Universities, China (Nos. 20CX06025A and 21CX06031A).
Author information
Authors and Affiliations
Contributions
Xia YAN and Jun YAO designed the research. Xia YAN and Pi-yang LIU processed the corresponding data. Xia YAN wrote the first draft of the manuscript. Zhao-qin HUANG helped to organize the manuscript. Hai SUN, Kai ZHANG, and Jun-feng WANG revised and edited the final version.
Corresponding author
Additional information
Conflict of interest
Xia YAN, Pi-yang LIU, Zhao-qin HUANG, Hai SUN, Kai ZHANG, Jun-feng WANG, and Jun YAO declare that they have no conflict of interest.
Electronic supplementary materials
Section S1
Electronic Supplementary Materials
Rights and permissions
About this article
Cite this article
Yan, X., Liu, Py., Huang, Zq. et al. Effect of hydraulic fracture deformation hysteresis on CO2 huff-n-puff performance in shale gas reservoirs. J. Zhejiang Univ. Sci. A 24, 37–55 (2023). https://doi.org/10.1631/jzus.A2200142
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1631/jzus.A2200142
Key words
- Enhanced gas recovery
- CO2 huff-n-puff
- Coupled geomechanics and multi-component flow
- Hydraulic fracture deformation hysteresis
- Embedded discrete fracture model (EDFM)