Upward movement of tritium from contaminated groundwaters:

a numerical analysis

Y. Belota *, B.M. Watkinsb, O. Edlundc, D. Galeriud, G. Guinoise, A.V. Golubevf, C. Meurvilleg, W. Raskobh,

M. Täschneri and H. Yamazawaj **

a Environment Consultant, 40 rue du Mont Valerien, 92210 Saint Cloud, France b Kingham Consultants, The Old Granary, The Moat, Kingham, Oxfordshire OX7 6XZ, UK

c Studsvik Eco & Safety AB, Sweden d IFIN-HH, Bucarest, Romania

e CEA/DASE, 91680 Bruyeres le Chatel, France f RFNC-VNIIEF, Sarov, N. Novgorod Reg., Russian Federation g ANDRA, rue Jean Monet, 92290 Chatenay Malabry, France

h FZK-IKET, 76021 Karlsruhe, Germany i ZSR, University of Hannover, Hannover, Germany

j JAERI, Tokai, Ibaraki, 319-1195 Japan Abstract This paper describes a research-oriented modelling exercise that addresses the problem of assessing the movement of tritium from a contaminated perched aquifer to the land surface. Participants were provided with information on water table depth, soil characteristics, hourly meteorological and evapotranspiration data. They were asked to predict the upward migration of tritium through the unsaturated soil into the atmosphere. Eight different numerical models were used to calculate the movement of tritium. The modelling results agree within a factor of two, if very small time and space increments are used. The agreement is not so good when the near-surface soil becomes dry. The modelling of the alternate upward and downward transport of tritium close to the ground surface generally requires rather complex models and detailed input because tritium concentration varies sharply over short distances and is very sensitive to many interactive factors including rainfall amount, evapotranspiration rate, rooting depth and water table position.

Key words: Coupled water flow and tritium transport; Tritiated water evaporation

Introduction

Contaminants that have penetrated into shallow groundwaters can migrate upward through the unsaturated layer and reach the soil surface. The net upward migration of such contaminants was already studied for strontium-90, cesium-137 and iodine-139 (Elert et al 1999; Butler et al 1999). In the present work, the study was extended to tritiated water (HTO), which behaves like a passive contaminant, has a volatile character and can easily diffuse in ordinary water and move with it, either in liquid phase or in vapour phase . The first objective of the work reported here was to find or develop a coupled water flow and tritium transport model that calculates the transport of * Corresponding author, mailto yves_belot@orange.fr ** Now at Nuclear Engineering Institute, Nagoya University, Furo-Cho, Chikusa-ku, 464-8603

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HTO from a contaminated aquifer to the soil surface. The second objective was to investigate the influence of different parameters on the evolution of the net upward flux of tritium to the atmosphere over a long time period.

The modelling exercise was undertaken in the framework of the BIOMASS programme by a Tritium Working Group (TWG) of modellers and experimentalists from twelve different organisations. Modellers were asked to predict the movement of tritium from a contaminated shallow aquifer to a vegetated or bare soil surface; the soil was assumed to be uncontaminated at time zero of the simulation. They were provided with detailed information on water table depth, soil characteristics, and hourly meteorological and evapotranspiration data for a period of one year. They were asked to predict the vertical profiles of tritium concentration in soil water at specified times after the start of tritium upward migration, and also the monthly values of HTO vapour flux from the soil surface to the atmosphere. Nine institutions participated in the modelling exercise itself, which was carried out over three years in parallel to other TWG activities. Representatives of all the twelve institutions participated in joint discussions on methods and results.

For this specific application, some participants used multipurpose computer codes that are available commercially. The other participants developed their own codes based on process models and techniques developed elsewhere. The eight sets of results presented below were obtained from numerical models. The ninth set of results obtained from an analytical model are not presented because it was recognized that this model is more applicable for scoping calculations rather than detailed predictions (a full set of results are presented in BIOMASS Tecdoc, Part F, 2002). The first section of this paper outlines the scenario which served as a basis for testing and comparing the different models used in the exercise and also provides brief descriptions of the models. The second section summarizes and compares the predictions obtained, and highlights questions that require further investigation.

A. SCENARIO AND MODELLING APPROACH

Scenario description

The scenario considers a contaminated perched aquifer, which has a water table that does not appreciably fluctuate during the course of the period to be modelled. The aquifer is assumed to be covered by a 1m-thick layer of uniform well-characterised soil, either bare or covered with a wheat crop. The concentration of tritium in the aquifer is taken as constant throughout the period of study.

