Mathematical Geosciences

, Volume 44, Issue 2, pp 187–208 | Cite as

Multiphase Transport of Tritium in Unsaturated Porous Media—Bare and Vegetated Soils

  • J. Jiménez-Martínez
  • K. Tamoh
  • L. Candela
  • F. J. Elorza
  • D. Hunkeler
Special Issue


Tritium is a short-lived radioactive isotope (T1/2=12.33 yr) produced naturally in the atmosphere by cosmic radiation but also released into the atmosphere and hydrosphere by nuclear activities (nuclear power stations, radioactive waste disposal). Tritium of natural or anthropogenic origin may end up in soils through tritiated rain, and may eventually appear in groundwater. Tritium in groundwater can be re-emitted to the atmosphere through the vadose zone. The tritium concentration in soil varies sharply close to the ground surface and is very sensitive to many interrelated factors like rainfall amount, evapotranspiration rate, rooting depth and water table position, rendering the modeling a rather complex task. Among many existing codes, SOLVEG is a one-dimensional numerical model to simulate multiphase transport through the unsaturated zone. Processes include tritium diffusion in both, gas and liquid phase, advection and dispersion for tritium in liquid phase, radioactive decay and equilibrium partitioning between liquid and gas phase. For its application with bare or vegetated (perennial vegetation or crops) soil surfaces and shallow or deep groundwater levels (contaminated or non-contaminated aquifer) the model has been adapted in order to include ground cover, root growth and root water uptake. The current work describes the approach and results of the modeling of a tracer test with tritiated water (7.3×108 Bq m−3) in a cultivated soil with an underlying 14 m deep unsaturated zone (non-contaminated). According to the simulation results, the soil’s natural attenuation process is governed by evapotranspiration and tritium re-emission. The latter process is due to a tritium concentration gradient between soil air and an atmospheric boundary layer at the soil surface. Re-emission generally occurs during night time, since at day time it is coupled with the evaporation process. Evapotranspiration and re-emission removed considerable quantities of tritium and limited penetration of surface-applied tritiated water in the vadose zone to no more than ∼1–2 m. After a period of 15 months tritium background concentration in soil was attained.


Re-emission Effective diffusion Natural attenuation Unsaturated zone Tritium Multiphase transport 


