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Investigating the age distribution of fracture discharge using multiple environmental tracers, Bedrichov Tunnel, Czech Republic

Abstract

The transit time distribution (TTD) of discharge collected from fractures in the Bedrichov Tunnel, Czech Republic, is investigated using lumped parameter models and multiple environmental tracers. We utilize time series of \(\delta ^{18}O\), \(\delta ^{2}\)H and \(^3\)H along with CFC measurements from individual fractures in the Bedrichov Tunnel of the Czech Republic to investigate the TTD, and the uncertainty in estimated mean travel time in several fracture networks of varying length and discharge. We compare several TTDs, including the dispersion distribution, the exponential distribution, and a developed TTD which includes the effects of matrix diffusion. The effect of seasonal recharge is explored by comparing several seasonal weighting functions to derive the historical recharge concentration. We identify best fit mean ages for each TTD by minimizing the error-weighted, multi-tracer \(\chi ^{2}\) residual for each seasonal weighting function. We use this methodology to test the ability of each TTD and seasonal input function to fit the observed tracer concentrations, and the effect of choosing different TTD and seasonal recharge functions on the mean age estimation. We find that the estimated mean transit time is a function of both the assumed TTD and seasonal weighting function. Best fits as measured by the \(\chi ^2\) value were achieved for the dispersion model using the seasonal input function developed here for two of the three modeled sites, while at the third site, equally good fits were achieved with the exponential model and the dispersion model and our seasonal input function. The average mean transit time for all TTDs and seasonal input functions converged to similar values at each location. The sensitivity of the estimated mean transit time to the seasonal weighting function was equal to that of the TTD. These results indicated that understanding seasonality of recharge is at least as important as the uncertainty in the flow path distribution in fracture networks and that unique identification of the TTD and mean transit time is difficult given the uncertainty in the recharge function. However, the mean transit time appears to be relatively robust to the structural model uncertainty. The results presented here should be applicable to other studies using environmental tracers to constrain flow and transport properties in fractured rock systems.

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References

  1. Bullister JL (2011) Atmospheric CFC-11, CFC-12, CFC-113, CCl4 and SF6 histories. Tech. rep., Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, US Department of Energy, Oak Ridge. http://cdiac.ornl.gov/ftp/oceans/CFC_ATM_Hist/

  2. Cook PG, Solomon DK (1995) Transport of atmospheric trace gases to the water table. Implications for groundwater dating with chlorofluorocarbons and krypton 85. Water Resour Res 31(2):263–270

    Article  Google Scholar 

  3. Cook P, Herczeg AL (2000) Environmental tracers in subsurface hydrology. Kluwer Academic, Norwell

    Book  Google Scholar 

  4. Cook P, Robinson N (2002) Estimating groundwater recharge in fractured rock from environmental H-3 and Cl-36. Water Resour Res. doi:10.1029/2001WR000772

    Google Scholar 

  5. Cook P, Love A, Robinson N, Simmons C (2005) Groundwater ages in fractured rock aquifers. J Hydrol 308(1–4):284–301. doi:10.1016/j.jhydrol.2004.11.005

    Article  Google Scholar 

  6. Danckwerts P (1953) Continuous flow systems. Chem Eng Sci 2(1):1–13. doi:10.1016/0009-2509(53)80001-1

    Article  Google Scholar 

  7. Doyon B, Molson JW (2012) Groundwater age in fractured porous media: analytical solution for parallel fractures. Adv Water Resour 37:127–135. doi:10.1016/j.advwatres.2011.11.008

    Article  Google Scholar 

  8. Evaristo J, Jasechko S, McDonnell JJ (2015) Global separation of plant transpiration from groundwater and streamflow. Nature 525(7567):91–94. doi:10.1038/nature14983

    Article  Google Scholar 

  9. Gardner WP, Susong DD, Solomon DK, Heasler HP (2010) Snowmelt hydrograph interpretation: revealing watershed scale hydrologic characteristics of the Yellowstone volcanic plateau. J Hydrol 383(3–4):209–222. doi:10.1016/j.jhydrol.2009.12.037

    Article  Google Scholar 

  10. Gardner WP, Susong DD, Solomon DK, Heasler HP (2011) A multitracer approach for characterizing interactions between shallow groundwater and the hydrothermal system in the Norris Geyser Basin area, Yellowstone National Park. Geochem Geophys Geosyst 12(8):Q08005. doi:10.1029/2010GC003353

    Article  Google Scholar 

  11. Grabczak J, Ròzański K, Maloszewski P, Zuber A (1984) Estimation of the tritium input function with the aid of stable isotopes. Catena 11(2):105–114. doi:10.1016/0341-8162(84)90001-8