In an initial version of the scenario, the hourly transpiration and/or evaporation data were not provided and the modellers had to derive values from hourly weather data. However, the calculated evaporation rates were different from one model to another and this prevented to examine the performance of the tritium transport models. So, it was decided to omit the evaporation calculations and concentrate instead on the transport process itself. Consequently, in the final version of the scenario, all the modellers were invited to use the same pre–calculated values of evaporation and transpiration rates, and to focus their attention on the transport processes. They were asked to first test the relative importance of diffusion, dispersion and advection

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processes, and secondly to give results for tritium transport in the soil with and without vegetation rooted on that soil.

In the final version of the scenario, the modellers were provided with soil data, hourly meteorological data, hourly actual evaporation rates for a bare soil and hourly evaporation/transpiration rates for a wheat-covered soil. From this information they were asked to predict the vertical profile of tritium concentration in soil water, and the flux of tritium to the atmosphere as a function of time, over a period of at least one year, both for the bare and vegetated soils. The modellers were asked to start from the assumption that the column of soil does not contain any tritium at the beginning of the simulation and that initially no flow is occurring within the soil (i.e. the total head throughout the soil water profile is the same as that at the water table). The main simplifying assumption concerns the water table, which is considered to remain at a stable depth during the course of a year. It is recognised that this may be different from reality in those cases where the water table depth changes appreciably as a function of the seasonal water supply. At this stage in the development of transport models for subsurface sources of tritium, the simplification was imposed to prevent the difficulty that would have arisen in model comparison if a more complex situation had to be modelled. It was considered to be more beneficial to start with simple models that could then be used as a basis for the development of more complex ones in the future. Hydrological conditions The unsaturated soil above the water table is of a sandy loam type (SL), made of 70% of sand, 20% of silt and 10% of clay, with a total porosity equal to 0.387. It is imposed to the modellers that the hydraulic functions that relate head pressure, hydraulic conductivity and water content should be taken from van Genuchten (1980) with the appropriate parameters derived from Schaap and Leij (1998). The dispersivity of the unsaturated SL-soil was taken equal to 0.05 m, a value in the range of those obtained by Forrer et al. (1999). In the present test scenario, hourly meteorological conditions are given as input data. The meteorological conditions, including wind speed, precipitation, air temperature, air humidity, air stability and net radiation are those monitored over a one year period in the region of Karlsruhe, Germany. The climate of the region over this time period is characterized by an annual precipitation of 770 mm, without any marked seasonal trend. The annual mean temperature is 9.5°C with monthly averages between 0°C in January and 19°C in August.

The hourly actual transpiration and/or evaporation rates are provided also as input data. They have been pre-determined by Raskob from the observed meteorological data presented above, through the use of a submodel included in the UFOTRI code (Raskob 1993). The hypothetical wheat crop has a 30–cm rooting depth. The percentages of the total transpired water that are extracted from the 0-10 cm, 10-20 cm and 20-30 cm soil layers are 30%, 35% and 35% respectively. The monthly-averaged balance of evaporation, transpiration and precipitation is very different depending on whether the soil is bare or vegetated. In the first case, the balance shows a net downward flux for each month of the year. In the second case, there is a net upward flux from April to September and a net downward flux for the other months when the soil is bare or only sparsely vegetated Governing equations

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The numerical models used in the present comparison exercise differ from each other by their degree of complexity. The most comprehensive and versatile models can take into account every process that may influence the tritium movement. Such models solve a set of coupled transport equations for fluid velocities, head pressure, temperature, and concentration of tritium in the liquid and vapour phases of the unsaturated soil. These equations may be solved in their two- or three-dimensional, transient or steady state form.

If the soil column is assumed to be isothermal, and the tritium transport to occur mainly in liquid phase, most of the models reduce to the following set of coupled equations for moisture-flow and tritium transport respectively:

!

S"h"t

= ""zK"h"z#K[ ]-w (1)

!

"#C#t

= ##zD#C#z[ ]$q#C#z (2)

where the coordinate z, termed depth, originates at ground level and is oriented positively downward (L); t is the time (T); h is the negative pressure head otherwise called matric head (L); C is the tritium concentration in soil liquid water (1/L3); θ is the volumetric liquid water content in soil (L3/L3); S = dθ / dh is the specific water capacity (1/L); K(h) is the hydraulic conductivity (L/T); D is the coefficient of dispersion in the soil (L2/T); w is a positive fluid withdrawal term that describes the root uptake of water at different times and depths (1/T) and q is the advective liquid water flow (L/T).

