DOI QR코드

DOI QR Code

Review on Discontinuum-based Coupled Hydro-Mechanical Analyses for Modelling a Deep Geological Repository for High-Level Radioactive Waste

고준위방사성폐기물 심층처분장 모델링을 위한 불연속체 기반 수리-역학 복합거동 해석기법 현황 분석

  • Kwon, Saeha (Korea Atomic Energy Research Institute (KAERI)) ;
  • Kim, Kwang-Il (Korea Atomic Energy Research Institute (KAERI)) ;
  • Lee, Changsoo (Korea Atomic Energy Research Institute (KAERI)) ;
  • Kim, Jin-Seop (Korea Atomic Energy Research Institute (KAERI)) ;
  • Min, Ki-Bok (Department of Energy Resources Engineering, Seoul National University (SNU))
  • Received : 2021.09.03
  • Accepted : 2021.10.08
  • Published : 2021.10.31

Abstract

Natural barrier systems surrounding the geological repository for the high-level radioactive waste should guarantee the hydraulic performance for preventing or delaying the leakage of radionuclide. In the case of the behavior of a crystalline rock, the hydraulic performance tends to be decided by the existence of discontinuities, so the coupled hydro-mechanical(HM) processes on the discontinuities should be characterized. The discontinuum modelling can describe the complicated behavior of discontinuities including creation, propagation, deformation and slip, so it is appropriate to model the behavior of a crystalline rock. This paper investigated the coupled HM processes in discontinuum modelling such as UDEC, 3DEC, PFC, DDA, FRACOD and TOUGH-UDEC. Block-based discontinuum methods tend to describe the HM processes based on the fluid flow through the discontinuities, and some methods are combined with another numerical tool specialized in hydraulic analysis. Particle-based discontinuum modelling describes the overall HM processes based on the fluid flow among the particles. The discontinuum methods that are currently available have limitations: exclusive simulations for two-dimension, low hydraulic simulation efficiency, fracture-dominated fluid flow and simplified hydraulic analysis, so it could be improper to the modelling the geological repository. Based on the concepts of various discontinuum modelling compiled in this paper, the advanced numerical tools for describing the accurate coupled HM processes of the deep geological repository should be developed.

고준위방사성폐기물 심층처분장 내 천연방벽은 방사성핵종의 누출을 방지 및 지연할 수 있는 수리학적 특성을 갖춰야 한다. 결정질 암반의 경우 불연속면에 의해 수리학적 성능이 결정되기 때문에, 불연속면의 수리-역학적 복합거동에 대한 자세한 모사가 필요하다. 불연속체 기반 해석기법은 불연속면의 생성, 전파, 변형, 미끄러짐과 같은 복잡한 거동을 구현할 수 있어 결정질 암반 모사에 적합하다. 본 연구에서는 불연속면에서의 수리-역학 복합거동에 초점을 맞추어, UDEC, 3DEC, PFC, DDA, FRACOD, TOUGH-UDEC과 같은 상용화된 불연속체 기반 수리-역학 복합거동 해석기법을 조사하였다. 블록 기반 불연속체 해석기법의 경우 주로 불연속면 상에서 진행되는 유체 유동을 바탕으로 수리-역학 복합거동을 해석하였고, 그중 일부는 다른 수리학적 해석기법과의 결합을 통하여 모델 전체에 대한 수리-역학적 복합거동을 제공하였다. 입자 기반 불연속체 해석기법의 경우에는 입자 사이로 흐르는 유체를 반영하여 불연속체 모델 전체에 해당하는 수리-역학적 복합거동 모사가 가능하다. 현재까지 상용화된 불연속체 기반 복합거동 해석기법은 2차원 해석만 제공하거나, 수리학적 해석 성능이 떨어지고, 불연속면에서의 유체 유동만 고려되거나, 자세한 수리학적 해석을 지원하지 않는 등의 한계점이 있어 고준위방사성폐기물 심층처분시스템의 정확한 수리-역학 모델링에는 적합하지 않을 수 있다. 본 기술보고에서 검토한 다양한 해석기법들의 장단점을 참고하여 향후 처분시스템을 정확하고 자세하게 모사할 수 있는 불연속체 기반 수리-역학 복합거동 해석기법의 개발이 필요하다.

Keywords

Acknowledgement

이 연구는 2021년도 과학기술정보통신부의 재원으로 사용후핵연료관리핵심기술개발사업단 및 한국연구재단의 지원을 받아 수행되었습니다(과제번호: 2021M2E1A1085193).

References

  1. Barton, N. and V. Choubey, 1977, The shear strength of rock joints in theory and practice. Rock Mechanics 10(1-2): 1-54. https://doi.org/10.1007/BF01261801
  2. Hokmark, H., M. Uonnqvist and B. Faith, 2010, THM-issues in repository rock:. SKB TR-10-23, Stockholm, Sweden: Svensk Karnbranslehantering AB (SKB).
  3. Ben, Y.X., Y. Wang and G. Shi, 2013, Development of a model for simulating hydraulic fracturing with DDA. In: Chen, G.Q., Y. Ohoishi, L. Zheng, T. Sasaki, editors, Frontiers of discontinuous numerical methods and practical simulations in engineering and disaster prevention. Boca Raton, FL: CRC Press. pp. 169-175.
  4. Chao, L.Q., Z. Zhao, H. Chen and Q. Tian, 2016, Hydraulic fracturing modeling using the discontinuous deforamtion analysis (DDA) method Computers and Geotechnics 76: 12-22. https://doi.org/10.1016/j.compgeo.2016.02.011
  5. Cuodall, P., 2000, Fluid formulation for PFC2D. Minneapolis, Minnesota: Itasca Consulting Group Inc.
  6. Hazzard, J.F., RP. Young and S.J. Oates, 2002, Numerical modeling of seismicity induced by fluid injection in a fractured reservoir. In: Proceedings of the 5th North American Rock Mechanics Symposium, Mining and Tunnel Innovation and Opportunity, Toronto, Canada, 7-10 July 2002, pp. 1023-1030.
  7. Itasca Consulting Group, 2018, UDEC 7.0 User's Guide. Minneapolis, Minnesota: Itasca Consulting Group Inc.
  8. Itasca Consulting Group, 2019, 3DEC 7.0 User's Guide. Minneapolis, Minnesota: Itasca Consulting Group Inc.
  9. Itasca Consulting Group, 2021, PFC 7.0 User's Guide. Minneapolis, Minnesota: Itasca Consulting Group Inc.
  10. Jaeger, J.C., N.G.W. Cook and R W. Zimmerman, 2007, Fundamentals of Rock Mechanics, Fourth edition, Malden, MA: Blackwell Publishing.
  11. Janiszewski, M., B. Shen and M. Rinne, 2019, Simulation of the interactions between hydrualic and natural fractures using a fracgture mechanics approach. Journal of Rock Mechanics and Geotechnical Enineering 11: 1138-1150. https://doi.org/10.1016/j.jrmge.2019.07.004
  12. Jiao, Y.-Y., X.-L. Zhang and J. Zhao, 2012, Two-dimensional DDA contact constitutive model for simulating rock fragmentation. Journal of Engineering Mechanics 138(2):199-209. https://doi.org/10.1061/(asce)em.1943-7889.0000319
  13. Jiao, Y.-Y., H.-Q. Zhang, X.-L. Zhang, H.-B. Li and A-H. Jiang, 2015, A two-dimensional coupled hydromechanical discontinuum model for simulating rock hydraulic fracturing. International Journal for Numerical and Analytic Methods in Geomechanics 39:457-481. https://doi.org/10.1002/nag.2314
  14. Jing, L., Y. Ma and Z. Fang, 2001, Modeling of fluid flow and solid deformation for fractured rocks with discontinuous deformation analysis (DDA) method, International Rock Mechanics and Mining Sciences 38:343-355. https://doi.org/10.1016/S1365-1609(01)00005-3
  15. Jing, L., 2003, A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering. International Journal of Rock Mechanics and Mining Sciences 40(3):283-353. https://doi.org/10.1016/S1365-1609(03)00013-3
  16. Khristianovich, S.A. and Y.P. Zheltov, 1955, Formation of vertical fractures by means of highly viscous liquid. In: Proceedings fourth world petroleum conference. Rome, June 6-15, 1955. pp. 579-586.
  17. Kim, H.-M., E.-S. Park, B. Shen, J.-H. Synn, T.-K Kim, S.-C. Lee, T.-Y. Ko, H.-S. Lee and J.-M. Lee, 2011, Development of thermal-hydraulic-mechanical coupled numerical analysis code for complex behavior in jointed rock mass based on fracture mechanics, Tunnel & Underground Space 21(1):66-81. https://doi.org/10.7474/TUS.2011.21.1.066
  18. Kim, H.-M. and S. Kwon, 2017, Deep Geological Disposal of High-Level Radioactive Wastes and Coupled Thermal-Hydraulic-Mechanical-Chemical Analysis, Journal of the Korean Socienty of Mineral and Energy Resources Engineerings 54(4):319-327. https://doi.org/10.12972/ksmer.2017.54.4.319
  19. Lee, J., K-I. Kim, K-B. Min and J. Rutqvist, 2019, TOUGH-UDEC: A simulator for coupled multiphase fluid flows, heat transfers and discontinous deformations in fractured porous media. Computers and Geosciences 126:120-130. https://doi.org/10.1016/j.cageo.2019.02.004
