Movement of tritium-labelled water in soils

ht. 1. Appl. Printed in

Radiat.

ht.

Vol.

Great Britain. All

36. No. 3, pp. rights reserved

209-213,

1985 Copyright

Movement

of Tritium-labelled in Soils

P. FODOR-CS.bYI,’

0020-708X/85 53.00 + 0.00 C 1985 Pcrgamon Press Ltd

Water

J. KASZA,’ L. FEHkR2 and K. BkRC13

‘Laboratory of Nuclear Chemistry, EiitvGs University, Budapest VIII, Puskin u. 1I-13, Hungary H-1088, ‘Plant for the Processing and Storage of Radioactive Waste, Wsp6ksxilagy. Hungary H-2166 and power Station and Network Engineering Company, Budapest P.O. Box 23, Hungary H-1361 (Received

20 February

1984; in revised form 20 July 1984)

In order to investigate the possibility of the disposal of solid waste directly in the soil, the movement of HTO-labelled water was studied in the soil of Ptispdkszihigy, Hungary (Plant for the Processing and Storage of Radioactive Waste) at depths from 2.0 to 2.9 m under the surface level. To characterize the water movement a time-independent quantity-migration distance divided by the amount of irrigated water-was chosen. Its value diminished from the initial 0.3 to 0.2cm/L with the increase of the clay content of the soil. The developed mathematical model fits the experimental results adequately.

Introduction The operation of nuclear power stations, the production and the widespread use of radioactive isotopes result in a growing quantity of radioactive waste which needs careful and circumspect handling for centuries ahead. In case of inappropriate disposal these materials may endanger human life and the environment. For the storage and tinal disposal of the radioactive waste the most frequent method is to use the upper layers of the soil. Since 1976 this method has been applied to the disposal of solid radioactive wastes of low and medium activity in the Plant for the Processing and Storage of Radioactive Waste at Piipiikszilagy (Hungary). According to the present technology, reinforced concrete underground basins serve for the disposal of the waste. Should the geological conditions of the site be suitable, it can be taken into consideration whether solid waste of low concentration could be disposed directly in the soil. If so, this much cheaper method might be used for the disposal of the waste from the Nuclear Power Station Paks. The safe storage is decisively determined by the geohydrological characteristics of the soil, which greatly influences the migration of the radioactive materials. This means that the interaction of the soil with the radioactive materials, and the soil characteristics (such as density, porosity, permeability, moisture content, etc.) should be known. The water movement plays an important role in the migiation process as the radioactive materials spread into the environment by the transmission of water (infiltrating and ground water). In the soil above the ground water table (in the unsaturated zone) the behaviour of the infiltrating 209

water is influenced by the capillary forces, diffusion and adhesive phenomena. In the saturated zone (under the ground water table) the diffusion dominates over the convection (according to the literature).“) These phenomena are, however, influenced by other factors, such as the weather and the mechanical characteristics (first of all permeability) of the soil. The movement of HTO labelled water was studied as a function of time and amount of irrigated water onto the soil, A mathematical model was developed to interpret the experimental results.(2’ The experiments were based on the Finnish experience.‘”

Experimental The experiments were carried out in the area of the Plant for the Processing and Storage of Radioactive Waste and began at 2m depth, since: -the soil was guaranteed to be of original composition (not being disturbed by agricultural cultivation); -the water permeability of the soil between 2 and 4m was greater than in the deeper layers, so the more unfavourable safety conditions were investigated; -the impact of weather (temperature, precipitation, soil frost, etc.) could be neglected at this depth (and with the plot being covered); -this depth was still convenient for the work. The ground water table was at a depth of 25 m below the surface level. In the experimental plot the 2 m upper layer of the soil was removed. Four plots were formed, 1 m2 each. They were separated from one another by concrete walls (Fig. 1) and received a top cover. One of them

‘10

P. Foooa-Q.&n

SOLI

Fig. 1. Experimental plot.

was used for this experiment, the other three for the migration studies of %, ‘34Cs and HTO applied as point sources, one in each plot. The plot was horizontal, without holes. It was irrigated once with HTO labelled water (1.32 GBq activity in 4 L water) applied directly to the soil by an ordinary garden sprinkler (14 July 1982). Having been labelled, the plot was regularly irrigated with 4 L water, first 1 day after the labelling and then every work-day. The soil sampling began 2 days after labelling and was carried out 8 times; every time 2 parallel soil cores were taken by a special device (4 1.8 cm) every 1Ocm from 2.00 to 2.90m depth. (This volume is hereinafter mentioned as core.) This means that during the whole experiment only 0.5% of the experimental surface was used for the sampling holes. After sampling, the holes were filled with soil of the same composition and marked with a stick to avoid sampling from the same place or near it. During the experimental period the total amount of irrigated water was 364 L. (This is equal to 364 mm of precipitation on a 1 m* area.) The total amount of tritium was determined in each sample by measuring the amount and the activity of the soil water. The amount of water in the cores was determined by weighing the cores before and after drying them at 108 “C. The activity was determined by isotope dilution method, viz. 30cm3 water was added to the core, mixed, and after several hours, filtered. The process was repeated with another 30 cm3 water. The activity of the water was measured by a liquid scintillation counter (NE 6500 A) using 8 cm3 water and 8 cm3 Insta-Gel scintillation solution.

et al.

sand contents increased from 27 and 13:; to 31 and 16x, respectively; the mud and loess components decreased from 23 and 35g/, to 21 and 3 I:/,. respectively. In this area the annual precipitation is 470 mm (as a 10-y average). This precipitation was planned for irrigation of the soil as fast as possible. Having irrigated 364L, the experiment had to be stopped because the 1 m* area was found to be too small for further sampling. The activity as a function of depth decreased continuously, even after the 7th day (20 L) of the labelling, i.e. the maximum activity was between 2.00 and 2.lOm (Fig. 2 and Table 1). After 121 days (236 L) the maximum was found between 2.40 and 2.50 m and after 182 days (364 L) 75% of the activity was between 2.00 and 2.60m. As a function of time, the activity slowly decreased in the 2.00-2.10 m layer (Fig. 3). In the layers 2.20-2.30 m, 2.30-2.40 m and 2.50-2.60 m the activity reached the maximum after 48 (120 L), 99 (180 L), and 182 days (364 L), respectively. This corresponds to 0.9 cm/d velocity at the beginning and 0.4 cm/d at the end of the experiment under the irrigation conditions as mentioned above. This is in agreement with the change of the clay content of the soil, increasing from 27 to 31% between 2.00 and 2.90m. Expressing the water velocity in cm/d gives a value which is of general use only if the plot is irrigated regularly without any break. But in the experiment there was a 21-day break after the 48th day. Therefore, a time-independent quantity-migration distance divided by the amount of irrigated water (in litres or in mm)-was chosen to characterize the water movement. Its value diminished from the initial 0.3 to 0.2cm/L as the clay content of the soil increased.

Mathematical Model For better understanding of important processes determining the water movement in the soil and for

Y 265

Results The experimental plot in Piispiiksziligy was carefully selected to represent the mean composition of the soil. At depths from 2.00 to 2.90 m the clay and

2’S F I

J!

2951 i’

1c HTO

ocr~v~ty

ICO

CkBq/core)

Fig. 2. Tritium activity of soil water as a function of depth.