Equation (1) is the moisture flow equation that describes the isothermal transport of water in liquid phase for an isothermal soil profile. The relations K(h ) and h(θ ) are strongly non-linear and are expressed by hydraulic functions taken from van Genuchten (1980) with parameters selected from Schaap & Leij (1998). The positive withdrawal term w(z,t) is the volume of water extracted per volume of soil per unit of time at a given depth z and time t. At a given time t, the mean value of w(z,t) over the whole extent of the root zone can be calculated by dividing the total transpiration rate in m s–1 by the rooting depth in m. For the wheat crop considered in the scenario, the mean withdrawal term is multiplied by the coefficients 0.91, 1.06 and 1.06, in the layers 0-10 cm, 10-20 cm and 20-30 cm respectively.

Equation (2) is the traditional advection-dispersion equation that expresses solute transport in porous media in the case of a solute that does not appreciably react with the soil particles. The equation, written for the concentration in soil water C, is classically obtained by combining the activity and mass balance equations. No withdrawal term appears in the transport equation so derived, because the loss of HTO due to water extraction is indirectly accounted for by the decrease of water content on the left hand side of the equation. Notice that HTO is practically indiscernible from ordinary water in its movement from the soil to the atmosphere through the root pathway, which is a major difference between HTO and most of the other solutes. This specific character of HTO is to be taken into consideration when using versatile codes that are made for predicting the movement of any solute in soil water. The dispersion coefficient D is given by the following equation as the sum of a term for molecular diffusion and a term for mechanical dispersion:

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!

D="#DL+$q (3) where τ is a tortuosity coefficient (τ = 0.66); θ is the volumetric liquid water content in soil; DL is the molecular diffusion coefficient of HTO in liquid phase; α is the dispersivity in liquid water and q the advective liquid water flow. Auxiliary equations The upper boundary condition of Equation (1) is formulated as a prescribed flux of ordinary water at the soil surface. The imposed water flux is negative for evaporation and transpiration, positive for rain infiltration. For the conditions of the scenario given above, the hourly actual evaporation and transpiration rates are those given as entry to the model, Consequently, all the modellers have to switch off any sub–model allowing to determine the potential and actual rates.

The upper boundary condition of Equation (2) is formulated as a prescribed flux of HTO at the surface. In dry conditions, the HTO flux is proportional to the difference between the HTO concentration in the free atmosphere and that in the boundary layer of the atmosphere close to the soil surface. The coefficient of proportionality, otherwise called exchange velocity (Garland 1980), is the reciprocal of the resistance of the boundary layer to the transfer of HTO. In the evaporation process at the very top of soil surface, the movement of HTO is not the same as that of ordinary water, since each of the two water isotopes diffuses independently from the other along its own concentration gradient. The bottom of the soil column is kept at a constant concentration.

The initial conditions are those of no flow and no tritium in the soil. The concentration of HTO in the aquifer is 104 Bq L-1 all through the year.

Numerical methods

The moisture-flow and tritium-transport equations are solved for pressure head (or water content) and tritium concentration, using the same time steps and grid layout. in the discretization of both equations. Numerically, the partial derivative equations are solved in tandem using a finite–difference or a finite-element method. The two equations are linked to each other by the liquid water flow that can be obtained, at each time step and depth increment, by solving the moisture–flow equation and deriving the liquid water flow from the head pressure gradient (Darcy’s equation). They are also linked by the water content that can be derived from the head pressure using the hydraulic function cited above. A brief summary of the characteristics of the models (including the numerical method) is shown in Table 1.

B. RESULTS AND DISCUSSION

Readers are asked to note that Figures 1 to 3 represent only the region of the graphs in which a majority of results (six or seven out of eight) are grouped together. This restriction in graphical presentation of results is made in the interests of clarity and

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readability. The entire set of results with duly labelled curves can be found in the BIOMASS Tecdoc Report, Part F, (2002). Influence of elemental processes

The results to be compared are presented and discussed below. They were obtained by taking into account all the three main processes that contribute to the transport of tritium in the soil, namely advection, molecular diffusion and mechanical dispersion. An important initial task assigned to the modellers was to assess the relative importance of the three different transport processes. The participants in the exercise were asked to calculate the profiles of tritium concentration at a given date/time, when taking into account all three transport processes together or with selected processes switched off. This first task was limited to the case of a bare soil, the specific configuration of soil and water table given in the scenario description and the set of actual evaporation data provided to the modellers.

The profiles obtained when only advection and molecular diffusion processes are assumed to operate differ considerably from those obtained when it is assumed that mechanical dispersion also operates. The concentration at a 10 cm-depth is at least six orders of magnitude lower in the first case than in the second one. This indicates that the mechanical dispersion due to the irregularities of the flow pattern must be considered in the moisture-flow equation.

These preliminary calculation tests can only be considered to be indicative. They were not sufficiently extensive to study the interdependency of the different elemental processes that operate within the soil, and the contribution of each of them to the movement of tritium and its evaporation at soil surface. .

This was studied in more detail by one of the TWG participants (Yamazawa, 2000). In this parallel work, simulations were carried out, in which the different factors contributing to tritium movement were varied in order to obtain an insight into their respective influence. The factors included in a complete set of equations were molecular diffusion in liquid phase, molecular diffusion in gas phase and advection in liquid phase. It was inferred from the results obtained in this parallel work that the increase of the HTO concentration at the surface and hence the evaporation from the surface in the very early stage are mainly caused by the dispersion. Advection is dominant in determining the HTO evaporation in a later period. The question was also addressed of knowing if one can ignore the diffusion of HTO in gas phase. It was concluded that if the gas diffusion cannot be ignored in dry climate and sandy soil with a low water capacity, it can be ignored for other cases, like the one considered in the present exercise. Profiles of soil water content

In the present work, every modeller started from the prescribed initial condition of no flow in the soil, assuming that tritium begins to move on the 1st of January. The majority of participants calculated the evolution of the water content profiles by numerical solution of the moisture-flow equation, using the pressure head, or the water content, as a variable. Most modellers used small depth increments (0.005 m to 0.01 m), while only one of the participants used large increments (0.1 m) (see Table 1). The time increment, chosen to ensure stability of calculation, varied from a few seconds to several hours depending on the selected depth increment. As requested in the scenario, the vertical profiles of volumetric water content were derived from the average values

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obtained over 10 cm intervals at specified depths below the soil surface and at two specified output times (i.e. 28 February and 28 July at 12:00 h). The results shown in Fig.1 correspond to the July profiles for bare and vegetated soils respectively. The profiles are shown with linear co-ordinates.

The water content increases quasi linearly from the top layer (0-10 cm) to the bottom layer (90-100 cm). In February, the water content varies on average between 0.25 and 0.37 from top to bottom, which does not differ appreciably from the initial equilibrium profile given at the start of the simulation. In July, it varies also from 0.23 to 0.37 for a bare soil, but from 0.17 to 0.37 for a vegetated soil. In the latter case the deficit in the near-surface soil water content is caused by the strong evapotranspiration that occurs at this time of the year. The average value in the bottom layer approaches the value of water content at saturation, i.e. 0.37. If the results of the different models are compared, it can be seen that the majority of profiles in each set of curves lie close together within narrow zones of the graph. At any depth below ground level, the difference between the extreme results is less than 10% of the average value. The only exception is the result of one participant who obtained a much drier soil in the wheat root zone, the reason of which was not explained. Profiles of tritium concentration

The scenario required modellers to simulate the upward transport of tritium from a contaminated aquifer into an initially uncontaminated overlying soil column. During the first months of tritium transport, the gradient of tritium concentration in the bottom layers of the soil column is very steep. It appears, at least at the beginning of the simulation, that the spatial resolution must be very fine to describe accurately the dispersion front and to obtain appropriate results. By comparing numerical and analytical results, in the case of a column of uniform water content, Yamazawa (2000) showed that the numerical solution is correct for a depth increment of 0.005m (200 layers), but becomes more and more erroneous as the depth increment increases. Applied to the present scenario, a numerical model with a depth increment of 0.1m for instance (10 layers) leads to errors that are particularly large in the very first months of the simulation and are still noteworthy later. The large error caused by the coarse resolution is mainly due to the steep initial distribution of tritium in the soil. A coarse resolution does not lead to a large error if the initial distribution of tritium in the soil is smooth or linear with depth.