  1. Allen RG, Pereira LS, Raes D, Smith M (1998) Crop evapotranspiration. Guidelines for computing crop water requirements. Irrigation and drainage. Paper No. 56, FAO, Rome, Italy Google Scholar
  2. Al Nakshabandi G, Kohnke H (1965) Thermal conductivity and diffusivity of soils as related to moisture tension and other physical properties. Agric Meteorol 2:271–279 CrossRefGoogle Scholar
  3. Andraski BJ, Stonestrom DA, Michel RL, Halford KJ, Radyk JC (2005) Plant-based plume-scale mapping of tritium contamination in desert soils. Vadose Zone J 4:819–827 CrossRefGoogle Scholar
  4. Auer LH, Rosenberg ND, Birdsell KH, Whitney EM (1996) The effects of barometric pumping on contaminant transport. J Contam Hydrol 24:145–166 CrossRefGoogle Scholar
  5. Barnes CJ, Jacobson G, Smith GD (1994) The distributed recharge mechanism in the Australian arid zone. Soil Sci Soc Am J 58(1):31–40 CrossRefGoogle Scholar
  6. Barry PJ, Watkins BM, Belot Y, Davis PA, Edlund O, Galeriu D, Raskob W, Rusell S, Togawa O (1999) Intercomparison of the model predictions of tritium concentrations in soil and foods following acute airborne HTO exposure. J Environ Radioact 42:191–207 CrossRefGoogle Scholar
  7. Bear J, Gilman A (1995) Migration of salts in the unsaturated zone caused by heating. Transp Porous Media 19:139–156 CrossRefGoogle Scholar
  8. Belot Y, Watkins BM, Edlund O, Galeriu D, Guinois G, Golubev AV, Meruville C, Raskob W, Täschner M, Yamazawa H (2005) Upward movement of tritium from contaminated groundwaters: a numerical analysis. J Environ Radioact 84:259–270 CrossRefGoogle Scholar
  9. BIOMOVS II (1996) Tritium in the food chain: comparison of predicted and observed behaviour. A. Re-emission from soil and vegetation. B. Formation of organically bound tritium in grain of spring wheat. Technical report No. 13, Swedish Radiation Protection Institute, 171 16 Stockholm, Sweden Google Scholar
  10. Burnham KP, Anderson DR (2002) Model selection and multimodel inference: a practical information-theoretic approach, 2nd edn. Springer, New York Google Scholar
  11. Campbell GS (1974) A simple method for determining unsaturated conductivity from moisture retention data. Soil Sci 117:311–314 CrossRefGoogle Scholar
  12. Campbell GS, Norman JM (1998) An introduction to environmental biophysics, 2nd edn. Springer, New York CrossRefGoogle Scholar
  13. Campbell GS, Shiozawa S (1992) Prediction of hydraulic properties of soils using particle-size distribution and bulk density data. In: van Genuchten MTh et al (eds) Indirect methods for estimating the hydraulic properties of unsaturated soils. University of California, Riverside, pp 317–328 Google Scholar
  14. Clapp R, Hornberger G (1978) Empirical equations for some soil hydraulic properties. Water Resour Res 14(4):601–604 CrossRefGoogle Scholar
  15. Cosby BJ, Hornberger GM, Clapp RB, Ginn TR (1984) A statistical exploration of the relationships of soil moisture characteristics to the physical properties of soils. Water Resour Res 20(6):682–690 CrossRefGoogle Scholar
  16. Cussler EL (1997) Diffusion: mass transfer in fluid systems. Cambridge University Press, New York Google Scholar
  17. Ellsworth PZ, Williams DG (2007) Hydrogen isotope fractionation during water uptake by woody xerophytes. Plant Soil 291:93–107 CrossRefGoogle Scholar
  18. Feddes RA, Kowalik PJ, Zaradny H (1978) Simulation of field water use and crop yield. Wiley, New York Google Scholar
  19. Garcia CA, Andraski BJ, Stonestrom DA, Cooper CA, Johnson MJ, Michel RL, Wheatcraft SW (2009) Transport of tritium contamination to the atmosphere in an arid environment. Vadose Zone J 8:450–461 CrossRefGoogle Scholar
  20. Gee GW, Or D (2002) Particle size analysis. In: Dane J, Topp C (eds) Methods of soil analysis, Part 4. SSSA book series, vol 5. Am Soc Agron, Madison, pp 255–294 Google Scholar