    Article  Google Scholar 

  12. Haggerty R, Gorelick SM (1995) Multiple-rate mass transfer for modeling diffusion and surface reactions in media with pore-scale heterogeneity. Water Resour Res 31(10):2383–2400. doi:10.1029/95WR10583

    Article  Google Scholar 

  13. Haggerty R, McKenna SA, Meigs LC (2000) On the late-time behavior of tracer test breakthrough curves. Water Resour Res 36(12):3467–3479. doi:10.1029/2000WR900214

    Article  Google Scholar 

  14. Haggerty R, Fleming SW, Meigs LC, McKenna SA (2001) Tracer tests in a fractured dolomite: 2. Analysis of mass transfer in single-well injection-withdrawal tests. Water Resour Res 37(5):1129–1142. doi:10.1029/2000WR900334

    Article  Google Scholar 

  15. Kennedy V, Kendall C, Zellweger G, Wyerman T, Avanzino R (1986) Determination of the components of stormflow using water chemistry and environmental isotopes, Mattole River basin, California. J Hydrol 84(12):107–140. doi:10.1016/0022-1694(86)90047-8

    Article  Google Scholar 

  16. Klomínský J, Woller Fe (2010) Geological studies in the Bedrichov water supply tunnel. RARWRA technical report 02/20 10, Czech Geological Survey, Prague

  17. Maloszewski P, Zuber A (1982) Determining the turnover time of groundwater systems with the aid of environmental tracers. J Hydrol 57(3):207–231. doi:10.1016/0022-1694(82)90147-0

    Article  Google Scholar 

  18. Maloszewski P, Zuber A (1985) On the theory of tracer experiments in fissured rocks with a porous matrix. J Hydrol 79(3):333–358. doi:10.1016/0022-1694(85)90064-2

    Article  Google Scholar 

  19. Maloszewski P, Zuber A (1990) Mathematical modeling of tracer behavior in short-term experiments in fissured rocks. Water Resour Res 26(7):1517–1528. doi:10.1029/WR026i007p01517

    Article  Google Scholar 

  20. Maloszewski P, Zuber A (1996) Lumped parameter models for the interpretation of environmental tracer data. IAEA technical report

  21. McCallum JL, Engdahl NB, Ginn TR, Cook PG (2014) Nonparametric estimation of groundwater residence time distributions: What can environmental tracer data tell us about groundwater residence time? Water Resour Res. doi:10.1002/2013WR014974

    Google Scholar 

  22. Neretnieks I (1980) Diffusion in the rock matrix: an important factor in radionuclide retardation? J Geophys Res Solid Earth 85(B8):4379–4397. doi:10.1029/JB085iB08p04379

    Article  Google Scholar 

  23. Neretnieks I (1981) Age dating of groundwater in fissured rock: influence of water volume in micropores. Water Resour Res 17(2):421–422. doi:10.1029/WR017i002p00421

    Article  Google Scholar 

  24. Neuman S (2005) Trends, prospects and challenges in quantifying flow and transport through fractured rocks. Hydrogeol J 13(1):124–147. doi:10.1007/s10040-004-0397-2

    Article  Google Scholar 

  25. Painter S, Cvetkovic V (2005) Upscaling discrete fracture network simulations: an alternative to continuum transport models. Water Resour Res 41(2):W02002. doi:10.1029/2004WR003682

    Article  Google Scholar 

  26. Painter S, Cvetkovic V, Mancillas J, Pensado O (2008) Time domain particle tracking methods for simulating transport with retention and first-order transformation. Water Resour Res 44(1):W01406. doi:10.1029/2007WR005944

    Article  Google Scholar 

  27. Penna D, Stenni B, Šanda M, Wrede S, Bogaard TA, Gobbi A, Borga M, Fischer BMC, Bonazza M, Chárová Z (2010) On the reproducibility and repeatability of laser absorption spectroscopy measurements for \(\delta ^{2}\)h and \(\delta ^{18}\)o isotopic analysis. Hydrol Earth Syst Sci 14(8):1551–1566. doi:10.5194/hess-14-1551-2010

    Article  Google Scholar 

  28. Rálek P, Hokr M (2013) Methods of water inflow measurement in the bedrichov tunnel. Explor Geophys Remote Sens Environ 2:30–39

    Google Scholar 

  29. Roubinet D, de Dreuzy JR, Tartakovsky DM (2013) Particle-tracking simulations of anomalous transport in hierarchically fractured rocks. Comput Geosci 50:52–58. doi:10.1016/j.cageo.2012.07.032

