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MICROCOPY RESOLUTION TEST CHART
NATIONAL BUREAU OF STANDARDS - 1963
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Onwrf 32 of
Con-671102--9
RECEIVED BY DTIE AUG 29 1967
MASTER
A Simplified Approach to Calculating
Convective Plateout of Fission Products*
T. S. Kress and F. H. Neill.
CESTI PICES
Oak Ridge National laboratory,
Oak Ridge, Tennessee
H.C. $23.00 MN 165
Many analyses!,2,3 of the transport and deposition of fission products
in a reactor coolant circuit share common deficiencies: the mathematical
models are cumbersome and impractical to apply; the physical models are
limited in the choice of surface reactions and do not readily describe the
simultaneous adsorption of several fission products onto a common surface.
The present model attempts to meliorate these shortcomings through the
use of two simplifications:
'1A quasi-equilibrium is assumed to exist at all times between the
adsorbate on the surface and in the gas stream in direct contact with the
surface. This is equivalent to assuming that' the transfer across the
boundary layer is the controlling rate;
2. Axial variations are not included in the derivation of the equa-
tions. These can be obtained, however, by progressive application of the
equations in downstream finite difference regions using mass balances to
establish the respective gas stream concentrations.
The transfer across the boundary layer is described by the product of
a mass-transfer film coefficient, h, and the average concentration poten-
tial, (N. - N :). Therefore, for each fission product in a mixture of n,
a mass balance on the surface gives
Wi
OM,
at - h(Ñ- Nyt) + 1 M = 0
i = i. 2, ...n,
[1]
where à may be either the radioactive decay constant or some other un-
specified removal rate constant.
*Research sponsored by the U. S. Atomic Energy Commission under con-
tract with the Union Carbide Corporation.
DISTRIBUTION OF THIS DOCUMENT IS UNLIMITED
Our first assumption allows us to express the concentration near
the surface, Nui, in terms of the mixed adsorption isotherm for the
system,
Ni = F; [ surface material, T, M, M, ...m
..
[2]
.
Equatior. I is then rewritten
.
*..
.
+
2
AM
of
at +14M= ;(t)
2
-
where
0 (t) = a[n, (t) – Fg(t)]
An analytical solution for Equation 3 is easily determined for a
constant gas stream concentration of a single species with F expressed
by the Langmuir Adsorption Isotherm. In general, however, time varia-
tions in gas stream concentration and the complexity of mixed adsorption
isotherms preclude finding an analytical solution. Numerical solution
on a digital computer is recommended using an integral form of Equa-
tion 3,
My(t) = 5* (t, 2) (2) dz ,
[4]
N
where
G(t,z) :3 a Green's function that must satisfy
OG(,2) + x4(t,2) = 0
ot
and
(5)
G(t,t) = 1 .
LEGAL NOTICE
This roport mo prepared no an account of Governmont sponsored work. Nolthor the Unitod
Statos, nor the Commission, nor any person acting on behalf of the Commission:
A. Makes any warranty or representation, expressed or implied, with respect to the accu-
racy, completeness, or usefulness of the information contained in this report, or that the use
of any information, apparatus, mothod, or procoso disclosed in this report may not infringo
privately owned rights; or
B. Assumos any llabilities with respect to the use of, or for damages resulting from the
As used in the above, "person acting on baball of the Commission" includes any on-
ployee or contractor of the Commission, or employee of such contractor, to the extent that
such employs or contractor of the Commission, or employee of such contractor properes,
diomminates, or provided accos to, eny Information pursuarit to his employment or contract
with the Commission, or his employment with such contractor.
3
Conditions [5] are met if
at
Az
G(t, z) = e
e
.
Equation 4 then becomes
nt 1,2 het
My(t) = 1*2****** (z) áz ,
hen
[6]
which is readily solved by several numerical techniques. A simple irc-
cedure would be to assume :(t) constant over any small finite difference
time interval, At, so that for the j'th time interval,
AM =
le
[7]
Application of Equavion requires that the mixed adsorption isotherm
be determined experimentally and the gas stream concentration, No, be
established through knowledge of release rates and through numerical
solution of gas stream mass balance equations.
Equation 7 was used to predict deposition rates, and the results
were compared with predictions from a more complex analysis that in-
cluded separate rates for adsorption and desorption. Agreement was
good under the conditions of the comparison which simulated conditions
in a Fission Product Deposition Experimental Systems at ORNI.
Nomenclature
F = Mnction defining mixed aäsorption isotherm
h = Mass transfer film coefficient
i - Subscript denoting the i'ti member of a mixture of fission
products
9 = Subscript denoting the j'th time interval in a finite dif-
ference calculation
M = Fission product concentration on the conduit surface
N = Radial average of fission product concentration in the gas
stream
N = Fission product concentration in the gas stream at the con-
" duit surface
t = Time coordinant
T = Surface temperature
z = Dummy integration variable
À = Fission product decay constant (alternatively, a removal
rate constant)
= Total ...mber of fission product species in the mixture.
References
1. E. R. Venerus and M. N. Ozisik, Theoretical Investigations of
Fission Product Deposition from Flowing Gas Streams, Trans.
Am. Nucl. Soc., 8(2): 337 (1965).
2. T. S. Kress and F. H. Neill, Parameters of Fission-Product
Transport and Deposition, Trans, Am. Nucl. Soc., 9(1): 302
(1966).
3. G. E. Raines, A. Abriss, D. L. Morrison, and R. A. Ewing,
Experimental and Theoretical Studies of Fission Product
Deposition in Flowing Helium, USAEC Report BMI-1688,
Battelle Memorial Institute, August (1964).
4.
F. H. Neill, D. L. Gray, and T. S. Kress, Iodine Transport
and Deposition in a High Temperature Helium Loop, USAEC
· Report ORNI-TM-1386, Oak Ridge National Laboratory, June
(1966).
TSK:vm

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