  21. GNIP/IAEA (2009) International atomic energy agency. Isotopes hydrology information system. Available via ISOHIS database. Accessed 1 April, 2008
  22. Gran M, Carrera J, Olivella S, Saaltink MW (2011) Modeling evaporation processes in a saline soil from saturation to oven dry conditions. Hydrol Earth Syst Sci 15:2077–2089. doi:10.5194/hess-15-2077-2011 CrossRefGoogle Scholar
  23. Grossman RB, Reinsch TG (2002) Bulk density and linear extensibility. In: Dane J, Topp C (eds) Methods of soil analysis, Part 4. SSSA book series, vol 5. Am Soc Agron, Madison, pp 201–228 Google Scholar
  24. Jackson DR, Reginato RJ, Kimball BA, Nakayama FS (1974) Diurnal soil water evaporation. Comparison of measured and calculated soil water fluxes. Soil Sci Soc Am Proc 38:861–866 CrossRefGoogle Scholar
  25. Jiménez-Martínez J, Skaggs TH, van Genuchten MTh, Candela L (2009) A root zone modelling approach to estimating groundwater recharge from irrigated areas. J Hydrol 367(1–2):138–149 CrossRefGoogle Scholar
  26. Joshi B, Maule C, De Jong C (1997) Subsurface hydrologic regime and estimation of diffuse soil water flux in a semi arid region. Electron J Geotech Eng. Accessed 15 May, 2008
  27. Kalisz PJ, Stringer JW, Volpe JA, Clark DT (1988) Trees as monitor of tritium in soil water. J Environ Qual 17:62–70 CrossRefGoogle Scholar
  28. Kline JR, Stewart ML (1974) Tritium uptake and loss in grass vegetation which has been exposed to an atmospheric source of tritiated water. Health Phys 26:567–573 CrossRefGoogle Scholar
  29. Kondo J, Saigusa N (1994) Modeling the evaporation from bare soil with a formula for vaporization in the soil pores. J Meteorol Soc Jpn 72(3):413–421 Google Scholar
  30. Kondo J, Xu J (1997) Seasonal variations in the heat and water balance for nonvegetated surfaces. J Appl Meteorol 36(12):1676–1695 CrossRefGoogle Scholar
  31. Kroes JG, Van Damm JC (2003) Reference manual SWAP: version 3.0.3. Rep. 773. Alterra Green World Res, Wageningen, The Netherlands Google Scholar
  32. Larsbo M, Jarvis N (2003) MACRO 5.0. A model of water flow and solute transport in macroporous soil. Technical description, Emergo 2003: 6, Studies in the Biogeophysical Environment, Department of Soil Sciences, Swedish University of Agricultural Sciences, Uppsala, Sweden, 47 p Google Scholar
  33. Maraqa MA, Wallace RB, Voice TC (1997) Effects of degree of water saturation on dispersivity and inmobile water in sandy soil columns. J Contam Hydrol 25:199–218 CrossRefGoogle Scholar
  34. Matsushima D, Kondo J (1995) An estimation of the bulk transfer coefficients for a bare soil surface using a linear model. J Appl Meteorol 34(4):927–940 CrossRefGoogle Scholar
  35. Mayers CJ, Andraski BJ, Cooper CA, Wheatcraft SW, Stonestrom DA, Michel RL (2005) Modeling tritium transport through a deep unsaturated zone in arid environment. Vadose Zone J 4:967–976 CrossRefGoogle Scholar
  36. McCumber MC, Pielke RA (1981) Simulations of the effects of surface fluxes of heat and moisture in a mesoscale numerical model 1 soil layer. J Geophys Res 86(C10):9929–9938 CrossRefGoogle Scholar
  37. Mills R (1973) Self-diffusion in normal and heavy water in the range 1–45. J Phys Chem 77:685–688 CrossRefGoogle Scholar
  38. Milly PCD (1982) Moisture and heat transport in hysteretic, inhomogeneous porous media: a matric head-based formulation and a numerical model. Water Resour Res 18(3):489–498 CrossRefGoogle Scholar
  39. Nagai H (2002) Validation and sensitivity analysis of a new atmosphere-soil-vegetation model. J Appl Meteorol 41:160–176 CrossRefGoogle Scholar
  40. Overman AR, Scholtz RV (2002) Mathematical models of crop growth and yield. Dekker, New York Google Scholar
  41. Pachepsky YA, Smettem KRJ, Vanderborght J, Herbst M, Vereecken H, Wosten JHM (2004) Reality and fiction of models and data in soil hydrology. In: Feddes RA et al (ed) Unsaturated-zone modeling. Kluwer Academic, Dordrecht Google Scholar
  42. Parker JC (2003) Physical processes affecting natural depletion of volatile chemicals in soil and groundwater. Vadose Zone J 2:222–230 Google Scholar
  43. Philip JR, de Vries DA (1957) Moisture movement in porous materials under temperature gradients. EOS Trans AGU 38(2):222–232 Google Scholar
  44. Phillips FM (1994) Environmental tracers for water movement in desert soils of the American Southwest. Soil Sci Soc Am J 58:15–24 CrossRefGoogle Scholar
  45. Pruess KA Oldenburg C Moridis G (1999) TOUGH2 user’s guide version 2.0. EO Lawrence Berkeley National Laboratory report LBNL-43134, Lawrence Berkeley Natl Lab, Berkeley, California Google Scholar
  46. Raskob W (1995) Assessment of the environmental-impact from tritium releases under normal operation conditions and after accidents. Fusion Technol 28:934–939 Google Scholar
  47. Richard WH, Kirby LJ (1987) Trees as indicators of subterranean water flow from a retired radioactive waste disposal site. Health Phys 52:201–206 CrossRefGoogle Scholar
  48. Richard WH, Price KR (1989) Uptake of tritiated groundwater by black locust trees. Northwest Sci 63:87–89 Google Scholar
  49. Roy WR, Krapac IG, Chou SFJ, Griffin RA (1991) Batch-type procedures for estimating soil adsorption of chemicals. Rep No US EPA/530-SW-87-006-F, US Environmental Protection Agency, Cincinnati Google Scholar
  50. Scanlon BR (1992) Evaluation of liquid and vapor water flow in desert soils based on chlorine 36 and tritium tracers and nonisothermal flow simulations. Water Resour Res 28(1):285–297 CrossRefGoogle Scholar
  51. SIAM (2008) Servicio de Información Agraria de Murcia. Climatology data. Available via Accessed 15 September 2009
  52. Šimunek J, van Genuchten MTh, Šejna M (2005) The HYDRUS-1D software package for simulating the movement of water, heat, and multiple solutes in variability saturated media, version 3.0. Department of Environmental Sciences University of California Riverside, Riverside, California, USA, 270 p Google Scholar
  53. Täschner M, Bunnenberg C, Camus H, Belot Y (1995) Investigations and modelling of tritium re-emissions from soil. Fusion Technol 28:976–981 Google Scholar
  54. Täschner M, Bunnenberg C, Raskob W (1997) Measurements and modeling of tritium reemission rates after HTO depositions at sunrise and at sunset. J Environ Radioact 36:219–235 CrossRefGoogle Scholar
  55. Thatcher LL, Janzer VJ, Edwards KW (1977) Methods for determination of radioactive substances in water and fluvial sediments. USGS techniques of water resources investigations. Book 5, Chap A5. US Gov Print Office, Washington, DC Google Scholar
  56. Taylor SA, Ashcroft GM (1972) Physical edaphology. Freeman, San Francisco, pp 434–435 Google Scholar
  57. Wesseling JG, Elbers JA, Kabat P, van den Broek BJ (1991) SWATRE: instructions for input. Internal note, Winand Staring Centre, Wageningen, The Netherlands Google Scholar
  58. Yamazawa H (2001) A one-dimensional dynamical soil atmosphere tritiated water transport model. Environ Model Softw 16:739–751 CrossRefGoogle Scholar
  59. Yamazawa H, Nagai H (1997) Development of one-dimensional atmosphere-bare soil model. JAERI-Data/Code 97-401 Google Scholar

Copyright information

© International Association for Mathematical Geosciences 2012

Authors and Affiliations

  • J. Jiménez-Martínez
    • 1
    • 2
  • K. Tamoh
    • 1
  • L. Candela
    • 1
  • F. J. Elorza
    • 3
  • D. Hunkeler
    • 4
  1. 1.Department of Geotechnical Engineering and GeosciencesTechnical University of CataloniaBarcelonaSpain
  2. 2.Geosciences Rennes UMR 6118 CNRS Université de Rennes 1RennesFrance
  3. 3.Department of Geological EngineeringTechnical University of MadridMadridSpain
  4. 4.Centre for Hydrogeology and GeothermicUniversity of NeuchâtelNeuchâtelSwitzerland

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