The profiles of tritium concentration in soil water were determined from the numerical solution of the dispersion-advection equation using the dispersivity given in the scenario description and the water velocity obtained from solving the moisture–flow equation. Both equations, generally coupled, were operated with the same time and depth increments. Results of tritium concentrations were requested for the same segments of the soil column and the same dates/time as for the soil water content calculations. The results are given in Fig.2, at the end of February and at end of July for a bare soil, and at end of July for a vegetated soil, from left to right respectively. The results are shown with semi–logarithmic co-ordinates, with concentrations on the logarithmic scale. Notice that the upward movement of tritium from the aquifer through the above soil layer starts on the first of January. When there is no vegetation growing in the soil, the tritium concentration decreases nearly exponentially from the bottom to the top of the unsaturated zone. The

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presence of vegetation (in this case wheat) in July results in a more complex profile. There is a great difference between concentrations at the soil surface according to whether it is vegetated or not. The concentrations in the 30 cm-rooting zone of the crop are up to three orders of magnitude greater than for the non–vegetated soil. This shows the importance of root uptake in determining tritium rise from a shallow water table. The factors involved in tritium rise could be further investigated by varying the water table depth and the characteristics of the unsaturated soil above, but this was outside the scope of the present work.

The results show that the various soil concentration profiles, although being similar, are not as closely grouped as they are for water content. Although the curves are generally well grouped for the deep layers where the calculated concentrations differ only by a factor 2 or 3, they are not so well grouped in the upper 20-cm layer, particularly in the case of a vegetated soil during summer. This is probably due to differences in modelling the behaviour of water and tritium in the near-surface layers where transpiration and/or evaporation take place. It is recommended that the specific features of each model, regarding the treatment of the near-surface processes, should be addressed and considered with greater attention in further studies.

Fluxes of tritium from soil to the atmosphere

The flux of tritium from a bare soil to the atmosphere is usually determined by an exchange between the top soil layer and the atmosphere just above. The flux from a vegetated soil originates from both soil and vegetation. During Spring and Summer months the flux from vegetation dominates; it was calculated by multiplying the extraction rate by the tritium concentration in each layer of the root zone and summing up the products so obtained.

The monthly flux of tritium from soil/plant to the atmosphere, expressed in Bq m-2 per month, is shown in Figure 3 for bare and vegetated soil respectively, and for a constant concentration of 104 Bq L-1 in the aquifer. For a bare soil, the monthly flux is maximal in July and August, with values between 2 x10+1 and 4 x10+1 Bq m-2 per month. For a wheat-covered soil, the monthly flux, during the same period, varies between 9 × 10+4 and 1.2 × 10+5 Bq m-2 per month. The enhanced tritium flux caused by vegetation is related to an increase in the net rise of ordinary water between April and September when there is a strong excess of evapotranspiration over precipitation. The monthly-averaged fluxes obtained here from the different models vary within a factor of two, which indicates a rather good agreement between the different models that have been tested.

Conclusions

The present study was devoted to the comparison of results obtained by applying different models to the same scenario. The profiles of soil water content or those of tritium concentration in soil water do not differ considerably from one model to another. The fluxes of tritium to the atmosphere are also very similar for the different models. Generally, the results agree within a factor of two for most of the models if very small time and space increments are used.

The only exception concerns the profiles of tritium concentration in the near–surface layers, particularly for vegetated soils, during the summer months when the soil tends to become dry. In this case, the different models are not in so good agreement,

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probably because of differences in the treatment of the coupled movement of ordinary water and tritiated water, in the region where evaporation and root uptake take place. This specific problem needs further studies. .

References

BIOMASS Tecdoc (2002) Modelling the Environmental Transport of Tritium in the Vicinity of Long-Term Atmospheric and Sub-Surface Sources., Part F, (B. Watkins ed) IAEA, Vienna.

Butler, A.P., Chen, J., Aguero, A., Edlund, O., Elert, M., Kirchner, G., Raskob, W., Sheppard, M. (1999) Performance assessment studies of models for water flow and radionuclide transport in vegetated soil using lysimeter data. Journal of Environmental Radioactivity, 42, 271–288

Elert, M., Butler, A., Chen, J., Dovlete, C., Konoplev, A., Golubenkov, A., Sheppard, M., Togawa, O., Zeevoert, T. (1999). Effects of model complexity on uncertainty estimate. Journal of Environmental Radioactivity, 42, 255–270.Forrer, I., Kasteel, R., Flury, M., & Flühler, H., (1999). Longitudinal and lateral dispersion in an unsaturated field soil. Water Resour. Res. 35, 3049-3060

Garland, J. A. (1980) The absorption and evaporation of tritiated water vapor by soil and grassland. Water, Air and Soil Pollution 13, 317.

Raskob, W., (1993). Description of the new version 4.0 of the tritium model UFOTRI including user guide. Report KfK 5194.

Runchal A.K. (1985) PORFLO-A contiuum model for fluid flow, heat transfer and mass transport in porous media. Model theory, numerical methods and computational tests. Report RHO-BW-CR-150-P, 104 p.

Schaap, M.G., & Leij, F.J. (1998) Database related accuracy and uncertainty of pedotransfer functions. Soil Science, 163 (10), 765-779.

Van Genuchten, M.Th. (1980) A closed form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J., 44, 892-898.

Yamazawa, H (2000) Numerical study on soil-atmosphere tritiated water transfer. Proceedings of the International Workshop of the Environmental Behaviour of Tritium. Kumatori, Japan, May 8-9, 2000.

Yamazawa, H. (2001) A one-dimensional dynamical soil-atmosphere tritiated water transport model. Environmental Modelling & Software, 16, 739-75

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Figures captions

Fig.1: Vertical profiles of water content in the unsaturated soil above a water table situated at a depth of 1 m below ground level. The water content of the saturated sandy loam soil is 0.39. The upward movement of tritium starts on the 1st of January. The lines connecting calculated points refer to a bare soil at end of July. The solid lines without points refer to a wheat-covered soil. Most of the curves obtained from the different models lie between the extreme curves shown on the graph for each of the two groups Fig.2: Vertical profiles of HTO in the unsaturated soil above a water table situated at 1 m below ground level. The tritium concentration in the perched aquifer is 10000 Bq L-1. The upward movement of tritium starts on the 1st of January. The left curves refer to the profiles at end of February ; the central curves to the profiles at end of July for a bare soil; the right curves to the profiles at end of July for a vegetated soil covered with wheat. Most of the results from the eight different models lie between the extreme curves shown on the graph for each of the three situations. Fig 3: Flux of HTO from soil and vegetation to the atmosphere for the conditions given in the scenario i.e. a constant water table depth (1 m) and a constant concentration of tritium in the aquifer (104 Bq L-1). The upward movement of tritium starts on the 1st of January.

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TABLE 1. NUMERICAL MODELS USED IN THE INTERCOMPARISON EXERCISE

Institution (Modeller)

Modelling Approach for Transient Moisture Flow and Tritium Transport

ANDRA (C. Meurville)

Approach: 3-D finite-volume code (PORFLOW developed by ACRI from the earlier work of Runchal (1985)) Solution Method: Preconditioned conjugate gradient for pressure; Alternate Direction Implicit method (ADI) for transport Discretisation: Vertical 1-D grid: 196 layers 0.005 m, 2 boundary layers 0.0025 m. Time increment: modified by user to ensure stability (360 s for earlier version of the scenario and 36 s for later version)

Consultant (Y. Belot)

Approach: 1-D finite-difference code (TRIMOVE developed by Y. Belot). Solution Method: Implicit method for moisture flow and tritium transport Discretisation: vertical 1-D grid: 101 layers 0.01 m. Time increment to ensure stability (30 s)

CEA (G. Guinois)

Approach: 2-D finite-volume code (METIS developed by Ecole des Mines). Solution method: Conjugate gradient method Discretisation: 100 layers of 0.01 m. Time increment automatically calculated

STUDSVIK (O. Edlund)

Approach: 1-D finite-difference code Solution method: Implicit method for moisture flow and tritium transport Discretisation: vertical 1-D grid: 101 layers of 0.01 m. Time increment (30 s)

FZK, IKET (W. Raskob)

Approach: 1-D compartment model (developed by W. Raskob) Solution method: Explicit method for moisture flow and tritium transport Discretisation: 10 layers 0.1 m and 1 surface layer 0.01 m. Time increment 360 s

NIPNE (D. Galeriu)

Approach: 1-D finite-difference code Solution method: Implicit method. Discretisation: 40 layers of 0.0 25 m. Time increment 3.6 s to 324 s

JAERI (H. Yamazawa)

Approach: 1-D finite-difference code with tritium routines (SOLVEG developed by H. Yamazawa) Solution method: semi-implicit for diffusion; explicit for transport (low numerical dispersion scheme) Discretisation: 200 layers of 0.005 m. Time increment: 2 s

VNIIEF (A. V. Golubev)

Approach: 1-D finite-difference code (developed by S. Mavrin) Solution method: implicit method Discretisation: 50 layers of 0.02 m. Automatic time increment 1 s to 86 s

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Fig. 1

13

Fig. 2

14

1E+0

1E+1

1E+2

1E+3

1E+4

1E+5

1E+6

1 2 3 4 5 6 7 8 9 10 11 12

month

BARE SOIL

WHEAT-COVERED SOIL

Fig. 3