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Upscaling of a dual-permeability Monte Carlo simulation model for contaminant transport in fractured networks by genetic algorithm parameter identification

  • F. CadiniEmail author
  • J. De Sanctis
  • I. Bertoli
  • E. Zio
Original Paper

Abstract

The transport of radionuclides in fractured media plays a fundamental role in determining the level of risk offered by a radioactive waste repository in terms of expected doses. Discrete fracture networks methods can provide detailed solutions to the problem of modeling the contaminant transport in fractured media. However, within the framework of the performance assessment (PA) of radioactive waste repositories, the computational efforts required are not compatible with the repeated calculations that need to be performed for the probabilistic uncertainty and sensitivity analyses of PA. In this paper, we present a novel upscaling approach, which consists in computing the detailed numerical fractured flow and transport solutions on a small scale and use the results to derive the equivalent continuum parameters of a lean, one-dimensional dual-permeability, Monte Carlo simulation model by means of a genetic algorithm search. The proposed upscaling procedure is illustrated with reference to a realistic case study of \( {}^{239}{\text{Pu}} \) migration taken from literature.

Keywords

Radioactive waste repository Performance assessment Fracture networks Upscaling Monte Carlo simulation Genetic Algorithms 

References

  1. Barenblatt GI, Zheltov IuP, Kochina IN (1960) Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks. J Appl Math Mech 24:1286–1303CrossRefGoogle Scholar
  2. Benke R, Painter S (2003) Modelling conservative tracer transport in fracture networks with a hybrid approach based on the Boltzmann transport equation. Water Resour Res 39(11):1324. doi: 10.1029/2003WR001966,2003 CrossRefGoogle Scholar
  3. Blum P, Mackay R, Riley MS (2009) Stochastic simulations of regional scale advective transport in fractured rock masses using block upscaled hydro-mechanical rock property data. J Hydrol 369:318–325CrossRefGoogle Scholar
  4. Cacas MC, Ledoux E, De Marsily G, Tillie B, Barbreau A, Durand E, Feuga B, Peaudecerf P (1990) Modeling fracture flow with a stochastic discrete fracture network: calibration and validation: 1. The flow model. Water Resour Res 26(3):479–489Google Scholar
  5. Cadini F, De Sanctis J, Girotti T, Zio E, Luce A, Taglioni A (2010a) Monte Carlo estimation of radionuclide release at a repository scale. Ann Nucl Energy 37:861–866CrossRefGoogle Scholar
  6. Cadini F, De Sanctis J, Girotti T, Zio E, Luce A, Taglioni A (2010b) Monte Carlo-based assessment of the safety performance of a radioactive waste repository. Reliab Eng Syst Saf 95:859–865CrossRefGoogle Scholar
  7. Cadini F, De Sanctis J, Zio E (2011) Challenges in Monte Carlo simulation of non-linear radioactive contaminant release processes. In: Proceedings of the international high level radioactive waste conference, IHLRWC, Albuquerque, USA, April, 10–14, 2011Google Scholar
  8. Cadini F, Bertoli I, De Sanctis J, Zio E (submitted) Monte Carlo simulation of contaminant migration in a dual-permeability fractured medium. Water Resour ResGoogle Scholar
  9. Carr JR (1989) Fractal characterization of joint surface roughness in welded tuff at Yucca Mountain, Nevada. In: The 30th US symposium on rock mechanics (USRMS)Google Scholar
  10. Chapman NA (1997) Preliminary feasibility assessment for near-surface engineered LLW repositories at two sites. Technical Report, ENEAGoogle Scholar
  11. Chevalier S, Buès MA, Tournebize J, Banton O (2001) Stochastic delineation of wellhead protection area in fractured aquifers and parametric sensitivity study. Stoch Environ Res Risk Assess 15:205–227CrossRefGoogle Scholar
  12. Cvetkovic V, Painter S, Outters N, Selroos JO (2004) Stochastic simulation of radionuclide migration in discretely fractured rock near the Äspö hard rock laboratory. Water Resour Res 40(2):W02404CrossRefGoogle Scholar
  13. Dentz M, Cortis A, Scher H, Berkowitz B (2004) Time behavior of solute transport in heterogeneous media: transition from anomalous to normal transport. Adv Water Res 27(2):155–173CrossRefGoogle Scholar
  14. Ferrara A, Maseguerra M, Zio E (1999) A comparison between the advection–dispersion and the Komogorov–Dmitriev model for groundwater contaminant transport. Ann Nucl Energy 26(12):1083–1096CrossRefGoogle Scholar
  15. Gerke HH, van Genuchten MT (1993a) A dual-porosity model for simulating the preferential movement of water and soluted in structured porous media. Water Resour Res 29(2):305–319CrossRefGoogle Scholar
  16. Gerke HH, van Genuchten MT (1993b) Evaluation of a first-order water transfer term for variably saturated dual-porosity flow models. Water Resour Res 29(4):1225–1238CrossRefGoogle Scholar
  17. Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, ReadingGoogle Scholar