  20. Lei, Q., J.-P. Latham and C.-F. Tsang, 2017, The use of discrete fracture networks for modelling coupled geomechanical and hydrological behaviour of fractured rocks. Computers and Geotechnics 85: 151-176. https://doi.org/10.1016/j.compgeo.2016.12.024
  21. Lisjak, A and G. Grasselli, 2014, A reivew of discrete modeling techniques for fracturing processes in discontinuous rock masses. Journal of Rock Mechanics and Geotechnical Engineering 6:301-314. https://doi.org/10.1016/j.jrmge.2013.12.007
  22. Mas Ivars, D., 2006, Water inflow into excavations in fractured rock - a three-dimensional hydro-mechanical numerical study. International Journal of Rock Mechanics and Mining Sciences 43 :705-725. https://doi.org/10.1016/j.ijrmms.2005.11.009
  23. Min, K-B., J. Rutqvist, C.-F. Tsang and L. Jing, 2004, Stress-dependent permeability of fractured rock masses: an numerical study. International Journal of Rock Mechanics and Mining Sciences 41: 1191-1210. https://doi.org/10.1016/j.ijrmms.2004.05.005
  24. Min, K-B. and O. Stephansson, 2011, The DFN-DEM approach applied to investigate the effects of stress on mechanical and hydraulic rock mass properties at Forsmark, Sweden. Tunnel & Underground Space 21(2):117-127. https://doi.org/10.7474/TUS.2011.21.2.117
  25. Morgan, W.E. and M.M. Aral, 2015, An implicitly coupled hydro-geomecabnical model for hydraulic fracture simulation with the discontinuous deformation analysis. International Journal of Rock Mechanics and Mining Sciences 73 :82-94. https://doi.org/10.1016/j.ijrmms.2014.09.021
  26. Olivella, S., A Gens, J. Carrera and E.E. Alonso, 1996, Numerical formulation for a simulator (CODE BRIGHT) for the coupled analysis of saline media. Engineering with Computers 13(7):87-112. https://doi.org/10.1108/02644409610151575
  27. Olsson, R. and N. Barton, 2001, An improved model for hydromechanical coupling during shearing of rock joints. International Journal of Rock Mechanics and Mining Sciences 38:317-329. https://doi.org/10.1016/S1365-1609(00)00079-4
  28. Park, B. and K-B. Min, 2015, Bonded-particle discree element modelling of mechanical behavior of transversely isotropic rock. International Journal of Rock Mechanics and Mining Sciences 76:243-255. https://doi.org/10.1016/j.ijrmms.2015.03.014
  29. Park, J.-W., C.-H. Park and C. Lee, 2021, Hydro-mechanical modeling of fracture opening and slip using grain-based distinct element model: DECOV ALEX-2023 Task G (Benchmark Simulation), Tunnel & Underground Space 31(4):270-288. https://doi.org/10.7474/TUS.2021.31.4.270
  30. Parker, AP., 1981, The mechanics of fracture and fatigue: An introduction. London and New York: E. & F. N. Spon, Ltd.
  31. Potyondy, D.O. and P.A Cundall, 2004, A bonded-particle model for rock. International Journal of Rock Mechanics and Mining Sciences 41: 1329-1364. https://doi.org/10.1016/j.ijrmms.2004.09.011
  32. Pruess, K., C. Oldenburg and G. Moridis, 2012, TOUGH2 users's guide, version 2.1. LBNL-43134, Berkeley, CA: Lawrence Berkeley National Laboratory.
  33. Rutqvist, J. and C.-F. Tsang, 2002, A study of caprock hydromechanical changes associated with CO2-iojection into a brine formation. Enviromental Geology 42:296-305. https://doi.org/10.1007/s00254-001-0499-2
  34. Shen, B. and O. Stephansson, 1994, Modification of the G-criterion for crack propagation subjected to compression. Engineering Fracture Mechanics 47(2):177-189. https://doi.org/10.1016/0013-7944(94)90219-4
  35. Shen, B., 2002, Two Dimensional Fracture Propagation Code (Version 1.1) User's Manual. Kyrkslatt, Finland: Fracom Ltd.
  36. Shi, G.-H. and R.E. Goodman, 1985, Two dimensional discontinuous deformation analysis. International Journal far Numerical and Analytical Methods in Geomechanics 9:541-556. https://doi.org/10.1002/nag.1610090604
  37. Shen, B., 2010, Development of Hydro-Mechanical Coupling Function in FRACOD. CSIRO Earth Science and Resource Engineering Report EP106301, Kenmore, Australia: CSIRO.
  38. Shi, G., 2001, Three dimensional discontinuous deformation analysis, In: Elsworth, D., J.P. Tinucci, K.A. Heasley, editors, Rock mechanics in the national interest. Amsterdam, The Netherlands: Swets & Zeitlinger Lisse. pp. 1421-1428.
