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

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Abstract

Tritium is a short-lived radioactive isotope (T 1/2=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.

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Acknowledgements

CGL-2004-05963-C04-01 and CGL2007-66861-C04-03 research projects, Spanish Ministry of Science and Innovation. 08225/PI/08 research project, “Programa de Generación del Conocimiento Científico de Excelencia” of the Fundación Seneca, Región de Murcia (II PCTRM 2007-10). Support for this work was provided by the Technical University of Cartagena. We also thank D. Mallants and another, anonymous, reviewer for helpful comments on the manuscript.

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Appendix: Nomenclature

Appendix: Nomenclature

()0 :

values at the ground surface

α :

dimensionless water stress response function (–)

b :

pore size distribution index (–)

c E :

bulk transfer coefficient for evaporation (–)

C r :

HTO g concentration at reference height, Bq m−3 air

C a :

HTO g concentration of soil air, Bq m−3 air

C w :

HTO l concentration of soil water, Bq m−3 water

D :

soil water diffusivity function, m2 s−1

D T :

hydrodynamic dispersion, m2 s−1

D Ta :

molecular HTO g diffusion coefficient in air, m2 s−1

D Tw :

molecular HTO l diffusion coefficient in water, m2 s−1

D wa :

water vapor diffusion coefficient in air, m2 s−1

e e :

evaporation–condensation of HTO l in soil, kg m−3 s−1

e t :

transpiration of HTO l in soil, kg m−3 s−1

E e :

evaporation–condensation of water in soil, kg m−3 s−1

E r :

amount of runoff, kg m−2 s−1

E t :

actual transpiration due to root water uptake, kg m−3 s−1

ET p :

potential evapotranspiration, kg m−2 s−1

ET 0 :

reference evapotranspiration, kg m−2 s−1

f :

ground cover sigmoid function (–)

τ a :

tortuosity for soil air (–)

τ w :

tortuosity for soil water (–)

h :

pressure head, m

h s :

air entry potential, m

I :

irrigation, kg m−2 s−1

K :

unsaturated hydraulic conductivity of soil, m s−1

K c :

crop-specific coefficient (–)

K s :

saturated hydraulic conductivity of soil, m s−1

λ :

dispersivity, m

P :

precipitation, kg m−2 s−1

q :

vertical liquid water flux, kg m−2 s−1

q s :

maximum infiltration flux, kg m−2 s−1

r e :

resistance of evaporation in soil as function of water content, s−1

ρ a :

density of moist air as function of temperature, kg m−3

ρ s :

bulk density of soil, kg m−3

ρ w :

density of liquid water, kg m−3

t :

time, s

T p :

potential transpiration, kg m−2 s−1

T s :

soil temperature, K

θ :

volumetric soil water content, m3 m−3

θ s :

saturated volumetric soil water content, m3 m−3

u r :

wind speed at reference height, m s−1

v :

seepage velocity, m s−1

W r :

specific humidity of air at reference height, kg kg−1

W a :

specific humidity of soil air, kg kg−1

W sat :

specific humidity of soil air at saturation, kg kg−1

z :

vertical space coordinate, m

z root :

root depth, m

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Jiménez-Martínez, J., Tamoh, K., Candela, L. et al. Multiphase Transport of Tritium in Unsaturated Porous Media—Bare and Vegetated Soils. Math Geosci 44, 187–208 (2012). https://doi.org/10.1007/s11004-012-9383-8

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