The Transport of Fission-Product Cesium from Sodium - Advances in

5 The Transport of Fission-Product Cesium from Sodium I. N. TANG, A. W. CASTLEMAN, JR., and H. R. MUNKELWITZ

Downloaded by UNIV OF CINCINNATI on May 30, 2016 | http://pubs.acs.org Publication Date: January 1, 1970 | doi: 10.1021/ba-1970-0093.ch005

Brookhaven National Laboratory, Upton, Ν. Y. 11973

The vaporization of fission-product cesium from liquid sodium into flowing inert gases was investigated at 730°K. The cesium release rate was found to depend on both the liquid depth of sodium and the molecular weight of the inert carrier gases. A general release equation is developed by considering diffusion in both the liquid and gas phases. This equation is shown to represent the experimental results very well. The limiting case of maximum extent of release, expressed in terms of fractional fission-product vaporization as a function of the fraction of sodium vaporized, can often be calculated from thermodynamic considerations.

' T p h e possibility of the distribution of radioactive fission products in the environment is of major concern when making safety analyses of nuclear reactors. To predict the fission-product transport rates and the extents of vaporization, an understanding of the fundamental release mechanism is imperative. For instance, recent studies have led to an identification of mass-transfer processes controlling the release of fissionproduct iodine from molten uranium (12) and from solid hyperstoichiometric uranium monocarbide (2). The results from these studies make it possible to calculate the time dependence of iodine release from the respective systems. In considering the operational safety and accident analyses of sodiumcooled fast reactors, similar information on the release of fission products from sodium is needed. Although the extent of vaporization can often be calculated from thermodynamic considerations (3, 4), appropriate trans port models are required to describe the rate phenomena. In this chapter the results of an analytical and experimental investigation of cesium transport from sodium into flowing inert gases are presented. The limit ing case of maximum release is also considered. 71 Freiling; Radionuclides in the Environment Advances in Chemistry; American Chemical Society: Washington, DC, 1970.

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Analytical Studies Transport Model. A general release equation is developed b y considering diffusion i n both the liquid and gaseous phases. Figure 1 is a sketch of a vessel containing liquid sodium, blanketed b y a flowing inert gas and maintained at constant temperature. The assumed cesium concentration profiles for both phases are shown i n the sketch. Fick's law of diffusion may be applied to the liquid phase: ^ = D ^ dt dy

(1) '


2

v

If we consider cases where only a small fraction of sodium is vaporized during the time period of interest, the boundary conditions ( B C ) become BC

I. f = 0 , C = C a t 0 < t / < Z o

BC II. t>0,-D—

= 0atf/ = 0

dy

B C I I I . t>0, — D— = J aty = l dy l

A stagnant gas layer, through which cesium diffuses, is assumed to exist between the liquid-gas interface and the top edge of the vessel. In addition, a linear concentration gradient within the stagnant gas and a negligible cesium partial pressure at the edge of the vessel are also assumed. Thus, the mass flux i n the gas phase may be represented b y the following equation: RT dy

K

}

Integrating between I and I + b i n the direction of diffusion leads to J= g

(D /bRT) v2

Pi

(3)

The eqirilibrium partial pressure at the interface may be expressed i n terms of vapor pressure, activity coefficient, and mole fraction at the liquid surface: Pi = P2 y *i 0

2

() 4

Since i n practical cases the concentration of fission-product cesium in the sodium coolant is usually very dilute, the molar density of the mixture is essentially that of pure sodium, p. It follows that Xi = CJo

(5)

Substituting Equations 4 and 5 into 3, we obtain J = «C g

i

Freiling; Radionuclides in the Environment Advances in Chemistry; American Chemical Society: Washington, DC, 1970.

(6)

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Transport of Cesium

where ) = constant

« = ( D^/b ) ( p °y / RT 2

2

P

(7)

Applying the condition of mass flux continuity at the interface—i.e., J Ji at y = I—we can rewrite B C III into the following form:

g

BC Ilia.