  18. Hendricks Franssen HJWM, Gomez-Hernandez JJ (2002) 3D inverse modelling of groundwater flow at a fractured site using a stochastic continuum model with multiple statistical populations. Stoch Environ Res Risk Assess 16:155–174CrossRefGoogle Scholar
  19. Hestir K, Long JCS (1990) Analytical expressions for the permeability of random two-dimensional poisson fracture networks based on regular lattice percolation and equivalents media theories. J Geophys Res 95:21565–21581CrossRefGoogle Scholar
  20. Hölttä P, Poteri A, Hakanen M, Hautojärvi A (2004) Fracture flow and radionuclide transport in block-scale laboratory experiments. Radiochim Acta/Int J Chem Aspects Nuclearsci Technol 92(9–11):775–779Google Scholar
  21. Long JCS, Billaux DM (1987) From field data to fracture network modeling: an example incorporating spatial structure. Water Resour Res 23(7):1201–1217CrossRefGoogle Scholar
  22. Long JCS, Remer JS, Wilson CR, Witherspoon PA (1982) Porous media equivalents for networks of discontinuous fractures. Water Resour Res 18(3):645–658CrossRefGoogle Scholar
  23. Marseguerra M, Zio E (1997) Modelling the transport of contaminants in groundwater as a branching stochastic process. Ann Nucl Energy 24(8):325–644CrossRefGoogle Scholar
  24. Marseguerra M, Patelli E, Zio E (2001) Groundwater contaminant transport in presence of colloids: a stochastic nonlinear model and parameter identification. Ann Nucl Energy 28(8):777–803CrossRefGoogle Scholar
  25. McDonald MG, Harbaugh AW (1988) A modular three-dimensional finite-difference ground-water flow model. Department of the Interior, RestonGoogle Scholar
  26. National Research Council (1996) Rock fractures and fluid flow: contemporary understanding and applications. The National Academies Press, Washington, DCGoogle Scholar
  27. Neuman SP (1990) Universal scaling of hydraulic conductivities and dispersivities in geological media. Water Resour Res 26(8):1749–1758CrossRefGoogle Scholar
  28. Painter S, Cvetkovic V (2005) Upscaling discrete fracture network simulations: an alternative to continuum models. Water Resour Res 41:W02002. doi: 10.1029/2004WR003682
  29. Papoulis A, Pillai SU (2002) Probability, random variables, and stochastic processes. McGraw-Hill, BostonGoogle Scholar
  30. Reeves DM, Benson DA, Meerschaert MM (2008) Transport of conservative solutes in simulated fracture networks: 1. Synthetic data generation. Water Resour Res 44:W05404CrossRefGoogle Scholar
  31. Reeves DM, Pohlmann KF, Pohll GM, Ye M, Chapman JB (2010) Incorporation of conceptual and parametric uncertainty into radionuclide flux estimates from a fractured granite rock mass. Stoch Environ Res Risk Assess 24:899–915CrossRefGoogle Scholar
  32. Roubinet D, De Dreuzy J-R, Tartakovsky DM (2012) Semi-analytical solutions for solute transport and exchange in fractured porous media. Water Resour Res 48:w01542. doi: 10.1029/2011wr011168
  33. Sahimi M (1994) Applications of percolation theory. Taylor & Francis, LondonGoogle Scholar
  34. Sahimi M (1995) Flow and transport in porous media and fractured rock: from classical methods to modern approaches. VCH, WeinheimGoogle Scholar
  35. Smith L, Schwartz FW (1984) An analysis of the influence of fracture geometry on mass transport in fractured media. Water Resour Res 20(9):1241–1252CrossRefGoogle Scholar
  36. Sudicky EA, Gillham RW, Frind EO (1985) Experimental investigation of solute transport in stratified porous media: 1 the nonreactive case. Water Resour Res 24(7):1035–1041CrossRefGoogle Scholar
  37. Tang DH, Frind EO, Sudicky EA (1981) Contaminant transport in fractured porous media: analytical solution for a single fracture. Water Resour Res 17(3):555–564CrossRefGoogle Scholar
  38. Vanderborght J, Kasteel R, Vereecken H (2006) Stochastic continuum transport equations for field-scale solute transport: overview of theoretical and experimental results. Vadose Zone J 5:184–203CrossRefGoogle Scholar
  39. Warren JE, Root PJ (1985) The behavior of naturally fractured reservoirs. Soc Petrol Eng J 3:1861–1874Google Scholar
  40. Zheng C, Wang PP, Alabama University (1999) MT3DMS: a modular three-dimensional multispecies transport model for simulation of advection, dispersion, and chemical reactions of contaminants in groundwater systems; documentation and user’s guide. US Army Corps of Engineers, Engineer Research and Development CenterGoogle Scholar
  41. Zuloaga P, Andrade C, Saaltink MW (2006) Long term water scenario in low-level waste disposal vaults, with particular regard to concrete structures in El Cabril, Cordoba, Spain. J Phys IV Proc 136:49–59Google Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • F. Cadini
    • 1
    Email author
  • J. De Sanctis
    • 1
  • I. Bertoli
    • 1
  • E. Zio
    • 1
    • 2
  1. 1.Dipartimento di EnergiaPolitecnico di MilanoMilanItaly
  2. 2.Chair on Systems Science and the Energetic Challenge, European Foundation for New Energy—Électricité de France Ecole Centrale Paris and SupelecParisFrance

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