Question 10.3: A thermal reactor fueled with uranium has been operating at ......
A thermal reactor fueled with uranium has been operating at constant power for several days. Make a plot of the ratio of concentration of xenon-135 to uranium-235 atoms in the reactor versus its average flux. Determine the maximum value that this ratio can take.
To find the ratio we begin with Eq. (10.15)
X=\frac{(\gamma_{I}+\gamma_{X})}{\lambda_{X}+\sigma_{a X}\phi}\Sigma_{f}\phi=\frac{(\gamma_{I}+\gamma_{X})}{\lambda_{X}+\sigma_{a X}\phi}{\sigma_{f}^{25}N^{25}\phi}
Thus
{\frac{X}{N^{25}}}={\frac{(\gamma_{I}+\gamma_{X})}{\lambda_{X}+\sigma_{a X}\phi}}{\sigma_{f}^{25}\phi}
From Eq. (10.11):
\lambda_{X}=0.693/t_{1/2X}=0.693/9.2=0.0753\,\mathrm{h}\mathrm{r}^{-1}=2.09\times 10^{-5}\,\mathrm{s}^{-1}
\sigma_{a X}=2.65.10^{6}\ {\mathrm{b}}
From Table 10.1 for uranium-235 \gamma_{I}=0.0639,\ \ \ \gamma_{X}=0.00237\,,
And from Table 3.2 \sigma_{f}^{25}=505\,{\mathrm{b}} Thus
\frac{{X}}{N^{25}}=\frac{(0.0639+0.00237)}{2.09\cdot10^{-5}+2.65\cdot10^{-18}\phi}\,505\cdot10^{-24}\phi
\frac{X}{N^{25}}=\frac{1}{1+1.27\cdot10^{-13}\phi}1.60\cdot10^{-18}\phi
When the flux is very large, the maximum value occurs. It is
{\frac{X}{N^{25}}}={\frac{1.60\cdot10^{-18}}{1.27\cdot10^{-13}}}=1.26\cdot10^{-5}
This may also be seen from the plot:
