Question 17.2: Suppose that a thermal water reactor is fueled with Plutoniu......
Suppose that a thermal water reactor is fueled with Plutonium-239 instead of Uranium-235, that the thermal utilization of the fuel is 0.90, and that the average neutron flux is 3 × 10^{14} neutrons/cm²/s. If one-third of the neutrons in the reactor are thermal neutrons, how much of the Pu-239 will be left in the core after 6 months, based on the presence of the thermal neutrons alone?
From Appendix C, we know that the thermal fission cross section of Plutonium-239 is 747 barns and that the thermal capture cross section of Plutonium-239 is 270 barns, so the total absorption cross section is σ_a = σ_c + σ_f = 270 barns + 747 barns = 1017 barns. We also know that the average thermal flux is 0.33 × is 3 × 10^{14} neutrons/ cm²/s = 1 × 10^{14} neutrons/cm²/s and that there are 1.56 × 10^7 seconds in 6 months. Since the thermal utilization of the fuel is 0.90, the plutonium in the fuel can absorb 90% of these thermal neutrons or 0.90 × 1 × 10^{14} neutrons/cm²/s. From our previous discussion, it is easy to see that the time-dependent concentration of the plutonium will be given by
{\mathrm{Pu}}(\mathbf{t})={\mathrm{Pu}}_{\mathrm{e}}\mathrm{e}^{-\sigma_{\mathrm{apu}}\phi t}
where Pu_o is the initial concentration, in atoms/cm³, at start-up. Therefore, after 6 months, the remaining concentration of Plutonium-239 is
Pu (6 months) =Pu_oe^{-(0.9× 10^{14}× 1.56 × 10^7 × 1.017 × 10^{-21})} = Pu_oe^{-(1.44)} = Pu_oe^{-(1.44)} = 0.24 Pu_o
So, only 24% of the Plutonium-239 in the fuel will still be left after 6 months of full power operation.