  39. Shi, J., B. Shen, O. Stephansson and M. Rinne, 2014, A three-dimensional crack growth simulator with displacement discontinuity method Engineering Analysis with Boundary Elements 48:73-86. https://doi.org/10.1016/j.enganabound.2014.07.002
  40. Sneddon, I.F. and M. Lowengrub, 1969, Crack problems in the classical theory of elasticity. New York: Wiley.
  41. Tomac, I. and M. Gutierrez, 2017, Coupled hydro-thermo-mechanical modeling of hydraulic fracturing in quasi-brittle rocks using BPM-DEM. Journal of Rock Mechanics and Geotechincal Engineering 9:92-104. https://doi.org/10.1016/j.jrmge.2016.10.001
  42. USNRC, 2011, Coupled processes workshop report. NRC-02-07-006, Rockville, ML: U.S. Nuclear Regulatory Commission, 76p.
  43. Watanabe, N., W. Wang, C.I. McDermott, T. Taniguchi and O. Kolditz, 2010, Uncertainty analysis of thermo-hydro-mechanical coupled processes in heterogeneous porous media. Computer Mechanics 45:263-280. https://doi.org/10.1007/s00466-009-0445-9
  44. Wijesinghe, A.M., 1986, An exact similarity solution for coupled deformation and fluid flow in discrete fractures. Technical Report UCID-20675, Livermore, CA: Lawrence Livermore National Laboratory.
  45. Xie, L., K.-B. Mia and B. Shen, 2016, Simulation of hydraulic fracturing and its interactions with a pre-existing fracture using displacement discontinuity method. Journal of Natural Gas Science and Engineering 36: 1284-1294. https://doi.org/10.1016/j.jngse.2016.03.050
  46. Yin, Z., H. Huang, L. Zhang and S. Maxwell, 2020, Three-dimensional distinct element modeling of fault reactivation and induced seismicity due to hydraulic fracturing injection and backflow. Journal of Rock Mechanics and Geotechnical Engineering 12:752-767. https://doi.org/10.1016/j.jrmge.2019.12.009
  47. Yoon, J.S., A. Zang and O. Stephansson, 2014, Numerical investigation on optimized stimulation of intact and naturally fractured deep geothermal reservoirs using hydro-mechanical coupled discrete particles joints model. Geothermics 52: 165-184. https://doi.org/10.1016/j.geothermics.2014.01.009
  48. Yoon, J.S., G. Zimmernamnn, A. Zang and O. Stephansson, 2015, Discrete element modeling of fluid injection-induced seismicity and activation of nearby fault. Canadian Geotechnical Journal 52:1457-1465. https://doi.org/10.1139/cgj-2014-0435
  49. Yoon, J.S., A. Zang, O. Stephansson, H. Hofmann and G. Zimmermann, 2017, Discrete Element Modelling of Hydarulic Fracture Propagation and Dynamic Interaction with Natural Fractures in Hard Rock. Procedia Engineering 191: 1023-1031. https://doi.org/10.1016/j.proeng.2017.05.275
  50. Yoon, J.S. and J. Zhou, 2020, Modelling of fault deformation induced by fluid injection using hydro-mechanical coupled 3D particle flow code: DECOVALEX-2019 Task B. Tunnel & Underground Space 30(4):320-334. https://doi.org/10.7474/TUS.2020.30.4.320
  51. Yow, J.L. and J.R. Hunt, 2002, Coupled processes in rock mass performance with emphasis on nuclear waste isolation. International Journal of Rock Mechanics and Mining Sciences 39: 143-150. https://doi.org/10.1016/S1365-1609(02)00064-3
  52. Zareidarmiyan, A., H. Salarirad, V. Vilarmsa, K.-I. Kim, J. Lee and K.-B. Min, 2020, Comparison of numerical codes far coupled thermo-hydro-mechanical simulations of fractured media. Journal of Rock Mechanics and Geotechnical Engineering 12:850-865. https://doi.org/10.1016/j.jrmge.2019.12.016
  53. Zhang, X, D.J. Sanderson, R.M. Harkness and N.C. Last, 1996, Evaluation of the 2-D Permeability Tensor for Fractured Rock Mass, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstract 33(1): 17-37. https://doi.org/10.1016/0148-9062(95)00042-9
  54. Zhang, F., Z. Yin, Z. Chen, S. Maxwell, L. Zhang and Y. Wu, 2020, Fault reactivation and induced seismicity during multi-stage hydraulic fracturing: microseismic analysis and geomechanical modelling. Society of Petroleum Engineers Journal 25(2):692-711.
  55. Zimmerman, R W. and G.S. Bodvarsson, 1996, Hydraulic conductivity of rock fractures. Transport in Porous Media 23(1): 1-30. https://doi.org/10.1007/BF00145263