=

i)C - D — = aC at y = I dy t


The solution to Equation 1 with the given boundary conditions was first obtained by Newman (9) and later summarized by Crank (7). The final expression, in terms of fractional release, takes the following form: ^ η

~ χ

2L*exp(-fi »Dt/P) n

j 9 . « ( j B . « + L« +

L)

(8)

where j8»'s are the positive roots of 0tan£ =

(9)

L

and :la/D

(10)

FLOW

Figure 1. Sketch of vaporization cell showing bound ary conditions and hypothetical concentration profiles The fractional cesium release during any given time period may be calculated, provided that all of the constants in Equation 8 are known. Unfortunately, however, liquid-phase diffusivities can be estimated only to within an order of magnitude. A n alternative approach, therefore, is to evaluate the constants D and a from two sets of experimental release data and to use these values to predict the fractional release for other conditions.



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M a x i m u m Release. The analytical model described above assumes that the liquid phase is completely stagnant. W h i l e this may be true i n an ideal laboratory experiment where a small sample can be kept iso thermal at a specified temperature, i n large scale systems where nonisothermal conditions exist, both natural convection and molecular diffusion w i l l contribute to mass transfer. This combined effect, which is often very difficult to assess quantitatively, w i l l result in an increase in fission-product release rate. Therefore, i n making reactor safety analyses, it is desirable to be able to estimate the maximum release under all possible conditions. In considering the case of maximum release, it is apparent that com plete rnixing i n the liquid phase w i l l lead to a greater release rate than that expected i n cases where diffusion operates i n two phases. Therefore, consider the case where both the solvent ( N a ) and the solute (volatile fission product) diffuse through a gas layer of constant thickness. It follows from the solution to Fick's law w i t h appropriate boundary conditions that

and Κ

1

" »

—

W

T

< I 2 )

It can be shown from the Chilton-Colburn analogy (6) that under identi cal flow conditions the ratio of foi to b is equal to the 1/3 power of the ratio of the respective diffusivities. Substituting and combining Equations 11 and 12 leads to 2

t [ l - f i

(ΡΛ»/Λ·) < -/ 0

Β

*>

β / β

=

Α

Φ

or f, = l

- (l-fx)**

(13)

where A^fVWPi

0

φ=(Ό /Ό )ν* ν2

ν1

(14) (14a)

Equation 13 reduces to the Rayeigh equation (3) when the ratio of the gas-phase diffusivities, φ, is unity. Since gas-phase diffusivity is inversely proportional to the square root of the reduced mass, i n the case of fission product-sodium systems where sodium has the smallest molecular weight, the above diffusivity ratio is less than unity. There fore, the Rayleigh equation, which was derived on the basis of equilibrium vaporization, i n fact represents an upper limit for the fractional fission-


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Transport of Cesium

75

product release as a function of the fraction of sodium vaporized. The latter quantity may often be estimated by making a heat balance for the system under consideration.


Experimental Apparatus. A schematic of the apparatus is shown i n Figure 2. The main section of the apparatus is a 60-mm. quartz tube with ground joints fused onto both ends. This tube is positioned vertically inside a Marshall 2000-watt tubular resistance furnace. The quartz tube is lined with a length of type 321 seamless stainless steel tubing, 1.5 inches diameter by 0.016 inch wall thickness, to protect the quartz from attack by the alkali metal vapors at high temperatures. The resistance furnace, which is 3 ft. long, has three separately controlled heating zones and is operated with a flat axial temperature profile. A 7/16-inch i.d. nickel crucible with a 1/4-inch diameter by 3/4 inch deep w e l l at the bottom is tightly fitted on the sealed end of a stainless steel tube. A chromel-alumel thermocouple is positioned inside this tube with the beaded end extended into the crucible well. This is used to measure the crucible temperature during an experiment. Before a run, the crucible containing the sample can be withdrawn into a spool-piece located directly below a 5/8-inch

Figure 2.