Movement of HTO in soils Table Time and volume of irrigated water Depth W

2nd day

Cks8”)

7th day 20 L

I. Tritium 14th day 40L

(kB@

(kBq)

activity

211

in the soil

22nd day

2:)

48th day 120 L

CkBq)

99th day l8OL (k&I

l2lst day 236 L 0.1 0.4 4.7 50.5

2.00-2.10 2.10-2.20 2.20-2.30 2.30-2.40 2.4G2.50 2.50-2.60 2.60-2.70 2.70-2.80 2.80-2.90

206.0 7 3.9 0.9 0.7 0.1 I.2 1.2 -

188.4 38.5 0.5 0.3 -

63.9 99.9 5.4 0.4 0.2 0.1 0.1 -

8.4 123.6 41.7 1.1 3.4 0.4 0.1 -

0.8 11.1 89.7 68.4 10.0 0.2 -

3.0 16.4 54.9 83.9 50.5 13.5 1.5 -

EkBq

216.0

227.7

170.0

178.7

180.2

223.1

3 weeks bre$

the long-term extrapolation of the results of a relatively short experimental period it was necessary to elaborate a mathematical model that contained all the important parameters. In order to adapt the conclusions of theories dealing with the transport of isotopes to the water movement the following processes have to be considered?) (a) diffusion in water, partially or totally filling the soil pores; (b) dispersion caused by the granulate structure of the soil; (c) ground water movement; (d) sorption processes; (e) radioactive decay. In the case of HTO, both the sorption processes and, comparing the short experimental period to the half-life, the radioactive decay can be neglected.

10 I

o., i

20 1 I 7

50 .-.%c 200 500 1000 I bq..iI EI I Ix I I II I/ j II III1 14 22 4899 182 121 Time

(days)

Fig. 3. Tritium activity of soil water as a function of amount of irrigated water and time, respectively.

(kB@

182nd day 364L (kW

8.8 -

0.3 0.5 2.4 23.6 53.4 61.3 29.7 13.3 4.2

190.4

187.7

z

in irrigation.

In most of the physical models the soil is considered as a two-phase system (the total volume of soil pores is filled with water) and the water infiltration follows Darcy’s law. On the other hand, in these experiments the activity transport proceeded in the unsaturated zone in a three-phase medium (‘pores contained air in addition to water). According to published data, the three phase medium has essentially greater resistance than the two phase one, and in the three phase medium the water velocity can be characterized by the following equation:“)

where w is the infiltration velocity in the three phase medium (m/s); k, is Darcy’s infiltration coefficient, describing the vertical laminar flow in the two phase medium (m/s); 0 is the relative saturation of the pore volume, i.e. the ratio of the volume of water in pores to the total volume of pores; 6, is the relative saturation value, characterizing the soil dried out to its fixed water content (for soils having saturation inferior to this value the transport of water is possible only in vapour state); 2 is the empirical factor (its value is between 3 and 3.5); I is the hydraulic gradient; IK is the gradient of the capillary potential characterizing the additional adhesive forces between the solid structure and fluid (for the calculations, the values Ik were taken from the literature using pF curves of soils). For setting up the equations characterizing the process, the activity and mass balance of an elementary soil volume dV has to be studied. For simplification, it is quoted for a one-dimensional case. In the model the soil is regarded as a homogeneous isotropic medium in respect to the soil characteristics which are not time-dependent. Let the porosity of the soil be marked f,and the relative water saturation of the pores 0, at time t (both are dimensionless). Thus in the soil volume d V (=dr.dy.&) the total pore volume is given by f .dV and the volume of the chemically free water by kl;f-dV. The variation of the water content in vol-

112

P. Forma-C&~

ume dV during time dt is the difference of the inlet and outlet water. The infiltration velocity can be calculated by equation (1) (index : marks the value at the given point): (0 ,+d,-B,).f.dV=(w,--~I+d,)dK.dy.df.

