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Optimization of Moderator to UO2 Ratio for 16×16 and 17×17 Fuel Assemblies with Varied Enrichment and Boron Concentration

image credit: Nuclear Reactor Core and Fuel Assembly (image from google)

by Mark Gino Aliperio

Introduction

The moderator-to-fuel ratio is the ratio of the number of moderator nuclei within the volume of a reactor core to the number of fuel nuclei. As the core temperature increases, fuel volume and number density remain essentially constant. The volume of moderator also remains constant, but the number density of moderator decreases with thermal expansion. This, in turn, causes a hardening of neutron spectrum in the reactor core resulting in higher resonance absorption. With this, reactor engineers must balance the composite effects of moderator density, fuel temperature, and other phenomena to ensure system stability under all operating conditions.

From the moderator - fuel ratio point of view, any multiplying system can be designed as: Under-moderated which means that there is less than optimum amount of moderator between fuel plates or fuel rods; or Over-moderated which means that there is higher than optimum amount of moderator between fuel plates or fuel rods.

In practice, water-moderated reactors are designed with a moderator – fuel ratio so that the reactor is operated in an under moderated condition. The reason that some reactors are designed to be under moderated is if the reactor were over moderated, an increase in temperature would decrease the moderator – fuel ratio due to the expansion of the water as its density became lower. This decrease in moderator – fuel ratio would be a positive reactivity addition, increasing k-eff and further raising power and temperature in a dangerous cycle. If the reactor is under moderated, the same increase in temperature results in the addition of negative reactivity, and the reactor becomes more self-regulating.

In this report, the moderator – fuel ratio is calculated by getting the ratio of moderator volume to fuel volume and not by the number density of nuclides. The optimum moderator – fuel ratio is determined by the maximum value of k-inf in the k-inf vs moderator – fuel ratio curve. In addition, the change in the moderator – fuel ratio values with respect to varying boron concentration (1000 ppm), enrichment (3.0 % and 4.5 %), and fuel assembly configuration (16×16 and 17×17) is discussed.

Experimental Design and Methodology

The simulations in this report were done using CASMO3. The source codes for both assemblies (16×16 and 17×17) are provided in the Appendix. The configuration was set for no fuel zoning. For both assemblies, the fuel enrichment was varied to be 3.0% and 4.5%, as well as the boron concentration to be 1000 ppm and 10 ppm. Take note that there is a difference in the pin configuration for both assemblies (see figure below). The reference state condition was also set to constant where Tf (fuel temperature) = 690 K, Tm (moderator temperature) =586 K.

As shown in the figure above, (a) the pin configuration for 16×16 assembly consists of a fuel with canning. The pin pitch was set to a single value of d = 1.2882 cm. R1 and R2 are the inner and outer radius of the fuel rod respectively. For 17×17 assembly (b), the fuel pin consists of fuel, gap, and canning as described by R1, R2, and R3. Similarly, the pin pitch was also fixed at d = 1.2623 cm. For all simulations, the thickness of the canning and gap was fixed during the optimization of the moderator-fuel ratio. Consider the case of 16×16 assembly for example, the radius of the fuel was varied to obtain data for moderator-fuel ratio but the difference between R1 and R2 (a) was fixed, i.e., R2 – R1 = 0.07331 mm. Moreover, the differences in radii for 17×17 assembly (b) was also fixed to be R3 – R2 = 0.05715 mm and R2 – R1 = 0.00825 mm. In this report, the moderator – fuel ratio is calculated by getting the ratio between the volume of the moderator to the volume of fuel rod as described by the equation, Moderator−Fuel ratio= 𝑉𝑚𝑜𝑑𝑒𝑟𝑎𝑡𝑜𝑟/𝑉𝑓𝑢𝑒𝑙= (𝑑2−𝜋𝑅2)/ℎ𝜋𝑅2ℎ, where d is the pin pitch; R is the outermost radius of the fuel rod; and h is the length of the pin.

As shown in the equation above, varying the radius on the fuel will change the moderator – fuel ratio. For each condition of different enrichment and boron concentration, k-inf (at zero burnup) vs moderator-fuel ratio plots were generated from the simulation results. A sample of such plot is shown in the figure above. The highest point of the plot (vertical red dashed line) represents the optimum moderator – fuel ratio which was approximated by data analysis.

Results and Discussions

Using the procedure presented in the previous section, the optimum moderator – fuel ratio value was obtained for both 16×16 and 17×17 assemblies with different fuel enrichment (3.0% and 4.5%) and boron concentration (1000 ppm and 10 ppm). Figure 2 shows a sample of such plot for the case of 17×17 assembly with boron concentration of 10 ppm and fuel enrichment of 4.5%. As mentioned that the highest point (maximum value of k-inf) in the curve represents the optimum moderator – fuel ratio, the region to the right side is over moderated while the left is under moderated. Over moderation means that there is higher than optimum amount of moderator between fuel rods. An increase in moderator temperature and voids inserts positive reactivity. An over-moderated core would create a positive temperature and void feedback resulting in an unstable system. On the other hand, Under-moderation means that there is less than optimum amount of moderator between fuel rods. An increase in moderator temperature and voids inserts negative reactivity. An under-moderated core would create a negative temperature and void feedback required for a stable system.

The graph above presents the optimum moderator – fuel ratio for all cases. It is shown that as fuel enrichment was increased from 3.0% to 4.5%, the optimum moderator – fuel ratio also increases for both assemblies and boron concentration. Also, k-inf increases with increasing fuel enrichment. This can be attributed to the reason that more enriched fuels have contain more fissile uranium atoms than less enriched fuels. Moderator – fuel ratio needs to compensate for this, thus the increase to ensure the criticality of the reactor.

In addition, an increase in the moderator-to-fuel ratio decreases k-inf due to the dominance of the decreasing thermal utilization factor. Below this point, a decrease in the moderator-to-fuel ratio decreases k-inf due to the dominance of the increased resonance absorption in the fuel.

When boron concentration is increased, it is noted that optimum moderator – fuel ratio decreases for the same enrichment and fuel assembly. This is obvious because of the presence of boron in the coolant that aids moderation as boron is a neutron poison due to its neutron absorbing properties. Thus, lesser moderator volume is needed to achieve the optimum moderator – fuel ratio. With small boron concentration, more moderation is needed to slow down neutrons from fission to thermal energies.

For the comparison between two assemblies for same values of boron concentration and fuel enrichment, 17×17 assembly has higher moderator to fuel – ratio compared to its corresponding configuration for 16×16 assembly. It can be also observed from the graph above that curves for both assemblies are almost identical and has close values for k-inf.

Conclusion

In this report, the optimum moderator – fuel ratio is determined when k-inf reaches its maximum value. The effect on the moderator – fuel ratio by varying boron concentration (1000 ppm), enrichment (3.0 % and 4.5 %), and fuel assembly configuration (16×16 and 17×17) was presented. When fuel enrichment is increased, optimum moderator – fuel ratio increases, while it decreases with increasing boron concentration. Moreover, there is no significant difference on the k-inf and moderator – fuel ratio for both assemblies.

This report on the optimization of moderator to UO2 ratio, has been conducted in partial fulfillment of the requirements of the course EN304 Nuclear Design Codes and Methodologies.

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