The temperature coefficient of a PWR based on an in-rod heterogeneous thorium/uranium fuel design

Abstract

The effect of temperature change in nuclear reactors is of high importance due to the influence on the reactivity of the reactor and its implication for reactor safety. The temperature coefficient of reactivity due to change of either fuel or moderator temperature determines the temperature and hence reactivity feedback properties of the fuel; the reactor and fuel have to be designed to be safe under normal operating conditions as well as postulated transients following initiating events. In this study, the change of reactivity as a function of the temperature of fuel and moderator is investigated for thorium-uranium equilibrium fuel designs proposed by Van der Walt (2015) and compared to reference equilibrium fuel. In addition, the delayed neutron fraction is determined for these fuel models to determine the impact on the safety and control of the reactor. The study aims to simulate the effect of temperature change in the moderator and fuel using the MNCP 6.2 code to model the fuel pin reactivity at the beginning of cycle (BOC), middle of cycle (MOC) and end of cycle (EOC), and SERPENT 2.1 on the full-core reactivity at BOC respectively on the proposed fuel models. Furthermore, the influence of boron on the Moderator Temperature Coefficient (MTC) will be investigated when the density of the coolant changes with the change of temperature at constant boron concentration. A delayed neutron fraction will be calculated due to its influence on the safety and control of the proposed fuel designs and reference fuel. Using the calculated keff values at different temperatures (simulated with MCNP 6.2), reactivity and keff as a function of temperature (for both the fuel and the coolant) are obtained for the proposed fuel designs and reference fuel. A function with a form based on the underlying physics is fitted to the simulated data points in a procedure which rendered the optimal equation constants. By differentiating the equations, the Fuel Temperature Coefficient (FTC) and Moderator Temperature Coefficient (MTC) were derived. Delayed neutron fraction is calculated using the prompt method, where the first criticality calculation using MCNP (Monte Carlo Neutron-Particle) is performed to find the prompt effective multiplication factor kp (which includes only prompt neutrons) and lastly followed by a second criticality calculation to find the total effective multiplication factor (which includes prompt and delayed neutrons). At BOC, the

effective multiplication factor curves for the fuel temperature change show that an increase in the temperature of the fuel will result in a decrease in keff for all the fuel designs (including reference fuel). Due to the negative slope of the curves between keff and fuel temperature, the FTC is negative for all the fuel models. All Moderator Temperature Coefficients calculated at 0ppm and 1000ppm conditions are negative except for the 5Th1U (5cm Th and 1cm U axial loaded) fuel design when 1000ppm boron is present. All the keff curves as a function of moderator temperature have a negative slope, except the 5Th1U fuel design. A reduction in coolant density due to an increase in the moderator temperature causes the keff to decrease. This occurs because of the less neutron moderation that results due to a reduction of the number of coolant atoms present per unit volume of the moderator which is present at BOC, MOC and EOC burnup points. Furthermore, the boron effect is also reduced due to coolant density reduction, because fewer boron atoms are present per unit volume to absorb neutrons, however neutron absorption by the fuel increases which subsequently increases the keff. At MOC, the FTC is negative for all the fuel designs, however, the reference fuel has a less negative FTC compared to the fuel designs proposed by Van der Walt (2015). The keff for all the fuel designs is below unity when 1000ppm boron is added. The MTC at 0ppm and 1000ppm conditions is negative for all curves. The EOC for fuel temperature change and moderator temperature change the value of the keff is above unity and all the curves have a negative gradient. Therefore, FTC and MTC are negative at all temperature points at EOC. The keff curves for a full-core as a function of fuel temperature all display a negative slope which is associated with a negative FTC. The increase in fuel temperature results in a decrease in keff due to Doppler Broadening because fewer neutrons are available for fission thus resulting in a negative FTC. Furthermore, due to equilibrium fuel designs, the fuel matrix also influences neutron absorption. The MTC curves in the absence of boron in the moderator are negative, as mentioned above the MTC is influenced by the reduction in coolant density as the temperature increase which subsequently reduces neutron moderation. In the case of 1000ppm boron in the coolant, the MTC curves are all negative except for the 5Th1U curve due to the reduction in boron effect as the number of boron atoms decrease per unit volume in the moderator.

The delayed neutron fraction decreases as the burnup increases for all the fuel designs except for 5Th1U at MOC with an increase and rapid decrease at EOC. However, due to the depletion of U235 in UO2, the βeff decreases and the build-up of U233 for thorium-based fuel reduces βeff. The proposed designs by Van der Walt (2015) for an equilibrium fuel model show that the amount of thorium content influences the reactivity significantly and the change in reactivity due to temperature change. From all the proposed fuel designs by Van der Walt (2015) and the reference fuel, the FTC and MTC of 1Th1U are negative at all burnup points, i.e, BOC, MOC, and EOC. The keff, MTC and MTC curves for 1Th1U and UO2 both show slightly similar gradients for all the burnup points. Therefore, the results presented indicate that 1Th1U serves as the best fuel candidate among the proposed fuel designs due to favourable safety characteristics.