(2)

Expressing the differential changes of the arguments in spatial and temporal variables with the zero and the first order members of MacLaurin series, and completing the possible simplifications the following equation can be obtained:

ae

-=---, at

1 ?w f 2:

(3)

In case of HTO the changes of activity A, in volume dV during time dt can be described by the following

equation: (A,+dr-A,)=(~~~.al-ww,+,,.u.+,,)6~.dy.dt +D.dx.dy*f

[ - e:@);

+ K+,,(;):+b]dr

(4)

where a is the specific activity of HTO in the infiltrating water and D is the diffusion coefficient. It was concluded from the measured results that the changes in relative saturation 0 are very small in space. This is the reason for keeping the values 0 constant in the activity-distribution equation. If on the other hand 6 is variable, then we obtain a non-linear equation for A. The relationship between the specific activity and activity is given by dA = B.fa.dV.

(5)

It has to be taken into account that the influence of diffusion and dispersion cannot be separated, which is why the coefficient D* characterizing the results of the two processes is applied instead of diffusion coefficient D. dA 1 d(w.A) - --Tct - #g.f &

+ D* ?‘A

-’

(6)

For the solution of the system the initial conditions, i.e. the distribution of the water content and activity at the moment t = 0 and boundary conditions, i.e. the functions 0(0; t) and A(0; t) at the place z = 0, have to be fixed. Equations (I), (3) and (6) with the initial and boundary conditions are treated as a system of differential equations. From Q(:; f) the velocity field ~(2; t) can be determined, permitting the calculation of the changes of saturation A~(z, t) and activity distribution AA@; t) during time At; also the new values of 0(z; r + At) and A(z;t +At) can be determined. These steps are repeated until the ‘-end of calculations” time value is reached. From the experimental results the following data are available: the values of activity distribution in several moments, the amount of irrigated water as a

et al.

function of time, the water content in cores and the soil characteristics. In numerical calculations the data regarding 0(0; t), which in fact were as a series ofimpulses, were represented by the 4 L irrigation and replaced by a continuous function. The input data at issue were selected on the basis of the measurements of plot samples as follows: kn= 10Wscm/s

f =0.-l.

The value 0(:; 0) was taken to be 0.2, taking into account the drying of the layers, and. on the basis of published data,(s) it was supposed that z = 3.5 and

e,=o.l. It can be seen from the second day measurement that the loss of activity due to the evaporation of water is about 25%. In this result there was no lateral movement, because the plot was isolated by concrete walls of 20 cm. The plot was covered at the top but - 8 rnJ air layer was between the soil surface and the top cover (see Fig. 1). In the mathematical model published datai6’ were used to assess the evaporation processes. The self-diffusion coefficient of b-ater”) (labelled with HTO) is D,, = 2.51 x 10-scm212s. Diffusion in the porous medium is inhibited: according to published data(‘) it can be characterized by a virtual diffusion coefficient one order of magnitude lower than in solutions; this was the value used in our calculations, too. A computer code based on the finite element method was written for the calculations being utilized for parametric study, i.e. the actual values of e(=; 0) and &, were ranging from 0.5 to 0.2 and from 0 to 0.3, respectively, and values of kn and D* were changed within one order of magnitude. It was only the change of D* which significantly affected the distribution curves. As a special item the balance of irrigated water and losses should be mentioned. It was the most important parameter which determined the velocity of the distribution maximum. In our calculations, losses were considered as merely evaporation losses. The initial value was fixed so that the loss in activity of the first two days was taken to be equal to the evaporation and it was supposed to decrease linearly. reaching 0 mm/d by the 182nd day. Before discussing the calculated results it is necessary to examine Fig. 4. Previously it could be seen in Fig. 1 that the results deviated to various extents at different moments compared with difFusion distribution in a homogeneous semi-infinite medium. Gaussian distributions in infinite medium are symmetrical to the maximum, and from the border to the maximum the solutions of the diffusion equation for semi-infinite medium should exceed the Gaussian values (because of the reflection of the distribution on the impermeable wall). In the experiment at issue it was just the other way round. One of the reasons might be the evaporation loss of infiltrating water

Movement of HTO in soils

213

25

03 04 Normalzed lal

99rh

0.0 01 ~ctwty

day

0.2

03

04

lb1 121 51 day

Fig. 4. Calculated (-) and measured (W) distribution normalized to the 1.32 x lo5 Bq!cmr initial value (calculated results do not contain activity losses).