Schematic of the vaporization apparatus


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Veeco model SV62 vacuum solenoid valve. This enables the sample to be kept under an inert atmosphere during transfer from a dry box to the apparatus and during the time the apparatus is being evacuated. A scintillation counter, connected to a rate meter and a programmed printer, is sighted on the sample to monitor continuously the C s radioactivity during a run. The remaining part of the apparatus consists of a high vacuum system and a gas purification train also shown i n the schematic in Figure 2. Procedure. Prior to an experiment, an aqueous solution of carrierfree C s chloride is evaporated to dryness inside the crucible. This crucible then is brought inside a dry box, loaded with a weighed piece of purified sodium ( < 10 p.p.m. oxygen), mounted on the supporting stainless steel tube, and withdrawn into the spool-piece below the solenoid valve. After removal from the dry box, the solenoid valve is attached to the quartz tube by way of the lower ball joint and then sealed i n place. The furnace is brought to a temperature of 730° ± 5°K. while the system is being pumped down to a vacuum of at least 5 X 10' torr. Aiter the evacuation, the apparatus is filled with an inert gas, and a predetermined flow rate is set. The solenoid valve is opened, and the crucible is raised into the lower section of the furnace for sample equilibration at a temperature of 150° to 200°C. This equilibration period is usually continued overnight to ensure complete dissolution and conversion of cesium chloride to metallic cesium, thereby forming a homogeneous cesium-sodium solution. (In one run where the cesium-sodium alloy was formed before transfer into the crucible, the equilibration procedure was eliminated.) The experiment is started after the crucible is raised further into the middle section of the furnace. A t this time the scintillation counter is sighted directly on the sample by a quick scanning procedure. 1 8 7


137

5

Results and

Discussion

Vaporization of Pure Sodium. Several vaporization experiments using pure sodium tagged with N a were made to check the assumption that a stagnant gas layer exists above the liquid surface up to the edge of the crucible. In this case the following equation (11), which takes into consideration a changing liquid level during vaporization, is applicable: 2 2

fc, - V = 2t(D /RT ) 2

vl

P

( °/P ) Pl

BM

(15)

Here P M, the logarithmic mean pressure of the stagnant gas, may be taken as the total pressure of the system since the vapor pressure of sodium is negligible (pf = 1.60 mm. H g at 730°K.). Figure 3 shows the result from a typical experiment carried out with a helium flow of 300 cc./min., an initial liquid depth of 1.25 cm., and an initial gas-phase diffusion path, b , of 1.29 cm. Although Equation 15 is quadratic, the initial part of the release curve may be approximated by a straight line, as shown i n Figure 3. This arises from the fact that only a small change i n gas-film thickness took place initially. B

0


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Transport of Cesium

1.0

LU


ζ ζ

0.8

0.6

0

Figure 3.

5000

4000 3000 2000) RUN TIME, min.

1000

Vaporization of sodium into flowing helium at 730° K.

The gas-phase diffusivity of sodium i n helium D may then be evaluated from the experimental data by using Equation 15. A value of 1.96 cm. /sec. was obtained, which compares favorably with 2.11 c m . / sec. estimated from an equation given by Hirschfelder, Curtiss, and B i r d ( 8 ) , using Lennard-Jones parameters given by Chapman ( 5 ) . The close agreement obtained here seems to justify the assumption of a stagnant gas layer through which both sodium and cesium diffuse. Effect of Carrier-Gas Molecular Weight. Studies were also under taken to determine whether the release phenomenon was controlled by diffusion i n the liquid phase, i n the gaseous phase, or i n both phases. This was accomplished by fixing all the variables except the molecular weight of the carrier gas. The results, shown i n Figure 4, were obtained from two sets of experiments employing helium and argon, respectively. If liquid-phase diffusion were predominant, the two sets of release data should have grouped together, thereby showing no dependence on the molecular weight of the carrier gas. O n the other hand, taking the results i n argon as a basis, the release in helium should follow the dashed line if only a gas-phase resistance were operational. According to Equation 12, the two release curves should be separated from each other by a constant value equal to the ratio of the cesium diffusivity in helium to that i n argon—namely, vl

2

2

ln(l-/) ln(l-f)

(D )

e

H

A

r

He

v2

_

(D„ ) 2

A r

1.53 = 3.56 0.43


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Here the diffusivities were estimated by the method described previously in the text. The fact that the two release curves show some separation but not enough to account solely for gas-phase diffusion, indicates that the release is actually governed by mass transfer resistances i n both phases. This is in qualitative agreement with the transport model presented above. The quantitative agreement w i l l be demonstrated i n the next section.


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The Transport of Fission-Product Cesium from Sodium - Advances in

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