    Article  Google Scholar 

  30. Šanda M, Vitvar T, Kulasová A, Jankovec J, Císlerová M (2014) Run-off formation in a humid, temperate headwater catchment using a combined hydrological, hydrochemical and isotopic approach (Jizera Mountains, Czech Republic). Hydrol Process 28(8):3217–3229. doi:10.1002/hyp.9847

    Article  Google Scholar 

  31. Shapiro AM (2001) Effective matrix diffusion in kilometer-scale transport in fractured crystalline rock. Water Resour Res 37(3):507–522. doi:10.1029/2000WR900301

    Article  Google Scholar 

  32. Solomon DK, Genereux DP, Plummer LN, Busenberg E (2010) Testing mixing models of old and young groundwater in a tropical lowland rain forest with environmental tracers. Water Resour Res 46(4):W04518. doi:10.1029/2009WR008341

    Article  Google Scholar 

  33. Solomon DK, Gilmore TE, Solder JE, Kimball B, Genereux DP (2015) Evaluating an unconfined aquifer by analysis of age-dating tracers in stream water. Water Resour Res 51(11):8883–8899. doi:10.1002/2015WR017602

    Article  Google Scholar 

  34. Soltani SS, Cvetkovic V (2013) On the distribution of water age along hydrological pathways with transient flow. Water Resour Res 49(9):5238–5245. doi:10.1002/wrcr.20402

    Article  Google Scholar 

  35. Sudicky EA, Frind EO (1982) Contaminant transport in fractured porous media: analytical solutions for a system of parallel fractures. Water Resour Res 18(6):1634–1642. doi:10.1029/WR018i006p01634

    Article  Google Scholar 

  36. Tang DH, Frind EO, Sudicky EA (1981) Contaminant transport in fractured porous media: analytical solution for a single fracture. Water Resour Res 17(3):555–564. doi:10.1029/WR017i003p00555

    Article  Google Scholar 

  37. Therrien R, Sudicky E (1996) Three-dimensional analysis of variably-saturated flow and solute transport in discretely-fractured porous media. J Contam Hydrol 23(1–2):1–44. doi:10.1016/0169-7722(95)00088-7

    Article  Google Scholar 

  38. Thoma MJ, McNamara JP, Gribb MM, Benner SG (2011) Seasonal recharge components in an urban/agricultural mountain front aquifer system using noble gas thermometry. J Hydrol 409(12):118–127. doi:10.1016/j.jhydrol.2011.08.003

    Article  Google Scholar 

  39. Warren JE, Root PJ (1963) The behavior of naturally fractured reservoirs. Soc Petro Eng J 3(03):245–255

    Article  Google Scholar 

  40. Weiss R (1968) Piggyback sampler for dissolved gas studies on sealed water samples. Deep Sea Research and Oceanographic Abstracts, vol 15, no. 6, pp 695–699

  41. Zak J, Verner K, Klominsky J, Chlupacova M (2009) “Granite tectonics” revisited: insights from comparison of K-feldspar shape-fabric, anisotropy of magnetic susceptibility (AMS), and brittle fractures in the Jizera granite, Bohemian Massif. Int J Earth Sci 98(5):949–967

    Article  Google Scholar 

  42. Zuber A, Maloszewski P Yurtseveir Y (eds) (2001) Environmental isotopes in the hydrologic cycle, vol 6. International atomic energy agency

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Acknowledgments

The work described in this paper was conducted within the context of the international DECOVALEX 2015 Project. The authors are grateful to the funding organizations who supported the work. The views expressed in the paper are, however, those of the authors and are not necessarily those of the funding organizations. Technical University of Liberec (TUL) has been supported by the Radioactive Waste Repository Authority of the Czech Republic (SURAO), under contract No. SO2013-077. The results of the TUL authors were also obtained through the financial support of the Ministry of Education of the Czech Republic (MSMT) from the project LO1201 in the framework of the targeted support of the “National Programme for Sustainability I.” BGR’s work was supported by the BMWi (Bundesministerium fur Wirtschaft und Energie, Berlin). Sandia National Laboratory was supported under the DOE-Used Fuel Disposition campaign. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the US Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

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Correspondence to W. Payton Gardner.

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This article is part of a Topical Collection in Environmental Earth Sciences on “DECOVALEX 2015”, guest edited by Jens T Birkholzer, Alexander E Bond, John A Hudson, Lanru Jing, Hua Shao and Olaf Kolditz.

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Gardner, W.P., Hokr, M., Shao, H. et al. Investigating the age distribution of fracture discharge using multiple environmental tracers, Bedrichov Tunnel, Czech Republic. Environ Earth Sci 75, 1374 (2016). https://doi.org/10.1007/s12665-016-6160-x

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Keywords

  • Environmental isotopes
  • Hydrogeology
  • Isotope geochemistry
  • Surface water
  • DECOVALEX