# A Numerical Study of the Volume Oxidation of UO2 Pellets in the Oxidation Process

## Abstract

Dry storage and ultimate disposal of irradiated nuclear fuel in a power reactor are important problems to address in the nuclear industries. These problems involve the volume oxidation phenomenon that makes difficult the investigation of oxidation process of the uranium dioxide pellets in the air. In this study, a mathematical model is developed for this phenomenon at temperatures below 727 K, which simulates the diffusion of oxygen within the pores of the pellet and oxidation of the pellet body, simultaneously. Coupled equations of heat and mass transfers within this pellet with variation of its properties are solved for this simulation. Approving the predictions of this model using the experimental data approves the accuracy of the presented model and also the numerical calculations.

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## Abbreviations

$$C_{{P_{e} }}$$ :

Effective heat capacity of the pellet (j/kmol/K)

$$C_{{P_{{{\text{UO}}_{2} }} }}$$ :

Heat capacity of UO2 (j/kmol/K): $$C_{{P_{{{\text{UO}}_{2} }} }} = - 5.499 \times 10^{7} T^{ - 1.34} + 9.037 \times 10^{4}$$[51]

$$C_{{P_{{{\text{U}}_{3} {\text{O}}_{8} }} }}$$ :

Heat capacity of U3O8 (j/kmol/K): $$C_{{P_{{{\text{U}}_{3} {\text{O}}_{8} }} }} = - 3.507 \times 10^{7} T^{ - 1.019} + 3.431 \times 10^{5}$$ [51]

$$C_{{{\text{O}}_{2} }}$$ :

Concentration of oxygen (kmol/m3)

$$C_{{{\text{O}}_{2} }}^{b}$$ :

Concentration of oxygen in the bulk of the gas (kmol/m3): $$C_{{{\text{O}}_{2} }}^{b} = \frac{0.21P}{{RT^{b} }}$$

$$D_{{{\text{O}}_{2} - {\text{N}}_{2} }}$$ :

Molecular diffusivity of O2 in N2 (m2/s): $$D_{{{\text{O}}_{2} - {\text{N}}_{2} }} = 3.593 \times 10^{ - 13} P\sqrt {\frac{1}{{M_{{{\text{O}}_{2} }} + M_{{{\text{N}}_{2} }} }}} \left( {\frac{T}{{\sqrt {T_{{c_{{{\text{O}}_{2} }} }} T_{{c_{{{\text{N}}_{{2}} }} }} } }}} \right)^{2.334} \left( {T_{{c_{{{\text{O}}_{2} }} }} T_{{c_{{{\text{N}}_{2} }} }} } \right)^{\frac{5}{12}} \left( {P_{{c_{{{\text{O}}_{2} }} }} P_{{c_{{{\text{N}}_{2} }} }} } \right)^{\frac{1}{3}}$$[52]

D k :

Knudsen diffusivity (m2/s): $$D_{k} = 9.7 \times 10^{ - 11} \frac{{r_{p} \varepsilon }}{{\varepsilon^{0} }}\sqrt {\frac{2T}{{\sqrt {M_{{{\text{O}}_{2} }} + M_{{{\text{N}}_{2} }} } }}}$$ [53]

D e :

Effective diffusivity of oxygen within the pellet (m2/s)

E :

Activation energy (j/kmol)

f(X):

A function of the solid conversion

g(X):

A function of the solid conversion

k :

Reaction rate constant (1/s)

k 0 :

Pre-exponential constant (1/s)

k e :

Effective thermal conduction of the pellet (w/m/K)

$$k_{{{\text{UO}}_{2} }}$$ :

Thermal conduction of UO2 (w/m/K): $$k_{{{\text{UO}}_{2} }} = \frac{100}{{5.33 + 2.35 \times 10^{ - 2} T}}$$ [54]

$$k_{{{\text{U}}_{3} {\text{O}}_{8} }}$$ :

Thermal conduction of U3O8 (w/m/K): $$k_{{{\text{U}}_{3} {\text{O}}_{8} }} = \frac{1}{{0.293 + 5.39 \times 10^{ - 4} T}}$$ [55]

$$M_{{{\text{O}}_{2} }}$$ :

Molecular weight of oxygen (kmol/kg)

$$M_{{{\text{N}}_{2} }}$$ :

Molecular weight of nitrogen (kmol/kg)

P :

Pressure (Pa)

$$P_{{c_{{{\text{O}}_{2} }} }}$$ :

Critical pressure of O2 (Pa)

$$P_{{c_{{{\text{N}}_{2} }} }}$$ :

Critical pressure of N2 (Pa)

R :

Universal gas constant (Pa.m3/kmol/K)

R 2 ln( k ) :

R-square value based on ln(k) in a certain 1/T: $$R_{\ln (k)}^{2} = \tfrac{{\ln (k)_{{{\text{Model}}}}^{2} - \ln (k)_{{{\text{Experimental}}}}^{2} }}{{\ln (k)_{{{\text{Experimental}}}}^{2} - \overline{{\ln (k)_{{{\text{Experimental}}}}^{2} }} }}$$

R t 2 :

R-square value based on the required time for a certain solid conversion: $$R_{t}^{2} = \tfrac{{t_{{{\text{Model}}}}^{2} - t_{{{\text{Experimental}}}}^{2} }}{{t_{{{\text{Experimental}}}}^{2} - \overline{{t_{{{\text{Experimental}}}}^{2} }} }}$$

R X 2 :

R-square value based on the solid conversion in a certain time: $$R_{X}^{2} = \tfrac{{X_{{{\text{Model}}}}^{2} - X_{{{\text{Experimental}}}}^{2} }}{{X_{{{\text{Experimental}}}}^{2} - \overline{{X_{{{\text{Experimental}}}}^{2} }} }}$$

r :

Coordination in the radius of the cylindrical pellet (m)

r p :

T :

Temperature (K)

T b :

Temperature of the bulk of the gas (K)

$$T_{{c_{{{\text{O}}_{2} }} }}$$ :

Critical temperature of O2 (K)

$$T_{{c_{{N_{2} }} }}$$ :

Critical temperature of N2 (K)

t :

Time (s)

X :

Solid conversion

X c :

The critical conversion at the breaking-down point

z :

Coordination in the length of the cylindrical pellet (m)

ΔH reac . :

Heat of the reaction (j/kmol): $$\Delta H_{{{\text{reac}}{.}}} = 665.6T^{ - 1.31} - 1.078 \times 10^{8}$$ [31]

ε :

Pellet porosity

ε 0 :

Initial porosity of the pellet

ρ e :

Effective density of the pellet (kmol/m3)

$$\rho_{{{\text{UO}}_{2} }}$$ :

Density of UO2 (kmol/m3)

$$\rho_{{{\text{U}}_{3} {\text{O}}8}}$$ :

Density of U3O8 (kmol/m3)

τ :

Pellet tortuosity: $$\tau = \frac{1}{\varepsilon }$$ [56]s

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Abolpour, B. A Numerical Study of the Volume Oxidation of UO2 Pellets in the Oxidation Process. Oxid Met (2021). https://doi.org/10.1007/s11085-021-10040-z