A Study of Nuclear Fuel Burnup Wave Development in a Fast Neutron Energy Spectrum Multiplying Medium: Improved Model and Consistent Parametric Approach for Evaluation

Abstract

Considerable studies have been carried out to evaluate the feasibility of the breed and burn (B&B) concept over the last few decades by applying various simplified or more practical methodologies. In this note, similar studies are performed by improving the simplified methodology used by Kumar and Singh in “A Study of Transverse Buckling Effect on the Characteristics of Nuclides Burnup Wave in a Fast Neutron Multiplying Media,” [Journal of Nuclear Engineering and Radiation Sciience, Vol. 5, p. 4 (2019)] and in other international studies. A consistent parametric approach is adopted for the study on buildup and propagation of a nuclear fuel burnup wave in a fast neutron multiplying medium for two-dimensional cylindrical geometry with azimuthal symmetry. The Multiphysics finite element computational code COMSOL is utilized to solve coupled multigroup neutron diffusion and burnup equations in the U-Pu cycle. The characteristics of the wave are evaluated in terms of transient time (TT) and transient length (TL); TT and TL represent the time and distance covered by the wave in establishing a sustained fuel burnup wave, respectively. The steady-state space is characterized by wave velocity and reaction zone width (full-width at half-maximum and full-width at 10% of maximum).

The results of this study are presented in terms of the characteristics of the transient and steady-state parameters to assess the feasibility of a fuel burnup wave. It is concluded that a sustained fuel burnup wave (about 10 years in a reactor of 5-m length) is attainable in application of the B&B concept in traveling wave technology, although optimization of the transient wave parameters (TT of 1100 days and TL of 2.614 m) is necessary to prolong reactor operating life. The results of the present improved model are compared with the results of Kumar and Singh’s simplified model by performing a sensitivity study of the characterization parameters with radius. Variation of TL with respect to radius (decrement of about 10.6% in the modified model and about 5.4% in the simplified one with the increment in reactor radius from 1.1 to 1.3 m) is relatively less compared to the variation observed for TT (decrement of about 76.5% for the modified approach and about 19.1% for the simplified case). The sensitivity of the wave parameters is studied for different values of neutron source strength used in the analysis.

Keywords:

• Fuel burnup wave
• fast multiplying medium
• external neutron source
• transient time
• transient length

Nomenclature

$D_g$ =	=	group diffusion coefficient of the medium (m)
$J_{ex}$ =	=	neutron current density entering the bottom boundary of the cylindrical geometry $(\mathrm{n}/{\mathrm{m}}^2\cdot \mathrm{s})$
$l$ =	=	diffusion length (m)
$N$ =	=	neutron density (1/m3)
$N_{FP}$ =	=	nuclide density of fission products (1/m3)
$N_{\mathrm{N}\mathrm{p}}$ =	=	nuclide density of 239Np (1/m3)
$N_{\mathrm{P}\mathrm{u}}$ =	=	nuclide density of 239Pu (1/m3)
$N_5$ =	=	nuclide density of 235U (1/m3)
$N_8$ =	=	nuclide density of 238U (1/m3)
$q_g$ =	=	external source of neutrons for group g $(1/{\mathrm{m}}^2\cdot \mathrm{s})$
r =	=	distance in radial direction (m)
t =	=	time (s)
z =	=	distance in axial direction z (m)
${\vartheta }_g$ =	=	neutron velocity of a particular energy group of the medium (m/s)

Greek

$\lambda$ =	=	decay constant of nuclide (1/s)
${\lambda }_{\mathrm{P}\mathrm{u}1}$ =	=	decay constant of 241Pu (1/s)
$\nu$ =	=	number of neutrons produced per fission, dimensionless
${\mathrm{\Sigma }}_a$ =	=	macroscopic absorption cross section (b)
${\mathrm{\Sigma }}_f$ =	=	macroscopic fission cross section (b)
${\mathrm{\Sigma }}_{s,g^{\prime }\to g}$ =	=	macroscopic scattering cross section (group $g^{\prime }$ to $g$) (b)
${\mathrm{\Sigma }}_{s,g\to g^{\prime }}$ =	=	macroscopic scattering cross section (group $g$ to $g^{\prime })$ (b)
${\sigma }_a$ =	=	microscopic absorption cross section (b)
${\sigma }_{a5}$ =	=	microscopic absorption cross section of 235U (b)
${\sigma }_{a8}$ =	=	microscopic absorption cross section of 238U (b)
${\sigma }_c$ =	=	microscopic capture cross section (b)
${\sigma }_{c\mathrm{P}\mathrm{u}0}$ =	=	microscopic capture cross section of 240Pu (b)
${\sigma }_{c\mathrm{P}\mathrm{u}1}$ =	=	microscopic capture cross section of 241Pu (b)
${\sigma }_{c\mathrm{P}\mathrm{u}2}$ =	=	microscopic capture cross section of 242Pu (b)
${\sigma }_{c\mathrm{P}\mathrm{u}9}$ =	=	microscopic capture cross section of 239Pu (b)
${\sigma }_{c5}$ =	=	microscopic capture cross section of 235U (b)
${\sigma }_{c8}$ =	=	microscopic capture cross section of 238U (b)
${\sigma }_f$ =	=	microscopic fission cross section (b)
${\sigma }_{f\mathrm{P}\mathrm{u}}$ =	=	microscopic fission cross section of 239Pu (b)
${\sigma }_{f5}$ =	=	microscopic fission cross section of 235U (b)
${\varphi }_g$ =	=	group scalar neutron flux ($1/{\mathrm{m}}^2\cdot \mathrm{s}$)