26.08.2015   ACCELERATOR DRIVEN SUBCRITICAL REACTORS

Solubility as a limiting factor of the flow of radioactive nuclei

The above discussion implies that the radioelements are fully soluble in water. In truth, many elements are poorly soluble and that is liable to moderate their transfer. If the flow through the clay layer, or the man­made barrier, is insufficient to evacuate the radioelements as they are released by the fuel or the package, their concentration in the water that is in contact with them will increase until, possibly, a saturation limit Cmax is reached, beyond which they will precipitate in the vicinity of the source. To such a concentration limit corresponds a value of the flow entering the clay layer or the man-made barrier. This can be obtained from the stationary density equation:

d2

D dx2 ^stat (x) Xpstat (x) 0

(I.9)

with the condition for x = 0:

pstat(0) Cmax! S

(I.10)

where S is the area of the radioelement emitting source and ш the porosity of the clay. The porosity represents the fraction of the volume and, therefore, of the surface occupied by the water. The density, here, corresponds to the density of the dissolved radioelements. An approximation of the egression current out of the clay layer can be written as

J (‘Ll —kC e~XLV1/XD

max( ) s max

(I. ll)

with

ks = !SD0 v _________ .

tanh(^/ X/DL)

(1.12)