(and activity), which, at the beginning of the experiment, tends to equalize the distribution. In the calculations of the activity balance of the surface layer the evaporation of activity was not taken into account. The character and influence of the “degeneration” can be seen in Fig. 4 which shows that in the experiment the measured (interpolated) maximum point is determined not only by the balance of the irrigated water and evaporation losses but the initial evaporation of the activity also causes a virtual displacement, because the evaporation loss is decreasing by depth from one layer to the other. If these virtual displacements are taken into account when determining maximum points from the descending part of the measured distributions (which are labelled in Fig. 5 as measured and corrected values) then the calculated and the measured results are in adeqauate agreement with one another (between the 22nd and 182nd days) under the conditions of the field experiments. This can be seen in Fig. 5 where the values of maximum point displacement are calculated without evaporation, the virtual displacements interpolated from the measured distributions and the “measured and corrected” values are indicated (before the 22nd day the corrected maximum point data are not reliable).

Conclusions In our experiments the water movement diminished from the initial 0.3 to 0.2cm/L (0.3 to 0.2 cm/mm) between 2.0 and 2.9 m. The composition of the soil layers beneath a depth of 4 m is similar to that of the investigated ones, and the value 0.2 cm/mm can be used in calculation. The maximum activity runs the distance between 2 and 4m under the conditions of 1OOOmm of precipitation, i.e. it takes 2 y at 470 mm of average annual precipitation. Below 4 m depth the clay content of the soil increases (35 and 42% at 5 and 6 m, respectively), and the water

C

50

100 Dare

of

samplmg

1%

200

(days1

Fig. 5. Comparison of measured (a), measured and corrected (0). and calculated (-_) displacements at different times (displacement means the displacement of the distribution maximum); O-calculated from measured data. O-measured values corrected by eliminating the influence of the evaporation, (-) calculated results without evaporation.

movement is expected to be less than 0.2 cm/mm. Taking into consideration that the ground water table is 25 m under the surface level, the water-soluble radioactive isotopes not being absorbed by the soil will reach the ground water table after a very long time. On the basis of this calculation it is feasible to bury the solid wastes of low activity directly into the soil. The study of water movement will continue by using an HTO point source. The radioactive isotopes do not contaminate the soil in uniform distribution, therefore, it is necessary to know the water movement in that case, too. The developed mathematical model adequately fits the experimental results. It seems logical to further develop it to a multidimensional distribution model but a more realistic method would be needed to evaluate the capillary potential. The model can ‘be developed and verified by processing the results of the point source experiments. Acknowledgements-We

thank Mrs F. Borcsbk and Mr L. Krizsik for their assistance in the experiments.

References I. Lenda A. and Zuber A. Tracer Dispersion in Ground Water Experiments (Isotope Hydroloc/, IAEA-SM129/37, Vienna, 1970). 2. Evens G. V. Int. J. Appl. Radiat. Isot. 34, 451 (1983). 3. Fodor-Csinyi P., Takala S., Alhonen-Hongisto L., Miettinen J. K., Horvlth G. L., Vakkilainen P. and Soveri J. Nordic Hydrol. 11, I69 (1980). 4. Radioactive Waste Disoosai into the Ground. Safetv Series No. 15 (IAEA, Vienna, 1965). 5. Kovacs Gv. Seeouze Hvdraulics fPublishinn House .of the Hungarian Academy of Sciences Elsevier. Budapest/Amsterdam, 1981). 6. Juhasz J. Hydrogeology (Akademiai Kiado. Budapest, 1976). 7. Erdey-Grirz T., Inzelt Gy. and Fodor-Csin!i P. Acta I

Chim. Acad. Sci. Hung. 77, 173 (1973).