An approach for simulating the THMC process in single novaculite fracture using EPCA

  • Peng-Zhi Pan
  • Xia-Ting Feng
  • Hong Zheng
  • Alexander Bond
Thematic Issue
Part of the following topical collections:
  1. DECOVALEX 2015


An approach for simulating thermal, hydraulic, mechanical and chemical (THMC) coupled processes in single rock fractures has been developed under the framework of a self-developed numerical method, i.e., an elasto-plastic cellular automaton. The balance equations of multi-physics problems to describe the THMC process in single rock fracture are solved by using cellular automaton technique on space scale and finite difference method on time scale, respectively. Using the concept of cellular automaton, a single rock fracture surface is discretized into a system composed of cell elements. Different apertures, i.e., 0 for contact and nonzero for void, are assigned to each cell element based on the fracture surface topography. The fluid flow, stress-dependent chemical reaction and solute transport are simulated by using a cellular automaton updating rule, in which only local cell balance equation is considered. The contribution of cell elements in contact to cell’s transmissivity and convection can be ignored conveniently. The Lagrangian method is used to simulate the particle transport. Special treatment for particle transport to outer boundaries and internal boundaries is adopted. As a result, the local behaviors, such as the formation of local contact, dead ends in the fracture and the local aperture change, are conveniently updated dynamically. The approach is used to simulate the coupled THMC process in a single novaculite fracture. The behaviors of pressure dissolution caused by effective stress, free-face dissolution/precipitation, thermal-dependent fluid flow and ion transport are well reproduced by using the developed approach, subject to parameter calibration. The robustness of the general approach to such complex problems is demonstrated by comparing with experimental data.


Coupled THMC process Elasto-plastic cellular automaton Fracture aperture Chemical dissolution Solute transport Tortuous flow 



The authors appreciate and thank the Funding Organisations for their financial and technical support of the DECOVALEX project work described in this paper. This work was financially supported by National Natural Science Foundation of China under Grant Nos. 51322906 and 41272349 and Youth Innovation Promotion Association CAS under Grant No. 2011240. The statements made in the paper are, however, solely those of the authors and do not necessarily reflect those of the Funding Organisation(s).


  1. Baghbanan A, Jing L (2008) Stress effects on permeability in a fractured rock mass with correlated fracture length and aperture. Int J Rock Mech Min Sci 45(8):1320–1334CrossRefGoogle Scholar
  2. Bai M, Elsworth D (1994) Modeling of subsidence and stress-dependent hydraulic conductivity for intact and fractured porous media. Rock Mech Rock Eng 27(4):209–234CrossRefGoogle Scholar
  3. Bear J, Tsang CF, Marsily GD (1993) Flow and contaminant transport in fractured rocks. Academic Press, San DiegoCrossRefGoogle Scholar
  4. Berkowitz B (2002) Characterizing flow and transport in fractured geological media: a review. Adv Water Resour 25(8):861–884CrossRefGoogle Scholar
  5. Berlemont A, Desjonqueres P, Gouesbet G (1990) Particle lagrangian simulation in turbulent flows. Int J Multiph Flow 16(1):19–34CrossRefGoogle Scholar
  6. Bond A (2016) Task C1 final report, KTH report. ISBN 978-91-7595-829-3(06), ISSN 1650-86-10Google Scholar
  7. Bond A, Benbow S, Wilson J, Millard A, Nakama S, English M, McDermott C, Garitte B (2013) Reactive and non-reactive transport modelling in partially water saturated argillaceous porous media around the ventilation experiment, Mont Terri. J Rock Mech Geotech Eng 5(1):44–57CrossRefGoogle Scholar
  8. Constantin P (2015) Lagrangian–Eulerian methods for uniqueness in hydrodynamic systems. Adv Math 278:67–102CrossRefGoogle Scholar
  9. Diersch H-J, Kolditz O (2002) Variable-density flow and transport in porous media: approaches and challenges. Adv Water Resour 25(8):899–944CrossRefGoogle Scholar
  10. Feng XT, Pan PZ, Zhou H (2006) Simulation of the rock microfracturing process under uniaxial compression using an elasto-plastic cellular automaton. Int J Rock Mech Min Sci 43(7):1091–1108CrossRefGoogle Scholar
  11. Flemisch B, Darcis M, Erbertseder K, Faigle B, Lauser A, Mosthaf K, Müthing S, Nuske P, Tatomir A, Wolff M (2011) DuMu x: DUNE for multi-{phase, component, scale, physics, …} flow and transport in porous media. Adv Water Resour 34(9):1102–1112CrossRefGoogle Scholar
  12. Jeong W, Song J (2005) Numerical investigations for flow and transport in a rough fracture with a hydromechanical effect. Energy Sources 27(11):997–1011CrossRefGoogle Scholar
  13. Koyama T, Li B, Jiang Y, Jing L (2008) Numerical simulations for the effects of normal loading on particle transport in rock fractures during shear. Int J Rock Mech Min Sci 45(8):1403–1419CrossRefGoogle Scholar
  14. Koyama T, Li B, Jiang Y, Jing L (2009) Numerical modelling of fluid flow tests in a rock fracture with a special algorithm for contact areas. Comput Geotech 36(1–2):291–303CrossRefGoogle Scholar
  15. Lang P, Paluszny A, Zimmerman R (2015) Hydraulic sealing due to pressure solution contact zone growth in siliciclastic rock fractures. J Geophys Res Solid Earth 120(6):4080–4101CrossRefGoogle Scholar
  16. Lanru J, Xiating F (2004) Numerical modeling for coupled thermo-hydro-mechanical and chemical processes (THMC) of geological media—international and Chinese experiences. Chinese J Rock Mech Eng 22(10):1704–1715Google Scholar
  17. Li B, Zhao Z, Jiang Y, Jing L (2015) Contact mechanism of a rock fracture subjected to normal loading and its impact on fast closure behavior during initial stage of fluid flow experiment. Int J Numer Anal Meth Geomech 39(13):1431–1449CrossRefGoogle Scholar
  18. Matsuki K, Wang E, Sakaguchi K, Okumura K (2001) Time-dependent closure of a fracture with rough surfaces under constant normal stress. Int J Rock Mech Min Sci 38(5):607–619CrossRefGoogle Scholar
  19. Mayer KU, MacQuarrie KT (2010) Solution of the MoMaS reactive transport benchmark with MIN3P—model formulation and simulation results. Comput Geosci 14(3):405–419CrossRefGoogle Scholar
  20. Min K-B, Rutqvist J, Tsang C-F, Jing L (2004) Stress-dependent permeability of fractured rock masses: a numerical study. Int J Rock Mech Min Sci 41(7):1191–1210Google Scholar
  21. Moreno L, Tsang YW, Tsang CF, Hale FV, Neretnieks I (1988) Flow and tracer transport in a single fracture: a stochastic model and its relation to some field observations. Water Resour Res 24(12):2033–2048CrossRefGoogle Scholar
  22. Neretnieks I (2014) Stress-mediated closing of fractures: impact of matrix diffusion. J Geophys Res Solid Earth 119(5):4149–4163CrossRefGoogle Scholar
  23. Neuman SP (2005) Trends, prospects and challenges in quantifying flow and transport through fractured rocks. Hydrogeol J 13(1):124–147CrossRefGoogle Scholar
  24. Ochi J, Vernoux J-F (1998) Permeability decrease in sandstone reservoirs by fluid injection: hydrodynamic and chemical effects. J Hydrol 208(3):237–248CrossRefGoogle Scholar
  25. Oda M (1986) An equivalent continuum model for coupled stress and fluid flow analysis in jointed rock masses. Water Resour Res 22(13):1845–1856CrossRefGoogle Scholar
  26. Pan P, Feng X (2013) Numerical study on coupled thermo-mechanical processes in Äspö pillar stability experiment. J Rock Mech Geotech Eng 5(2):136–144CrossRefGoogle Scholar
  27. Pan PZ, Feng XT, Huang XH, Cui Q, Zhou H (2009a) Coupled THM processes in EDZ of crystalline rocks using an elasto-plastic cellular automaton. Environ Geol 57(6):1299–1311CrossRefGoogle Scholar
  28. Pan PZ, Feng XT, Hudson JA (2009b) Study of failure and scale effects in rocks under uniaxial compression using 3D cellular automata. Int J Rock Mech Min Sci 46(4):674–685CrossRefGoogle Scholar
  29. Pan P-Z, Feng X-T, Xu D-P, Shen L-F, Yang J-B (2011) Modelling fluid flow through a single fracture with different contacts using cellular automata. Comput Geotech 38(8):959–969CrossRefGoogle Scholar
  30. Piggott AR, Bobba AG, Xiang J (1994) Inverse analysis implementation of the SUTRA ground-water model. Groundwater 32(5):829–836CrossRefGoogle Scholar
  31. Prommer H, Barry D, Zheng C (2003) MODFLOW/MT3DMS-based reactive multicomponent transport modeling. Groundwater 41(2):247–257CrossRefGoogle Scholar
  32. Pruess K (2004) The TOUGH codes—a family of simulation tools for multiphase flow and transport processes in permeable media. Vadose Zone J 3(3):738–746Google Scholar
  33. Reeves HW, Thibodeau PM, Underwood RG, Gardner LR (2000) Incorporation of total stress changes into the ground water model SUTRA. Groundwater 38(1):89–98CrossRefGoogle Scholar
  34. Sorek S (1988) Eulerian-Lagrangian method for solving transport in aquifers. Adv Water Resour 11(2):67–73CrossRefGoogle Scholar
  35. Sudicky EA, Jones JP, Park Y-J, Brookfield AE, Colautti D (2008) Simulating complex flow and transport dynamics in an integrated surface-subsurface modeling framework. Geosci J 12(2):107–122CrossRefGoogle Scholar
  36. Taghavy A, Pennell KD, Abriola LM (2015) Modeling coupled nanoparticle aggregation and transport in porous media: a Lagrangian approach. J Contam Hydrol 172:48–60CrossRefGoogle Scholar
  37. Talman S, Perkins E, Gunter W (2000) Users manual for GAMSPATH a reaction path-mass transfer program DRAFT. Geochemical Applications and Modelling Software Ltd, p 39Google Scholar
  38. Tartakovsky AM, Meakin P, Scheibe TD, West RME (2007) Simulations of reactive transport and precipitation with smoothed particle hydrodynamics. J Comput Phys 222(2):654–672CrossRefGoogle Scholar
  39. Watanabe N, Bilke L, Fischer T, Kalbacher T, Nagel T, Naumov D, Rink K, Shao H, Wang W, Kolditz O (2014) OpenGeoSys: an open-source initiative for numerical simulation of thermo-hydro-mechanical/chemical (THM/C) processes in porous media. AGU fall meeting abstractsGoogle Scholar
  40. White MD, Oostrom M, Rockhold ML, Rosing M (2008) Scalable modeling of carbon tetrachloride migration at the Hanford site using the STOMP simulator. Vadose Zone J 7(2):654–666CrossRefGoogle Scholar
  41. Wienke BR, Hill TR, Whalen PP (1987) Eulerian and Lagrangian particle transport with drag. Comput Phys Commun 43(2):171–180CrossRefGoogle Scholar
  42. Witherspoon PA, Wang JSY, Iwai K, Gale JE (1980) validity of cubic law for fluid flow in a deformable rock fracture. Water Resour Res 16(6):1016–1024CrossRefGoogle Scholar
  43. Xu T, Sonnenthal E, Spycher N, Pruess K (2006) TOUGHREACT—a simulation program for non-isothermal multiphase reactive geochemical transport in variably saturated geologic media: applications to geothermal injectivity and CO 2 geological sequestration. Comput Geosci 32(2):145–165CrossRefGoogle Scholar
  44. Yasuhara H, Elsworth D (2006) A numerical model simulating reactive transport and evolution of fracture permeability. Int J Numer Anal Meth Geomech 30(10):1039–1062CrossRefGoogle Scholar
  45. Yasuhara H, Elsworth D (2008) Compaction of a rock fracture moderated by competing roles of stress corrosion and pressure solution. Pure appl Geophys 165(7):1289–1306CrossRefGoogle Scholar
  46. Yasuhara H, Elsworth D, Polak A (2004) Evolution of permeability in a natural fracture: significant role of pressure solution. J Geophys Res Solid Earth (1978–2012) 109(B3):1–11Google Scholar
  47. Yasuhara H, Polak A, Mitani Y, Grader AS, Halleck PM, Elsworth D (2006) Evolution of fracture permeability through fluid–rock reaction under hydrothermal conditions. Earth Planet Sci Lett 244(1):186–200CrossRefGoogle Scholar
  48. Yeh G (1990) A Lagrangian–Eulerian method with zoomable hidden fine-mesh approach to solving advection-dispersion equations. Water Resour Res 26(6):1133–1144CrossRefGoogle Scholar
  49. Yin S, Towler BF, Dusseault MB, Rothenburg L (2010) Fully coupled THMC modeling of wellbore stability with thermal and solute convection considered. Transp Porous Media 84(3):773–798CrossRefGoogle Scholar
  50. Zhao Z, Jing L, Neretnieks I, Moreno L (2011) Numerical modeling of stress effects on solute transport in fractured rocks. Comput Geotech 38(2):113–126CrossRefGoogle Scholar
  51. Zheng L, Samper J (2008) A coupled THMC model of FEBEX mock-up test. Phys Chem Earth Parts A/B/C 33:S486–S498CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Peng-Zhi Pan
    • 1
  • Xia-Ting Feng
    • 1
  • Hong Zheng
    • 1
  • Alexander Bond
    • 2
  1. 1.State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil MechanicsChinese Academy of SciencesWuhanChina
  2. 2.Quintessa LtdOxfordshireUK

Personalised recommendations