Fission products diffusion

To apply these equations to fission-product diffusion, we then make the analogy... 

In considering the case of maximum release, it is apparent that complete mixing in the liquid phase will lead to a greater release rate than that expected in cases where diffusion operates in two phases. Therefore, consider the case where both the solvent (Na) and the solute (volatile fission product) diffuse through a gas layer of constant thickness. It follows from the solution to Fick s law with appropriate boundary conditions that... 

Hocking, W.H., R.A. Verrall, and SJ. Bushby. 1998. A New Technique To Measure Fission-Product Diffusion Coefficients in UOjFuel, Proceedings of the IAEA Technical Committee Meeting on Fuel Cycle Options for LWRs and HWRs, April 28-May 1, Victoria, BC, IAEA Report, lAEA-TECDOC-1122 (1999 November). 

In fact, the low temperature of the fuel rods in the MARS core allows strong retention of fission products within the rods themselves (thanks to the huge reduction in fission products diffusion inside the fuel matrix) furthermore, the low operating temperature of the primary coolant limits stress on fuel cladding and eventual damage is highly reduced, in comparison to traditional PWRs. 

Fuel matrix - Fission products, bound in a ceramic matrix, may escape only by slow diffusion or melting of the matrix. 

Diffusion of fission-product species through the gas phase... 

Spheres Diffusion-Controlled Fission Product Release and Absorption... 

Concern about fission-product release from coated reactor fuel particles and fission-product sorption by fallout particles has provided stimulus to understand diffusion. In a fallout program mathematics of diffusion with simple boundary conditions have been used as a basis for (1) an experimental method of determining diffusion coefficients of volatile solutes and (2) a calculational method for estimating diffusion profiles with time dependent sources and. time dependent diffusion coefficients. The latter method has been used to estimate the distribution of fission products in fallout. In a fission-product release program, a numerical model which calculates diffusion profiles in multi-coated spherical particles has been programmed, and a parametric study based on coating and kernel properties has provided an understanding of fission product release. 

The diffusion coefficients for iodine are close to those measured previously in the same glass (12) at the experimental temperatures. However, the activation energies of these two measurements differ. The experiments differ to some degree in that iodine and other fission products were made from dissolved U02 in this experiment, while iodine only was made from Te02 under a neutron flux in the previous experiment. The latter mode of formation should lead to a greater excess of oxygen in the glass. 

A temperature-stepping diffusion-controlled fission product absorption model, where equilibrium is taken to occur at the surface of the... 

An important parameter in the evaluation of the safety of a reactor system is the release of fission products from the fuel. The fuel in the high-temperature gas-cooled reactor (HTGR) consists of spherical particles (U, ThC2) that are coated with a material presenting a diffusion... 

SLIDER is a Fortran IV computer program for investigating the diffusion of a single fission-product isotope in a multilayered spherical fuel particle. This code enables one to compute, on the basis of Fick s law of diffusion, the transient and steady-state fission product concentrations and releases in multilayered spherical geometry. 

To evaluate fission product release in a reactor, it is necessary to supply the appropriate particle geometry, diffusion coefficients, and distribution coefficients. This is a formidable task. To approach this problem, postirradiation fission product release has been studied as a function of temperature. The results of these studies are complex and require considerable interpretation. The SLIDER code without a source term has proved to be of considerable value in this interpretation. Parametric studies have been made of the integrated release of fission products, initially wholly in the fueled region, as a function of the diffusion coefficients and the distribution coefficients. These studies have led to observations of critical features in describing integrated fission product releases. From experimental values associated with these critical features, it is possible to evaluate at least partially diffusion coefficients and distribution coefficients. These experimental values may then be put back into SLIDER with appropriate birth and decay rates to evaluate inreactor particle fission product releases. Figure 11 is a representation of SLIDER simulation of a simplified postirradiation fission product release experiment. Calculations have been made with the following pertinent input data ... 

Figure 14. Effect of fission product recoil on release (parameter same as Fig. 11 except for thin high-diffusivity coating between kernel and outside coat)...

Calculations for Figure 14 illustrate a recoil source with the same parameters as those used in the study depicted by Figure 11, except that a buffer carbon layer 0.0006 cm. thick with a diffusion coefficient of 10"6 cm.2/sec. was placed between the coating and the kernel. Distribution coefficients were taken as unity. A recoil range of 0.0006 cm. was assumed in both the kernel and coating materials. Results of this calculation differ considerably from those for experiments with no recoil. These differences are consistent with. —4.5% release from the kernel during irradiation. After release of this quantity of fission product from the particle, the releases begin to approach those of the bare kernel. The recoil effects were unimportant after releases of 7 to 8%. 

Postactivation annealing fission product release data can be analyzed on the basis of a model that assumes the release to be a diffusion-con-trolled process from a spherical particle. The release is limited by diffusion either in the kernel or in the coating. This model is discussed by Norman and Winchell (9) in another chapter in this volume. 

Numerous studies by other workers (I, 10) have shown that the releases of iodine and the noble-gas fission products from pyrolytic carbon-coated fuel particles are controlled by diffusion of these nuclides through grain boundaries, cracks, and defects in the isotropic pyrolytic carbon coating. When coatings are intact, however, the release of these fission product nuclides is low. However, the pyrolytic carbon coating constitutes only a delaying barrier to the metallic nuclides barium and strontium through which they diffuse with diffusion coefficients of the order of 10 9 cm.2/sec. (at — 1400°C.). The steady-state release of these metallic nuclides is controlled instead by diffusion out of the fuel kernel,... 

Maximum Release. The analytical model described above assumes that the liquid phase is completely stagnant. While this may be true in an ideal laboratory experiment where a small sample can be kept isothermal at a specified temperature, in large scale systems where non-isothermal conditions exist, both natural convection and molecular diffusion will contribute to mass transfer. This combined effect, which is often very difficult to assess quantitatively, will result in an increase in fission-product release rate. Therefore, in making reactor safety analyses, it is desirable to be able to estimate the maximum release under all possible conditions. 

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

Impurities in the water and water activation products also contribute to the radioactivity of the coolant water. Tritium is produced as a low yield ( 0.01%) fission product that can diffuse out of the fuel, by activation of boron or fiLi impurities in PWRs. 24Na and 38C1 are produced by neutron activation of water impurities. In BWRs, the primary source of radiation fields in the coolant and steam systems during normal operations is 7.1s 16N. This nuclide is produced by 160(n, p)16N reactions from fast neutrons interacting with the coolant water. This 16N activity can exist as N07, NO in the coolant and NHj in the steam. 

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