Model for the vertical migration of 137Cs in the soil profile
Modeldata and Measurements
In the past the transport of 137Cs in the soil has often been described mathematically with compartment models, which were introduced basically by FRISSEL
(1981) and by FRISSEL and PENDERS (1983).
In the present research project a model was developed in order to describe the vertical distribution of 137Cs in the forest soil. The model subdivides the
vertical profile into soil compartments (layers) with a thickness of 2 cm, where migration, fixation and desorption of 137Cs take place (Figure 9).
Time dependent contamination pathways of the soil are litter fall and dripping water from the crowns of trees, which have been considered additionally in the model. It
is assumed, that this contribution is proportional to the 137Cs activity, which is available for root uptake in the soil range from 0-14 cm.
Fig. 1: Scheme for the 137Cs fluxes in the soil model with NB layers. The radionuclides in den
gray-shaded compartments are available for root uptake
The system of differential equations for the 137Cs flux in the soil layers is formulated as follows:
i: Index of a soil layer
NB = 7: Number of soil layers, which are considered for the calculation of litter fall
and water from the crowns of trees
NT = 15/25: Number of soil layers
n(i): Time function for the radionuclides available for root uptake in soil layer (i)
f(i): Time function for the radionuclides fixed in soil layer (i)
╬╗m(i): Time function of migration (a-1) from soil layer (i) to soil layer (i + 1)
╬╗f(i): Time constant of fixation (a-1) in soil layer (i)
╬╗d(i): Time constant of desorption (a-1) in soil layer (i)
╬╗b: Time constant for the entry of radionuclides on the soil surface caused
by litter fall and water from the crowns of trees (a-1).
The system of these differential equations can be solved numerically [T├Ârnig 1979]. The solution of the differential equations with the initial conditions n(i)(t=0) and f(i)(t=0) for i = 1, ..., NT describes
the temporal course of the activity concentration in the different soil layers:
Adep: Deposited activity (Bq m-2)
r(i): Density (kg m-3) of soil layer (i)
d = 2 cm: Thickness of a soil layer
t = 30 a: Half-life of radioactive decay for 137Cs
This research was conducted with funds of the
Federal Ministry for Environmental, Nature Protection and Reactor Safety.
This report reflects the views and opinions of the contractor and need not necessarily correspond to those of the sponsor.
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